--- tags: - sentence-transformers - sentence-similarity - feature-extraction - dense - generated_from_trainer - dataset_size:4091 - loss:MultipleNegativesRankingLoss base_model: sentence-transformers/all-MiniLM-L6-v2 widget: - source_sentence: magnetic order superconductor sentences: - "arXiv:0802.4093v2 [cond-mat.str-el] 27 Feb 2009 Meissner effect without superconductivity\ \ from a chiral d-density wave P. Kotetes∗and G. Varelogiannis† Department of\ \ Physics, National Technical University of Athens, GR-15780 Athens, Greece We\ \ demonstrate that the formation of a chiral d-density wave (CDDW) state generates\ \ a Topolo- gical Meissner effect (TME) in the absence of any kind of superconductivity.\ \ The TME is identical to the usual superconducting Meissner effect but it appears\ \ only for magnetic fields perpendicular to the plane while it is absent for in\ \ plane fields. The observed enhanced diamagnetic signals in the non-superconducting\ \ pseudogap regime of the cuprates may find an alternative interpretation in terms\ \ of a TME, originating from a chiral d-density wave pseudogap. PACS numbers:\ \ 75.20.-g, 71.27.+a, 74.72.-h The Meissner effect is considered to be the most\ \ direct signature of superconductivity [1]. However, the surpris- ing observations\ \ of such enhanced diamagnetic signals [2] well above the superconducting transition\ \ tempera- ture in the pseudogap regime of the cuprates [3], con- stitute a fascinating\ \ puzzle. There are two proposals for the nature of this regime that appear to\ \ dominate. The first, associates the pseudogap with a dx2−y2 density wave (DDW)\ \ [4, 5], also called orbital antiferromagnet [6, 7], which normally competes\ \ with superconductivity. The second associates the pseudogap with spontaneous\ \ vortex-antivortex unbinding leading to incoherent super- conductivity [8] that\ \ should persist well above the su- perconducting Tc. This theory is reminiscent\ \ of the well known Kosterlitz-Thouless transition [9]. The available ARPES [10]\ \ and STM [11] experiments cannot differentiate a SC from a density wave (DW) gap,\ \ and therefore appear somehow incapable in settling di- rectly the issue. On\ \ the other hand, the unusual Nernst effect and most importantly, the enhanced\ \ diamagnetic signal that accompanies it for a very large temperature region above\ \ the SC critical temperature [2], has been considered as a major argument in\ \ favor of the incoher- ent SC scenario. In fact, the enhanced diamagnetism is\ \ viewed as a signature of the usual Meissner effect associ- ated solely with the\ \ SC state, and would therefore contra- dict the dx2−y2 density wave scenario\ \ since no Meissner effect was expected in that case [7]. In this letter we put\ \ forward the Topological Meissner effect (TME), that results from a chiral dxy\ \ + idx2−y2 density wave (CDDW) state. In fact, the Nernst region of the pseudogap\ \ regime may well be associated with a CDDW. The most intriguing property of a\ \ CDDW is that parity (P) and time-reversal (T ) violation induces Chern-Simons\ \ terms in the effective action of the elec- tromagnetic field, providing the possibility\ \ of the TME and the Spontaneous Quantum Hall effect (SQHE) ear- lier discussed\ \ [12, 13, 14, 15, 16, 17, 18]. As we shall demonstrate, the TME is described\ \ by the same equa- tion we find in the usual Meissner effect of a supercon- ∗Electronic\ \ address: pkotetes@central.ntua.gr †Electronic address: varelogi@central.ntua.gr\ \ ductor. Though, its origin is radically different. In our system we encounter\ \ the realization of Parity Anomaly [13, 19], with the emerging Chern-Simons terms\ \ provi- ding a topological mass to the electromagnetic field, in a gauge invariant\ \ manner [20, 21]. Moreover, the pos- session of chirality perpendicular to the\ \ plane, implies that the TME is strongly anisotropic. Particularly, it takes\ \ place for magnetic fields perpendicular to the plane while it is absent for in\ \ plane fields, in accordance with the experimental observations [2]. Note finally\ \ that a chi- ral d-density wave state has also been shown recently [22] to explain\ \ the experimental results concerning the Polar Kerr effect in YBCO [23]. In order\ \ to demonstrate how the TME arises, we shall consider the following BCS hamiltonian\ \ for the CDDW HCDDW = 1 2 X k \x10 ∆kc† kck+Q + ∆∗ kc† k+Qck \x11 , (1) which\ \ describes a dxy+idx2−y2 state characterized by the wave-vector Q = (π, π), which\ \ is commensurate to the lattice (k + 2Q = k). Since spin degrees of freedom do\ \ not get involved we have considered spinless electrons, so that all our results\ \ will refer to one spin component. Fur- thermore, we use gµν = (1, −1, −1), ki\ \ = k = (kx, ky), kµ = k = (ω, k), qµ = q = (q0, q), µ = 0, 1, 2, i = 1, 2, e\ \ > 0, ℏ= 1 and we assume that repeated indices are summed. In the derivation\ \ of the Chern-Simons terms we shall restrict ourselves to the zero temperature\ \ case while necessary extensions to finite temperatures will be afterwards performed.\ \ In addition, the summation in k−space is all over the whole 1st Brillouin zone\ \ rather than the reduced Brillouin zone. This implies that the operators ck and\ \ ck+Q do not describe independent de- grees of freedom. In Eq.(1) we have introduced\ \ the CDDW order param- eter ∆k = η∆sin kx sin ky+i∆ \0cos kx −cos ky \x01 , where\ \ ∆ is the modulus of the idx2−y2 order parameter, η defines the relative magnitude\ \ of the two components and also determines the direction of the chirality of\ \ the state. The chiral character of the state implies the existence of an intrinsic\ \ angular momentum in k−space, perpendicular to the plane, originating from P\ \ −T violation. Specifi- cally, the dx2−y2 component violates T as it is imaginary,\ \ 2 while the dxy component is odd under P in two dimen- sions, which is defined\ \ as (kx, ky) →(kx, −ky). In order to obtain the total electronic Hamiltonian\ \ H, we have to add the corresponding kinetic part Hkin. For the kinetic part\ \ we keep only the nearest neighbors hop- ping term ǫk = −t \0cos kx + cos ky\ \ \x01 satisfying the nest- ing condition ǫk+Q = −ǫk, while we also set the chem-\ \ ical potential equal to zero. Our approximation can be justified by considering\ \ that our system is close to half- filling. Under these conditions the excitation\ \ spectrum consists of two bands which are fully gapped leading to the topological\ \ quantization of the Hall conductance [12, 13, 14, 15, 16, 17, 18], which is\ \ the coefficient of the Chern-Simons terms. Omitting the next nearest neigh- bors\ \ hopping term δk = t′ cos kx cos ky does not alter qualitatively the occurrence\ \ of the TME. However, its inclusion would destroy the quantization of the Hall\ \ con- ductance, as in this case, the system is not fully gapped. Similar effects\ \ would arise in the presence of disorder or by including the z-axis hopping term.\ \ Under this conditions, the total Hamiltonian of the system becomes H = 1 2 P\ \ k h ǫk \x10 c† kck −c† k+Qck+Q \x11 + \x10 ∆kc† kck+Q + h.c. \x11i . We obtain\ \ a compact representa- tion of H by introducing the spinor Ψ† k = 1 √ 2(c† k\ \ c† k+Q), the isospin Pauli matrices τ and the vector gk ≡ (Re∆k, −Im∆k, ǫk).\ \ This yields H = P k Ψ† k gk · τ Ψk. The latter indicates that the ground state\ \ of the sys- tem depends on the orientation of the g vector in isospin space.\ \ As a result, this hamiltonian supports skyrmion solutions which imply the presence\ \ of a Chern-Simons action (see e.g. [18]). To reveal the emerging Chern-Simons\ \ terms, we have to take into account the fluctuations of the U(1) gauge field Aµ.\ \ We add to the Hamiltonian the term Hem = R d2q (2π)2 P k Ψ† k+qΓµ k+q,kAµ(q)Ψk\ \ − R d2q (2π)2 P k Ψ† k+q e2 2mAi(−q)Ai(q)Ψk, which describes the interaction\ \ of the gauge field with the electrons. We have introduced the paramagnetic interaction\ \ vertex Γµ k+q,k = −(e , e ∂ ∂ki gk · τ), where µ = 0, 1, 2 and i = 1, 2. At\ \ one-loop level, the effective action Sem is given by the relation Sem = 1 2 R\ \ d3q (2π)3 Aµ(−q)Πµν(q)Aν(q), with the Polarization tensor Πµν, defined as Πµν(q)\ \ = i 2 R k T r \x10 GkΓµ k,k+qGk+qΓν k+q,k \x11 −e2 m ρeδi,j. ρe is the two-\ \ dimensional electronic density (without including spin), T r denotes trace over\ \ isospin indices, Gk is the CDDW fermionic propagator and we have used the abbreviation\ \ R k = R dω 2π P k. Computing Πµν up to linear order in q, yields the Chern-Simons\ \ action SCS = Z d3x σxy 4 εµνλAµF νλ, (2) with Fµν = ∂µAν −∂νAµ. The coefficient\ \ of the Chern- Simons action is the Hall conductance σxy. It can be shown that\ \ it is a topological invariant, reflecting the existence of a topologically non\ \ trivial, P −T violating ground state (see e.g. [18]). Using Eq.(2) we obtain\ \ σxy = i 2!ε0ji ∂Π0i ∂qj = e2 4π b N = e2 2π , (3) where we have introduced the\ \ winding number of the unit vector ˆgk = gk/| gk |, b N = 1 4π Z d2k ˆgk · ∂ˆgk\ \ ∂kx × ∂ˆgk ∂ky ! , (4) which is equal to 2, because the order parameter com-\ \ ponents are eigenfunctions of the angular momentum in k−space with eigenvalue\ \ l = 2. In the case of a perfect gap, the Hall conductance origi- nates only\ \ from the chirality b N of the lower energy band, E− k = −|gk|, which is fully\ \ occupied. In the same time, the upper band, E+ k = +|gk|, is totally empty while\ \ it is characterized by opposite chirality. Apparently, if both bands were equally\ \ occupied then σxy would be equal to zero. In the general case, the two bands,\ \ have different occupation numbers n−and n+, yielding a non-quantized Hall conductance\ \ σxy = e2 2π(n−−n+). Deviations from nesting, disorder or a chemical potential\ \ generally lead to such an effect. It is desirable to comprehend, even crudely,\ \ the effect of these parameters on the Hall con- ductance and the TME. For this\ \ purpose we consider that a finite chemical po- tential is added to the system.\ \ We shall consider that its magnitude is of the order of min|gk|. This minimum\ \ is realized at the points k0 = (± π 2 , ± π 2 ), when η << 1. In this case,\ \ we may linearize the spectrum about these points so to obtain an approximate\ \ analytical solution. The two energy bands are described by the dispersions E±\ \ k = −µ± p m2 + (v0 · δk)2, with m = min|gk| = |gk0|, v0 the velocity at these\ \ points and δk = k−k0. If |µ| ≥m and µ < 0, hole-pockets arise in the lower band\ \ decreas- ing the full occupancy from n−= 1 to n−= 1−nex, with nex the portion\ \ of the empty states. On the other hand, if µ ≥m, electron pockets emerge in\ \ the upper band ris- ing its occupancy from zero. However, if we take into consideration\ \ that the two bands have opposite chirality, it is evident that in both cases,\ \ the effect is the same. Consequently, σxy(µ) = σxy(1 −nex). The portion of the\ \ empty states will be determined by the area of the el- lipses defined by the\ \ four hole-pockets. Straightforward calculations yield the simple relation nex\ \ = (µ2 −m2)/2πt∆. (5) We observe that for small values of |µ|, compared to t\ \ and ∆, the effect of doping is negligible. We are now in position to obtain the\ \ equations of mo- tion of the gauge field which will allow us to discuss the TME\ \ in a Hall bar geometry setup. We consider that the 3 FIG. 1: (Color online)\ \ (a) Influence of doping on the Topo- logical Meissner effect. The relative change\ \ of magnetization hardly reaches 1% in the presence of a small chemical po- tential\ \ (∆= 20meV , t = 500meV ). (b) The magnetic field screening as a function of the\ \ position on the Hall bar extend- ing from −lx to +lx, for different values of\ \ the penetration depth λ over lx. The magnetic field is totally expelled from\ \ the sample when lx/λ >> 1 exactly as in the superconducting case. Hall bar has\ \ dimensions Lx = 2lx, Ly >> Lx extending from −lx to lx on the x-axis. The relation\ \ Ly >> Lx in- dicates that there is negligible y-dependence of the" - 'QCage - A New Microwave-cavity Sample Holder for High-fidelity Qubit Measurements | In this video, you will learn about a new sample holder system, targeted at superconducting quantum processors with tens of qubits. The QCage is a sample holder system for microwave resonator-based quantum devices that encloses the sample chip in an all-surrounding microwave cavity, with a total number of 24 coplanar transmission lines optimized for frequencies up to 18 GHz. The QCage is designed to hold the chip suspended inside the cavity, supported only by four corner pedestals and clamped d' - 'Elastic neutron scattering simultaneously probes both the crystal structure and magnetic order in a material. Inelastic neutron scattering measures phonons and magnetic excitations. Here, we review the average composition, crystal structure and magnetic order in the 245 family of Fe-based superconductors and in related insulating compounds from neutron diffraction works. A three-dimensional phase-diagram summarizes various structural, magnetic and electronic properties as a function of the sample composition. A high pressure phase diagram for the superconductor is also provided. Magnetic excitations and the theoretic Heisenberg Hamiltonian are provided for the superconductor. Issues for future works are discussed.' - source_sentence: superconductivity sentences: - 'Unveiling the Enigma: ''Demon'' Particle Found in Superconductor Offers Clues to Their Operation | A breakthrough discovery of a particle known as Pines''s demon within a superconducting crystal could hold the key to unraveling the mysteries behind these remarkable superconductor materials.' - 'et al., Phys. Rev. Lett. 62, 1532 (1989). 52. F. Creuzet et al., Synthetic Metals 19, 289 (1987). 53. B. Gotschy et al., J. Phys. I (France) 2, 677 (1992). 54. J. Pouget et al., Mol. Cryst. Liq. Cryst. 79, 129 (1982). 55. P. Foury-Leylekian et al., Phys. Rev. B 70, 180405(R) (2004). 56. M. Dumm et al., Phys. Rev. B 61, 511 (2000). 57. C. Bourbonnais and B. Dumoulin, J. Phys. I (France) 6, 1727 (1996). 58. L. G. Caron, C. Bourbonnais, F. Creuzet, and D. Jerome, Synthetic Metals 19, 69 (1987). 59. J. Riera and D. Poilblanc, Phys. Rev. B 62, R16243 (2000). 60. J. P. Pouget, in Low Dimensional Conductors and Superconductors, edited by D. J´erome and L. G. Caron (Plenum Press, New York, 1987), p. 17. 61. D. Chow et al., Phys. Rev. Lett. 81, 3984 (1998). 62. F. Zamborszky et al., Phys. Rev. B 66, 081103(R) (2002). 63. V. Ilakovac et al., Phys. Rev. B 50, 7136 (1994). 64. D. S. Chow et al., Phys. Rev. Lett. 85, 1698 (2000). 65. L. G. Caron et al., Synthetic Metals 27B, 123 (1988). 66. J. P. Pouget et al., Phys. Rev. Lett. 37, 437 (1976). 67. L. G. Caron and C. Bourbonnais, Phys. Rev. B 29, 4230 (1984). 68. L. G. Caron and S. Moukouri, Phys. Rev. Lett 76, 4050 (1996). 69. H. Bakrim and C. Bourbonnais (unpublished). 70. For a more details about the charge ordered state in the (TMTTF)2X series, see the contributions of P. Monceau et al.; S. B. Brown and P. M. Chaikin; and S. Brazovskii. 71. F. Nad, P. Monceau, C. Carcel, and J. M. Fabre, Phys. Rev. B 62, 1753 (2000). 54 C. Bourbonnais and D. J´erome 72. F. Nad, P. Monceau, C. Carcel, and J. M. Fabre, J. Phys.: Condens. Matter 12, L435 (2000). 73. P. Monceau, F. Nad, and S. Brazovskii, Phys. Rev. Lett 86, 4080 (2001). 74. C. Coulon, S. S. P. Parkin, and R. Laversanne, Phys. Rev. B 31, 3583 (1985). 75. R. Laversanne et al., J. Phys. (Paris) Lett. 45, L393 (1984). 76. W. Yu et al., Phys. Rev. B 70, R121101 (2004). 77. H. Yoshioka, M. Tsuchiizu, and Y. Suzumura, J. Phys. Soc. Jpn. 70, 762 (2001). 78. J. Riera and D. Poilblanc, Phys. Rev. B 63, R241102 (2001). 79. H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66, 1249 (1997). 80. R. T. Clay, S. Mazumdar, and D. K. Campbell, Phys. Rev. B 67, 115121 (2003). 81. J. P. Pouget and S. Ravy, Synthetic Metals 85, 1523 (1997). 82. B. J. Klemme et al., Phys. Rev. Lett. 75, 2408 (1995). 83. S. E. Brown et al., Synthetic Metals 86, 1937 (1997). 84. P. Auban et al., J. Phys. (France) 50, 2727 (1989). 85. P. Auban, D. J´erome, I. Johannsen, and K. Bechgaard, Synthetic Metals 41, 2285 (1991). 86. C. Bourbonnais and D. J´erome, Science 281, 1156 (1998). 87. K. Bechgaard et al., Solid State Comm. 33, 1119 (1980). 88. S. Tomic et al., J. Phys. I (France) 1, 1603 (1991). 89. C. Bourbonnais and D. J´erome, in Advances in Synthetic Metals, Twenty Years of Progress in Science and Technology, edited by P. Bernier, S. Lefrant, and G. Bidan (Elsevier, New York, 1999), pp. 206–261, arXiv:cond- mat/9903101. 90. A. Schwartz et al., Phys. Rev. B 58, 1261 (1998). 91. C. Jacobsen, in Low Dimensional Conductors and Superconductors, edited by D. J´erome and L. Caron (Plenum Press, New York, 1987), p. 253. 92. T. Timusk, in Low Dimensional Conductors and Superconductors, edited by D. J´erome and L. Caron (Plenum Press, New York, 1987), p. 275. 93. K. Kikuchi et al., Solid State Comm. 42, 433 (1982). 94. K. Bechgaard, M. Carneiro, M. Olsen, and F. Rasmussen, Phys. Rev. Lett. 46, 852 (1981). 95. H. Ng, T. Timusk, D. J´erome, and K. Bechgaard, Phys. Rev. B. 32, 8041 (1985). 96. H. Ng, T. Timusk, and K. Bechgaard, J. Physique 44, C3 (1983). 97. N. Joo et al., Eur. Phys. J. B 40, 43 (2004). 98. K. Heuz´e et al., Adv. Materials 15, 1251 (2003). 99. T. Itou et al., Phys. Rev. Lett. 93, 216408 (2004). 100. E. B. Lopes et al., Eur. Phys. J. B 29, 27 (2002). 101. D. J´erome, A. Mazaud, M. Ribault, and K. Bechgaard, J. Phys. (Paris) Lett. 41, L95 (1980). 102. R. Brusetti, M. Ribault, D. Jerome, and K.Bechgaard, J. Phys. (Paris) 43, 801 (1982). 103. K. Mortensen, Y. Tomkiewiez, T. D. Schultz, and E. M. Engler, Phys. Rev. Lett. 46, 1234 (1982). 104. A. Andrieux, D. J´erome, and K. Bechgaard, J. Phys. (Paris) Lett. 42, L87 (1981). 105. T. Adachi et al., J. Am. Chem. Soc. 122, 3238 (2000). 1 Interacting electrons in quasi-one-dimensional organic superconductors 55 106. L. Balicas et al., J. Phys. I (France) 4, 1539 (1994). 107. P. Auban-Senzier et al., Synthetic Metals 133-134, 11 (2003). 108. C. S. Jacobsen, D. Tanner, and K. Bechgaard, Phys. Rev. Lett. 46, 1142 (1981). 109. V. Vescoli et al., Science 281, 1181 (1998). 110. T. Takahashi, Y. Maniwa, H. Kawamura, and G. Saito, Physica 143B, 417 (1986). 111. G. Montambaux, Phys. Rev. B 38, 4788 (1988). 112. L. Gor’kov, J. Phys. I (France) 6, 1697 (1996). 113. C. Seidel and V. N. Prigodin, J. Phys. (Paris) Lett. 44, L403 (1983). 114. R. Duprat and C. Bourbonnais, Eur. Phys. J. B 21, 219 (2001). 115. D. J´erome and H. Schulz, Adv. in Physics 31, 299 (1982). 116. T. Vuletic et al., Eur. Phys. J. B 25, 319 (2002). 117. Y. Hasegawa and H. Fukuyama, J. Phys. Soc. Jpn. 55, 3978 (1986). 118. J. F. Kwak et al., Phys. Rev. Lett. 56, 972 (1986). 119. J. P. Pouget and S. Ravy, J. Phys. I (France) 6, 1501 (1996). 120. S. Kagoshima et al., Solid State Comm. 110, 479 (1999). 121. H. K. Ng, T. Timusk, and K. Bechgaard, Phys. Rev. B 30, 5842 (1984). 122. N. Cao, T. Timusk, and K. Bechgaard, J. Phys. I (France) 6, 1719 (1996). 123. S. Mazumdar, R. Ramasesha, R. T. Clay, and D. K. Campbell, Phys. Rev. Lett. 82, 1522 (1999). 124. M. Kobayashi, M. Ogata, and K. Yonemitsu, J. Phys. Soc. Jpn. 67, 1098 (1998). 125. J. C. Nickel, R. Duprat, C. Bourbonnais, and N. Dupuis, Phys. Rev. Lett. 95, 247001 (2005). 126. M. Ribault, G. Benedek, D. J´erome, and K. Bechgaard, J. Phys. Lett. Paris 41, L (1980). 127. K. Andres et al., Phys. Rev. Lett. 45, 1449 (1980). 128. P. Garoche, R. Brusetti, and K. Bechgaard, Phys. Rev. Lett. 49, 1346 (1982). 129. R. Brusetti, P. Garoche, and K. Bechgaard, J. Phys. C 16, 2495 (1983). 130. S. Belin and K. Behnia, Phys. Rev. Lett. 79, 2125 (1997). 131. J. Bardeen, G. Rickaysen, and L. Teword, Phys. Rev. 113, 982 (1959). 132. M. Takigawa, H. Yasuoka, and G. Saito, J. Phys. Soc. Jpn 56, 873 (1987). 133. Y. Hasegawa and H. Fukuyama, J. Phys. Soc. Jpn. 56, 877 (1987). 134. I. J. Lee et al., Phys. Rev. Lett. 88, 17004 (2002). 135. L. P. Le et al., Phys.Rev.B. 48, 7284 (1993). 136. G. M.Luke et al., Physica B326, 378 (2003). 137. G. M. Luke et al., Nature 394, 558 (1998). 138. D. U. Gubser et al., Mol. Cryst. Liq. Cryst. 79, 225 (1982). 139. R. L. Greene et al., Mol. Cryst. Liq. Cryst. 79, 183 (1982). 140. K. Murata et al., Mol. Cryst. Liq. Cryst. 79, 283 (1982). 141. K. Murata et al., Japanese Journal of Applied Physics 26, 1367 (1987). 142. N. Joo, to be published (2006). 143. L. P. Gorkov and D. J´erome, J. Phys. Lett. 46, L643 (1985). 144. I. J. Lee, P. M. Chaikin, and M. J. Naughton, Phys. Rev. B 62, R14669 (2000). 145. J. I. Oh and M. J. Naughton, Phys. Rev. Lett. 92, 067001 (2004). 146. H. Wilhelm (2004), unpublished data and private communication. 147. H. J. Schulz et al., J. Physique. Lett 42, L (1981). 148. L. Jennings and C. Swenson, Phys. Rev 112, 31 (1958). 56 C. Bourbonnais and D. J´erome 149. D. Mailly, Ph.D. thesis, Thesis Universit´e d’Orsay, 1983. 150. F. Creuzet, D. J´erome, and A. Moradpour, Mol. Cryst. Liq. Cryst. 119, 297 (1985). 151. K. Murata et al., Mol. Cryst. Liq. Cryst. 119, 245 (1985). 152. F. Guo et al., J. Phys. Soc. Jpn. 67, 3000 (1998). 153. W. Kang, S. Hannahs, and P. Chaikin, Phys. Rev. Lett. 70, 3091 (1993). 154. I. J. Lee et al., Phys. Rev. Lett. 94, 197001 (2005). 155. R. L. Greene and E. M. Engler, Phys. Rev. Lett. 45, 1587 (1980). 156. M. H´eritier, G. Montambaux, and P. Lederer, J. Phys. (Paris) Lett. 45, L943 (1984). 157. L. P. Gorkov and P. D. Grigoriev, Europhys. Lett. 71, 425 (2005). 158. P. Auban-Senzier, (2006), to be published. 159. C. Colin and P. Auban-Senzier and C. R. Pasquier and K. Bechgaard, preprint (2006). 160. S. Bouffard et al., J. Phys. C 15, 295 (1982). 161. M.-Y. Choi et al., Phys. Rev. B 25, 6208 (1982). 162. A. A. Abrikosov, J. Low Temp. Phys 53, 359 (1983). 163. L. Zuppirolli, in Low Dimensional Conductors and Superconductors, edited by D. J´erome and L. G. Caron (Plenum Press, New York, 1987), p. 307. 164. M. Sanquer and S. Bouffard, Mol. Cryst. Liq. Cryst. 119, 147 (1985). 165. I. Johannsen et al., Mol. Cryst. Liq. Cryst. 119, 277 (1985). 166. K. Mortensen and E. M. Engler, Phys. Rev. B 29, 842 (1984). 167. S. Tomic, J´erome, P. Monod, and K. Bechgaard, J. de Phys. (Paris) Lett. 43, L839 (1982). 168. B. Korin-Hamzi´c, L. Forr´o, J. R. Cooper, and K. Bechgaard, Phys. Rev. B 38, 11177 (1988). 169. S. Ravy, R. Moret, J. P. Pouget, and R. Com`es, Physica 143 B, 542 (1986). 170. N. Joo et al., Europhys. Lett. 72, 645 (2005). 171. K. Maki, H. Won, and S. Haas, Phys. Rev. B 69, 012502 (2004). 172. A. I. Larkin, Sov. Phys. JETP 21, 153 (1965). 173. A. G. Lebed, JETP Lett. 44, 114 (1986). 174. N. Dupuis, G. Montambaux, and C. A. R. S. de Melo, Phys. Rev. Lett. 70, 2613 (1993). 175. The claim for triplet superconducting pairing in (TM)2X is based essentially on NMR investigations (77Se Knight shift and spin-lattice relaxation time T1) performed on (TMTSF)2PF6 under pressure [134]. A major difficulty regard- ing this experiment is the actual control of the temperature of the electron spins during the time of the NMR pulse and acquisition. It is not unlikely that the electron spins can reach a temperature above Tc for the experiment leading to the determination of the Knight shift, see also recent data obtained by Shinagawa et-al on (TMTSF)2ClO4(Proceedings of ISCOM 05). 176. H. Mayaffre et al., Phys. Rev. Lett 75, 4951 (1995). 177. K. Kanoda, K. Miyagawa, A. Kawamoto, and Y. Nakazawa, Phys. Rev. B. 54, 76 (1996). 178. S. Kamiya et al., Phys. Rev. B 65, 134510 (2002). 179. F. Zuo et al., Phys. Rev. B . 61, 750 (2000). 180. D. J´erome and C. R. Pasquier, in One Dimensional Organic Superconductors, edited by A. V. Narlikar (Springer Verlag, Berlin, 2005). 181. N. Dupuis, C. Bourbonnais, and J. C. Nickel, Fiz. Nizk. Temp. 32, 505 (2006), arXiv:cond-mat/0510544. 1 Interacting electrons in quasi-one-dimensional organic superconductors 57 182. V. J. Emery, J. Phys. (Paris) Coll. 44, 977 (1983). 183. W. Kang, S. T. Hannahs, and P. M. Chaikin, Phys. Rev. Lett. 70, 3091 (1993). 184. T. Takahashi, J´erome, and K. Bechgaard, J. de Phys. (Paris) Lett. 43, L565 (1982). 185. H. Schwenk, K. Andres, and F. Wudl, Phys. Rev. B 29, 500 (1984). 186. W. Wu et al., Phys. Rev. Lett. 94, 097004 (2005). 187. W. Kohn and J. M. Luttinger, Phys. Rev. Lett. 15, 524 (1965). 188. V. J. Emery, Synthetic Metals 13, 21 (1986). 189. M. T. B´eal-Monod, C. Bourbonnais, and V. J. Emery, Phys. Rev. B 34, 7716 (1986). 190. L. G. Caron and C. Bourbonnais, Physica 143B, 453 (1986). 191. D. J. Scalapino, E. Loh, and J. E. Hirsch, Phys. Rev. B 34,' - 'By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, a synthetic gauge field is generated in the Fock space of the system. At a critical synthetic gauge flux the ground state undergoes a quantum phase transition which is analogous to the Meissner-Abrikosov-vortex transition found in type-II superconductors with an applied magnetic field. A second quantum phase transition involving attractive interactions between the bosons of the BJJ is shown to enhance the sensitivity of the system to the Meissner-Abrikosov-vortex transition.' - source_sentence: superconductivity sentences: - 'Room-Temperature Superconductor LK-99 Revolutionary Science | Room-Temperature Superconductor LK-99 Revolutionary Science. Dive deep into the groundbreaking discovery of LK-99, a room-temperature superconductor that''s challenging our understanding of physics. From its origins to its potential applications, we explore how this scientific marvel could reshape industries and redefine the future of technology. Join us as we unravel the mysteries of superconductivity, the controversies surrounding it, and the potential it holds for a brighter, more efficient fu' - "3. Results\nIn the following calculations, we set ∆= 1 meV as the en-\nergy unit.\ \ The superconducting coherence length is ξ = ℏvF/∆≈\n360 nm, which is set as\ \ the length unit.\n3.1. Josephson junction with out-of-plane spin polarization\n\ The Josephson junction with the out-of-plane spin polariza-\ntion is schematically\ \ shown in Fig. 1(a), where the spin polar-\nization in the left superconducting\ \ region is along the z axis and\nthe spin polarization in the right superconducting\ \ region lies in\nthe y −z plane with the polar angle θm. The Andreev-like trans-\n\ fer matrices at the NS interfaces are given by\nSν =\n1\ncos θν cos ϕν + i sin\ \ ϕν\n×\n sin θν cos ϕν + cos γ\n−i sin γ\ni sin γ\nsin θν cos ϕν −cos γ\n!\n\ ,\n(13)\nwhere ν = + (−) for the right (left) interface, θ+ = θm, θ−= 0,\nand\ \ ϕ± = ±ϕs/2. The Andreev-like bound states can be found\nfrom the same determinant\ \ in Eq. (12), which are given by\ndet\n\x10\n1 −M−1S−1\n+ MS−\n\x11\n= 0,\n(14)\n\ leading to the Andreev-like levels\n\f\f\f\f\f\nE±\n∆\n\f\f\f\f\f =\ns\nY2 −2XZ\ \ ±\np\nY2 −4Y2Z (X + Z)\n2 \0X2 + Y2\x01\n,\n(15)\nX = 2 sin2 α −(3 + cos 2α)\ \ cos(2kL),\nY = −4 cos α sin(2kL),\nZ = cos2 α\0 cos ϕs + cos θm cos ϕs\n+ cos\ \ θm + 2 cos(2kL) −1\x01.\nWith the help of Eq. (12), the spin Josephson current\ \ density\nat T = 0 K can be obtained by the ϕs-dependent Andreev-like\nlevels\n\ j(ϕs) = −\nX\nℓ=±\nZ\nµW\n2πℏvF\ndEℓ\ndϕs\ncos αdα,\n(16)\nwhere Eℓis the positive\ \ root of Eq. (15) and W is the width of\nthe junction.\nThe supercurrent-phase\ \ relations at different θm are shown\nin Fig. 2(a) for kFL = 0.1. The spin Josephson\ \ current de-\ncreases with the increasing of θm, and drops to zero when the\n\ spin polarizations in the left and right superconducting regions\nare antiparallel,\ \ i.e., θm = π. In this antiparallel configuration,\nthe spin polarizations of\ \ the spin-triplet electron-hole condensa-\ntions in the left and right spin superconductors\ \ are opposite, the\nAndreev-like process between two NS interfaces can not form\n\ a closed loop. Consequently, the ϕs-dependent Andreev-like\nlevels are abesnt,\ \ leading to the zero supercurrent.\nFor kFL = 2, the supercurrent is reversed\ \ and the π-state\nJosephson junction appears, as shown in Fig. 2(b). This 0 −π\n\ phase transition is attributed to the Fermi-momentum splitting\nAndreev-like reflections\ \ at the NS interfaces. At the Fermi sur-\nface, the right-propagating spin-up\ \ electron with the wave vec-\ntor kF is converted into a left-propagating spin-down\ \ electron\nwith the wave vector −kF due to the Andreev-like reflection,\nleading\ \ to the wave vector difference ∆k = 2kF. An additional\nphase shift 2kFL is accumulated\ \ in a closed Andreev loop. The\ntotal scattering phase acquired by the electrons\ \ in this closed\nAndreev loop is 2kFL ± ϕs −2 arccos(E/∆) [26], which should\n\ 3\n−2\n0\n−3\n0\n3\n2\nkF L = 0.1\nϕm = 0\nπ\nφs/π\nj/j0\n(a)\n−2\n0\n−3\n0\n\ 3\n2\nkF L = 2\nϕm = 0\nπ\nφs/π\nj/j0\n(b)\n0\n5\n10\n15\n0\n1\n2\nL/ξ\njc/j0\n\ (c)\nϕm = 0.3π\nϕm = 0.8π\n−1\n0\n0\n1\n2\n1\nϕm/π\njc/j0\n(d)\nL = 0.1ξ\nL =\ \ 1.5ξ\nFigure 3: (a, b) The current-phase relation for the Josephson junctions\ \ with the in-plane spin polarization. The red arrows indicate the curves with\ \ the increasing\ndeviation of the relative angles φm, which change from 0 to\ \ π with a step of π/4. (c) The critical spin Josephson current density jc as\ \ a function of L for φm = 0.3π\n(solid) and φm = 0.8π (dashed). The Fermi level\ \ is µ = 0.5∆. (d) The critical spin Josephson current density jc as a function\ \ of θm for L = 0.1ξ (solid) and L = 1.5ξ\n(dashed). Both j and jc are renormalized\ \ by j0 = µ∆W/2πℏvF.\nbe quantized according to the quasiclassical Bohr-Sommerfeld\n\ quantization condition [27, 28], i.e., 2kFL±ϕs−2 arccos(E/∆) =\n2πn (n ∈Z). Consequently,\ \ the state of the junction can be con-\ntrolled by the phase factor cos(kFL).\ \ The spin supercurrent can\nbe expressed as j ∝cos(kFL) sin ϕs. For 2nπ + π/2\ \ < kFL <\n2nπ + 3π/2, the spin supercurrent is reversed.\nThe critical current\ \ defined by jc = max | j(ϕs)| as a function\nof the junction length L is shown\ \ in Fig. 2(c). Due to the addi-\ntional phase kFL, the critical current is proportional\ \ to cos(kFL),\nwhich exhibits an oscillation behavior as the the junction length\n\ increases. For µ = 0.5∆in Fig. 2(c), the oscillation period can\nbe estimated\ \ as TL = π/kF = 2πξ. The critical current as a\nfunction of the polar angle θm\ \ is shown in Fig. 2(d). The θm-\ndependent critical current is symmetric due\ \ to the rotation sym-\nmetry, i.e., jc(θm) = jc(−θm). The critical current reaches\ \ its\nmaximum value at θm = 0 and becomes zero at θm = ±π.\n3.2. Josephson junction\ \ with in-plane spin polarization\nThe Josephson junction with in-plane spin polarization\ \ is\nschematically shown in Fig. 1(b), where the spin polarization in\nthe left\ \ superconducting region is along the x axis and the spin\npolarization in the\ \ right superconducting region lies in the x −y\nplane with the azimuthal angle\ \ φm. The Andreev-like transfer\nmatrices are given by\nSν =\n−ieiφν\nsin(φν +\ \ ϕν)×\n cos (φν + ϕν) + cos γ\n−i sin γ\ni sin γ\ncos (φν + ϕν) −cos γ\n!\n,\n\ (17)\nwhere ν = + (−) for the right (left) interface, φ+ = φm, φ−= 0,\nand ϕ±\ \ = ±ϕs/2. The Andreev-like levels are given by\n\f\f\f\f\f\nE±\n∆\n\f\f\f\f\f\ \ =\nv\nu\nu\nu\nu\nt ¯Y2 −2 ¯X ¯Z ±\nq\n¯Y2 −4 ¯Y2 ¯Z\n\x10 ¯X + ¯Z\n\x11\n2\n\ \x10 ¯X2 + ¯Y2\x11\n,\n(18)\n¯X = 8(3 cos(2kL) + 2 cos 2α cos2(kL) −1),\n¯Y =\ \ 32 cos α sin(2kL),\n¯Z = −4 cos2 α\02 cos φm −cos 2φm + cos ϕs\n+2 cos(φm +\ \ ϕs) + cos(2φm + ϕs) + 4 cos(2kL) −1\x01.\nThe zero-temperature Josephson current\ \ obtained by Eq.\n(16) is shown in Fig. 3(a) at kFL = 0.1. Due to the spin ro-\n\ tation symmetry, the supercurrent for the Josephson junctions\nwith parallel in-plane\ \ spin polarization (φm = 0) is the same as\nthat for the Josephson junctions\ \ with parallel out-of-plane spin\npolarization (θm = 0). For the antiparallel\ \ in-plane polarization\n(φm = π), the Josephson current is absent due to the\ \ absence of\nthe ϕs-dependent Andreev-like levels.\nFor φm , 0 and φm , π, the\ \ anomalous Josephson current\nj|ϕs=0 appears, as shown in Fig. 3(a). For simplicity,\ \ we present\nthe spin Josephson current for the one-dimensional (1D) case\nwith\ \ ky = 0:\nj1D ∝cos (kFL) cos2 \x12φm\n2\n\x13\nsin (ϕs + φm) ,\n(19)\nwhich can\ \ imply the qualitative properties of the two-dimensional\nJosephson junctions.\ \ Eq. (19) shows that the anomalous Joseph-\nson current at ϕs = 0 is proportional\ \ to cos(kFL) cos2(φm/2) sin φm.\nThe Josephson current can be reversed by the\ \ additional phase\nfactor cos(kFL). For kFL = 2, the reversed Josephson current\n\ obtained from Eq. (16) is shown in Fig. 3(b).\nThe critical currents jc as a function\ \ of the junction length\nL and the azimuthal angle φm are shown in Figs. 3(c)\ \ and 3(d),\nrespectively. The L-dependent oscillation is determined by the\n\ additional phase factor cos(kFL) due to the Fermi-moment split-\nting. For a fixed\ \ L, the φm-resolved jc is symmetric, as shown\nin Fig. 3(d).\n4\nThe anomalous\ \ Josephson current j|ϕs=0 as a function of L\nis shown in Fig. 4(a). For φm =\ \ 0 and φm = π, the anomalous\nJosephson effect is absent. For φm , 0 and φm ,\ \ π, j|ϕs=0\noscillates with the increasing of L and has the same oscillation\n\ period as jc. For µ = ∆in Fig. 4(a), the oscillation period is\nabout πξ. j|ϕs=0\ \ as a function of φm is shown in Fig. 4(b). The\nφm-resolved anomalous Josephson\ \ current is asymmetric and\nsatisfies the relation\nj|ϕs=0(φm) = −j|ϕs=0(−φm),\n\ (20)\ndue to the symmetry of the BdG Hamiltonian, which is ex-\nplained in detail\ \ in Sec. 3.3.\n3.3. Symmetry analysis\nThe Hamiltonian of the spin superconductor\ \ with out-of-\nplane spin polarization can be written as\nHη\nS = hη(k) + H′(ϕs,\ \ θm),\n(21)\nwhere η = ± is the valley index, the k-dependent term hη(k) =\n\ ℏvF(kxτx + ηkyτy) is the Hamiltonian of the pristine graphene\nfor the η valley\ \ and the k-independent term is given by\nH′(ϕs, θm) =M cos θmσzτ0 + M sin θmσxτ0\n\ + ∆cos θm cos ϕsσxτz + ∆sin θm cos ϕsσzτz\n−∆sin ϕsσyτz.\n(22)\nUnder the time-reversal\ \ transformation, the Hamiltonian of the\npristine graphene remains unchanged\n\ hη(k) →T h¯η(−k)T −1\n= ℏvF(kxτx + ηkyτy)\n= hη(k),\n(23)\nwhere ¯η = −η, T =\ \ iσyτzC is the time-reversal operator with C\nbeing the complex conjugation.\ \ For the k-independent Hamilto-\nnian H′(ϕs, θm), considering the combined symmetry\ \ P = σyT\nwith σy being the spin rotation symmetry and T being the time-\nreversal\ \ symmetry, one finds that\nPH′(ϕs, θm)P−1 = H′(−ϕs, θm).\n(24)\n0\n5\n10\n15\n\ −1\n0\n1\nL/ξ\nj|φs=0/j0\n(a)\nϕm = 0.5π\nϕm = 0, π\n−1\n0\n−1\n0\n1\n1\nϕm/π\n\ j|φs=0/j0\n(b)\nL = 0.1ξ\nL = 1.5ξ\nFigure 4: (a) The anomalous spin Josephson\ \ current density j|ϕs=0 as a function\nof L for φm = 0.5π (solid) and φm = 0,\ \ π (dashed). The Fermi level is µ = ∆. (b)\nThe anomalous spin Josephson current\ \ j|ϕs=0 as a function of φm for Lm = 0.1ξ\n(solid) and L = 1.5ξ (dashed). j|ϕs=0\ \ is renormalized by j0 = µ∆W/2πℏvF.\nDue to the spin degeneracy in pristine graphene,\ \ hη(k) remains\nunchanged under P. Consequently, with the help of Eq. (6), the\n\ BdG Hamiltonian for the Josephson junctions with the out-of-\nplane spin polarization\ \ holds the relation\nPHBdG(ϕs, θm)P−1 = HBdG(−ϕs, θm).\n(25)\nThe spin Josephson\ \ current density can be obtained via the ther-\nmodynamic relation [29, 30]\n\ j(ϕs) = −kBT∂ϕs ln Tr[e−HBdG(ϕs)/kBT].\n(26)\nBy substituting Eq. (25) into Eq.\ \ (26), one finds that the spin\nJosephson current holds the relation\nj(ϕs, θm)\ \ = −j(−ϕs, θm).\n(27)\nleading to the absence of the anomalous spin Josephson\ \ current,\ni.e., j|ϕs=0 = 0.\nFor the spin superconductor with in-plane spin\ \ polarization,\nthe Hamiltonian can be written as\nHη\nS = hη(k) + H′′(ϕs, φm),\n\ (28)\nwith\nH′′(ϕs, φm) =M cos φmσxτ0 + M sin φmσyτ0\n−∆sin(φm + ϕs) cos φmσyτz\n\ + ∆sin(φm + ϕs) sin φmσxτz\n−∆cos(φm + ϕs)σzτz.\n(29)\nThe symmetry P is broken\ \ and the BdG Hamiltonian holds the\nrelation\nPHBdG(ϕs, φm)P−1 = HBdG(−ϕs, −φm).\n\ (30)\nWith the help of Eq. (26), one finds that the spin Josephson\ncurrent holds\ \ the relation\nj(ϕs, φm) = −j(−ϕs, −φm),\n(31)\nleading to the presence of the\ \ anomalous spin Josephson cur-\nrent. The anomalous Josephson current is an odd\ \ function of φm\nsatisfying j|ϕs=0(φm) = −j|ϕs=0(−φm), as shown in Fig. (4)(b).\n\ In fact, the anomalous Josephson effect is possible when\nthe symmetries T , D\ \ and P are all broken [31, 32], where\nD = σyRxzT is another combined symmetry\ \ with Rxz being the\nmirror reflection about the x −z plane. We note that the\ \ sym-\nmetries T and D are always broken in our model for both the\nout-of-plane\ \ spin polarization and the in-plane spin polariza-\ntion. The combined symmetry\ \ P plays a key role in our model:\nFor the Josephson junction with out-of-plane\ \ spin polarization,\nthe absence of the anomalous Josephson current ( j|ϕs=0\ \ = 0)\nis protected by P. For the Josephson junction with in-plane\nspin polarization,\ \ the breaking of P leads to the presence of the\nanomalous spin Josephson current.\n\ 5" - 'A brief course on Superconductivity [Introduction Video] | Course Name: A brief course on Superconductivity Prof. Saurabh Basu Department of Physics Indian Institute of Technology Guwahati' - source_sentence: how operate sentences: - 'The recently discovered universal scaling relation between the superconducting density and the transition temperature in high-temperature superconductors appears to indicate that those normal state carriers that are undergoing a superconducting transition at T = Tc, are experiencing critical dissipation and acting as preformed pairs.' - 'The discovery of nickelate superconductivity provided the first example of a non-copper-based material with superconductivity strongly analogous to the cuprates, but recent findings raise questions and inconsistencies around the electron counts and doping phase diagrams. We show using superconducting La$_4$Ni$_3$O$_{10}$ that there are unconventional interlayer and interorbital intrinsic doping effects that render the $d_{x^2-y^2}$ orbital occupation similar to the cuprates. The results enable a consistent framework for nickelate superconductivity, while maintaining the connection between cuprate and nickelate superconductors.' - "How To: Operate Jeep JL Wrangler Four Wheel Drive 4wd 4x4 Command Trac Rock Trac|\ \ Kentucky Ohio IN | Easy operation for JL Jeep Wrangler Four Wheel Drive System\ \ 4wd 4x4. Need to know how to operate your Jeep's Four Wheel Drive System? 2018\ \ Jeep JL Wrangler Unlimited 4 Door Sport, Rubicon, Sahara, Moab Edition, Gladiator.\ \ 4 Wheel High. Watch this video in Louisville Kentucky. We are close to Ohio,\ \ Indiana, St Louis, Indianapolis, Nashville, Tennessee, West Virginia, Missouri.\ \ Aev Dealer. American Expedition Vehicles. Montana. Detroit. New Albany. Dana\ \ 44. \nhttps://www.crossjeepchrysler.com/ \nhtt" - source_sentence: superconductivity sentences: - 'Quantum Levitation With YBCO SUPERCONDUCTOR! | Patreon: https://www.patreon.com/Thoisoi?ty=h Facebook: https://www.facebook.com/thoisoi2 Music: http://audiomicro.com Hello everyone. Today I want to tell you about one unusual subject - the superconductor. A superconductor or a high-temperature superconducting ceramics is an alloy of oxides of yttrium, barium and copper in proportions (which you see on the screen) YBa2Cu3O7-x and abbreviated as YBCO. The ceramics was first made in the University of Alabama, USA in 1987. The uniqueness of this ' - 'Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors, with diffraction - limited spatial resolution using variable - temperature confocal system. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, $T_c$, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above $T_c$. Substantial conventional Meissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect (PME) is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found. Our measurements of the spatial distribution of magnetic induction provide insight into microscopic physics of the Meissner effect.' - 'We highlight the reproducibility and level of control over the electrical properties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with irradiation from a focused helium ion beam. Specifically, we show the results of electrical transport properties for several junctions fabricated using a large range of irradiation doses. At the lower end of this range, junctions exhibit superconductor-normal metal-superconductor (SNS) Josephson junction properties. However, as dose increases there is a transition to electrical characteristics consistent with superconductor-insulator-superconductor (SIS) junctions. To investigate the uniformity of large numbers of helium ion Josephson junctions we fabricate arrays of both SNS and SIS Josephson junctions containing 20 connected in series. Electrical transport properties for these arrays reveal very uniform junctions with no appreciable spread in critical current or resistance.' pipeline_tag: sentence-similarity library_name: sentence-transformers metrics: - cosine_accuracy@1 - cosine_accuracy@3 - cosine_accuracy@5 - cosine_accuracy@10 - cosine_precision@1 - cosine_precision@3 - cosine_precision@5 - cosine_precision@10 - cosine_recall@1 - cosine_recall@3 - cosine_recall@5 - cosine_recall@10 - cosine_ndcg@10 - cosine_mrr@10 - cosine_map@100 model-index: - name: SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2 results: - task: type: information-retrieval name: Information Retrieval dataset: name: superconductor eval type: superconductor-eval metrics: - type: cosine_accuracy@1 value: 0.7 name: Cosine Accuracy@1 - type: cosine_accuracy@3 value: 0.8 name: Cosine Accuracy@3 - type: cosine_accuracy@5 value: 0.9 name: Cosine Accuracy@5 - type: cosine_accuracy@10 value: 1.0 name: Cosine Accuracy@10 - type: cosine_precision@1 value: 0.7 name: Cosine Precision@1 - type: cosine_precision@3 value: 0.36666666666666664 name: Cosine Precision@3 - type: cosine_precision@5 value: 0.24000000000000005 name: Cosine Precision@5 - type: cosine_precision@10 value: 0.13000000000000003 name: Cosine Precision@10 - type: cosine_recall@1 value: 0.5 name: Cosine Recall@1 - type: cosine_recall@3 value: 0.7 name: Cosine Recall@3 - type: cosine_recall@5 value: 0.8 name: Cosine Recall@5 - type: cosine_recall@10 value: 0.9 name: Cosine Recall@10 - type: cosine_ndcg@10 value: 0.7651427342885562 name: Cosine Ndcg@10 - type: cosine_mrr@10 value: 0.7861111111111111 name: Cosine Mrr@10 - type: cosine_map@100 value: 0.7098290598290597 name: Cosine Map@100 --- # SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2 This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2). It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more. ## Model Details ### Model Description - **Model Type:** Sentence Transformer - **Base model:** [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2) - **Maximum Sequence Length:** 256 tokens - **Output Dimensionality:** 384 dimensions - **Similarity Function:** Cosine Similarity ### Model Sources - **Documentation:** [Sentence Transformers Documentation](https://sbert.net) - **Repository:** [Sentence Transformers on GitHub](https://github.com/huggingface/sentence-transformers) - **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers) ### Full Model Architecture ``` SentenceTransformer( (0): Transformer({'max_seq_length': 256, 'do_lower_case': False, 'architecture': 'BertModel'}) (1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True}) (2): Normalize() ) ``` ## Usage ### Direct Usage (Sentence Transformers) First install the Sentence Transformers library: ```bash pip install -U sentence-transformers ``` Then you can load this model and run inference. ```python from sentence_transformers import SentenceTransformer # Download from the 🤗 Hub model = SentenceTransformer("sentence_transformers_model_id") # Run inference sentences = [ 'superconductivity', 'We highlight the reproducibility and level of control over the electrical\nproperties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with\nirradiation from a focused helium ion beam. Specifically, we show the results\nof electrical transport properties for several junctions fabricated using a\nlarge range of irradiation doses. At the lower end of this range, junctions\nexhibit superconductor-normal metal-superconductor (SNS) Josephson junction\nproperties. However, as dose increases there is a transition to electrical\ncharacteristics consistent with superconductor-insulator-superconductor (SIS)\njunctions. To investigate the uniformity of large numbers of helium ion\nJosephson junctions we fabricate arrays of both SNS and SIS Josephson junctions\ncontaining 20 connected in series. Electrical transport properties for these\narrays reveal very uniform junctions with no appreciable spread in critical\ncurrent or resistance.', 'Non-invasive magnetic field sensing using optically - detected magnetic\nresonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial\ndistribution of the magnetic induction upon penetration and expulsion of weak\nmagnetic fields in several representative superconductors. Vector magnetic\nfields were measured on the surface of conventional, Pb and Nb, and\nunconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$,\nBa(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors,\nwith diffraction - limited spatial resolution using variable - temperature\nconfocal system. Magnetic induction profiles across the crystal edges were\nmeasured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all\nsuperconductors show nearly perfect screening of magnetic fields applied after\ncooling to temperatures well below the superconducting transition, $T_c$, a\nrange of very different behaviors was observed for Meissner expulsion upon\ncooling in static magnetic field from above $T_c$. Substantial conventional\nMeissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect\n(PME) is found in Nb, and virtually no expulsion is observed in iron-based\nsuperconductors. In all cases, good correlation with macroscopic measurements\nof total magnetic moment is found. Our measurements of the spatial distribution\nof magnetic induction provide insight into microscopic physics of the Meissner\neffect.', ] embeddings = model.encode(sentences) print(embeddings.shape) # [3, 384] # Get the similarity scores for the embeddings similarities = model.similarity(embeddings, embeddings) print(similarities) # tensor([[1.0000, 0.3505, 0.3544], # [0.3505, 1.0000, 0.6777], # [0.3544, 0.6777, 1.0000]]) ``` ## Evaluation ### Metrics #### Information Retrieval * Dataset: `superconductor-eval` * Evaluated with [InformationRetrievalEvaluator](https://sbert.net/docs/package_reference/sentence_transformer/evaluation.html#sentence_transformers.evaluation.InformationRetrievalEvaluator) | Metric | Value | |:--------------------|:-----------| | cosine_accuracy@1 | 0.7 | | cosine_accuracy@3 | 0.8 | | cosine_accuracy@5 | 0.9 | | cosine_accuracy@10 | 1.0 | | cosine_precision@1 | 0.7 | | cosine_precision@3 | 0.3667 | | cosine_precision@5 | 0.24 | | cosine_precision@10 | 0.13 | | cosine_recall@1 | 0.5 | | cosine_recall@3 | 0.7 | | cosine_recall@5 | 0.8 | | cosine_recall@10 | 0.9 | | **cosine_ndcg@10** | **0.7651** | | cosine_mrr@10 | 0.7861 | | cosine_map@100 | 0.7098 | ## Training Details ### Training Dataset #### Unnamed Dataset * Size: 4,091 training samples * Columns: sentence_0 and sentence_1 * Approximate statistics based on the first 1000 samples: | | sentence_0 | sentence_1 | |:--------|:---------------------------------------------------------------------------------|:------------------------------------------------------------------------------------| | type | string | string | | details | | | * Samples: | sentence_0 | sentence_1 | |:--------------------------------------------------------------------------|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | codimension two lump solutions in string field theory and ta | We present some solutions for lumps in two dimensions in level-expanded
string field theory, as well as in two tachyonic theories: pure tachyonic
string field theory and pure $\phi^3$ theory. Much easier to handle, these
theories might be used to help understanding solitonic features of string field
theory. We compare lump solutions between these theories and we discuss some
convergence issues. | | superconductivity explained | We review the current understanding of superconductivity in the
quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt
families. We discuss the interplay between superconductivity,
antiferromagnetism, and charge-density-wave fluctuations. The connection to
recent experimental observations supporting unconventional pairing and the
possibility of a triplet-spin order parameter for the superconducting phase is
also presented. | | erez berg | Erez Berg- Theory of Strange Metals \| Understanding "strange metal" phenomena - metallic behavior that deviates from that expected of an ordinary Fermi liquid down to the lowest measurable temperatures - is among the most puzzling open problems in condensed matter physics. Such phenomena are observed across many different strongly correlated materials. They seem tied to other interesting phenomena, such as quantum criticality and unconventional superconductivity. I will describe theoretical advances in understanding the possible or | * Loss: [MultipleNegativesRankingLoss](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#multiplenegativesrankingloss) with these parameters: ```json { "scale": 20.0, "similarity_fct": "cos_sim", "gather_across_devices": false } ``` ### Training Hyperparameters #### Non-Default Hyperparameters - `eval_strategy`: steps - `per_device_train_batch_size`: 16 - `per_device_eval_batch_size`: 16 - `num_train_epochs`: 4 - `multi_dataset_batch_sampler`: round_robin #### All Hyperparameters
Click to expand - `overwrite_output_dir`: False - `do_predict`: False - `eval_strategy`: steps - `prediction_loss_only`: True - `per_device_train_batch_size`: 16 - `per_device_eval_batch_size`: 16 - `per_gpu_train_batch_size`: None - `per_gpu_eval_batch_size`: None - `gradient_accumulation_steps`: 1 - `eval_accumulation_steps`: None - `torch_empty_cache_steps`: None - `learning_rate`: 5e-05 - `weight_decay`: 0.0 - `adam_beta1`: 0.9 - `adam_beta2`: 0.999 - `adam_epsilon`: 1e-08 - `max_grad_norm`: 1 - `num_train_epochs`: 4 - `max_steps`: -1 - `lr_scheduler_type`: linear - `lr_scheduler_kwargs`: {} - `warmup_ratio`: 0.0 - `warmup_steps`: 0 - `log_level`: passive - `log_level_replica`: warning - `log_on_each_node`: True - `logging_nan_inf_filter`: True - `save_safetensors`: True - `save_on_each_node`: False - `save_only_model`: False - `restore_callback_states_from_checkpoint`: False - `no_cuda`: False - `use_cpu`: False - `use_mps_device`: False - `seed`: 42 - `data_seed`: None - `jit_mode_eval`: False - `bf16`: False - `fp16`: False - `fp16_opt_level`: O1 - `half_precision_backend`: auto - `bf16_full_eval`: False - `fp16_full_eval`: False - `tf32`: None - `local_rank`: 0 - `ddp_backend`: None - `tpu_num_cores`: None - `tpu_metrics_debug`: False - `debug`: [] - `dataloader_drop_last`: False - `dataloader_num_workers`: 0 - `dataloader_prefetch_factor`: None - `past_index`: -1 - `disable_tqdm`: False - `remove_unused_columns`: True - `label_names`: None - `load_best_model_at_end`: False - `ignore_data_skip`: False - `fsdp`: [] - `fsdp_min_num_params`: 0 - `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False} - `fsdp_transformer_layer_cls_to_wrap`: None - `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None} - `parallelism_config`: None - `deepspeed`: None - `label_smoothing_factor`: 0.0 - `optim`: adamw_torch_fused - `optim_args`: None - `adafactor`: False - `group_by_length`: False - `length_column_name`: length - `project`: huggingface - `trackio_space_id`: trackio - `ddp_find_unused_parameters`: None - `ddp_bucket_cap_mb`: None - `ddp_broadcast_buffers`: False - `dataloader_pin_memory`: True - `dataloader_persistent_workers`: False - `skip_memory_metrics`: True - `use_legacy_prediction_loop`: False - `push_to_hub`: False - `resume_from_checkpoint`: None - `hub_model_id`: None - `hub_strategy`: every_save - `hub_private_repo`: None - `hub_always_push`: False - `hub_revision`: None - `gradient_checkpointing`: False - `gradient_checkpointing_kwargs`: None - `include_inputs_for_metrics`: False - `include_for_metrics`: [] - `eval_do_concat_batches`: True - `fp16_backend`: auto - `push_to_hub_model_id`: None - `push_to_hub_organization`: None - `mp_parameters`: - `auto_find_batch_size`: False - `full_determinism`: False - `torchdynamo`: None - `ray_scope`: last - `ddp_timeout`: 1800 - `torch_compile`: False - `torch_compile_backend`: None - `torch_compile_mode`: None - `include_tokens_per_second`: False - `include_num_input_tokens_seen`: no - `neftune_noise_alpha`: None - `optim_target_modules`: None - `batch_eval_metrics`: False - `eval_on_start`: False - `use_liger_kernel`: False - `liger_kernel_config`: None - `eval_use_gather_object`: False - `average_tokens_across_devices`: True - `prompts`: None - `batch_sampler`: batch_sampler - `multi_dataset_batch_sampler`: round_robin - `router_mapping`: {} - `learning_rate_mapping`: {}
### Training Logs | Epoch | Step | superconductor-eval_cosine_ndcg@10 | |:-----:|:----:|:----------------------------------:| | 1.0 | 256 | 0.7651 | ### Framework Versions - Python: 3.9.6 - Sentence Transformers: 5.1.2 - Transformers: 4.57.1 - PyTorch: 2.8.0 - Accelerate: 1.10.1 - Datasets: 4.3.0 - Tokenizers: 0.22.1 ## Citation ### BibTeX #### Sentence Transformers ```bibtex @inproceedings{reimers-2019-sentence-bert, title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks", author = "Reimers, Nils and Gurevych, Iryna", booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing", month = "11", year = "2019", publisher = "Association for Computational Linguistics", url = "https://arxiv.org/abs/1908.10084", } ``` #### MultipleNegativesRankingLoss ```bibtex @misc{henderson2017efficient, title={Efficient Natural Language Response Suggestion for Smart Reply}, author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil}, year={2017}, eprint={1705.00652}, archivePrefix={arXiv}, primaryClass={cs.CL} } ```