text: 7 then joint fusing and tracking using multiple independent ﬁlter formulation to accommodate different types of detectors TOA estimations from the energy detectors can yield better with varying characteristics. In the next section, we will assess performance. We employ Kalman structure as shown in Fig. ?? the performance of the proposed fusion and tracking method. to accomplish this. VII. SIMULATION STUDY The state of the system and its dynamic nature is represented A. AWGN Channel by the state equation in the Kalman ﬁlter formulation, and is given by AWGN channel is simulated with F = 8 GHz with s − Tf = 200 ns, Ns = 1 and B = 4 GHz. We set Tb = 1 ns, s[n] = As[n 1] + u[n], (32) thus resulting sampling rate of the energy detector is 1/8-th the Nyquist rate. Consider a linear variation of TOA (τtoa) observed by a set of four independent energy detectors (refer where s[n], A, and u[n] is given by Fig. ??). The observed TOA of the four detectors are as shown (cid:20) τ[n](cid:21) in Fig. ?? at SNR = 12 dB. The tracked TOA using the s[n] = , (33) Kalman formulation is shown in the Fig. ??. We consider prior vtoa[n] state, covariance of prior state and plant noise variance equal to [20, 1], 0.01I and σ2 = 0.0001 respectively. (cid:20) (cid:21) 2 p 1 1 The mean square error (MSE) variation with time for the A[n] = , (34) 0 ν detection schemes with multiple energy detectors at various SNRs (E /N ) are illustrated in the Fig. ??. Notice that b 0 the steady state variance decreases as the number of energy (cid:20) (cid:21) 0 detector estimates increases. Also, from Fig. ??, at high SNRs, u[n] = , (35) uv[n] only few energy detectors (operating at 1/8-th rate of matched ﬁlter) are sufﬁcient to achieve same performance as digital where u [n] is the noise with variance σ2 and ν < 1 is a matched ﬁlter. v p constant. The τ[n] is the TOA at n-th time interval and vtoa is Figure ??, shows the variation of steady state MSE with an AR(1) processes with constant ν, representing the dynamic number of energy detectors (operating at F /8). Notice that ∼ N Q Q s nature of TOA. The plant noise u[n] (0, ), where is steady state MSE of fusing 4 independent energy detector given by estimates reaches that of digital matched ﬁlter estimate. (cid:20) (cid:21) Figure ??, shows the number of energy detectors operating Q 0 0 = 0 σ2 . (36) in sub-Nyquist (Fs/8) rate needed to match the performance p of matched ﬁlter operating at Nyquist rate (F ). At lower s SNRs, more number of energy detectors, (NED), are required The measurement matrix, y = [τˆt1oa, τˆt2oa, . . . , τˆtNoa], is the in- to meet the matched ﬁlter performance. The number of en- dependent TOA estimates from N receivers. The measurement ergy detectors, NED, reduces with the increase of SNR and equation is given by asymptotically approaches to 4, conﬁrming with the analytical derivation of the previous section. y[n] = H[n]s[n] + w[n], (37) B. Multipath Channel IEEE 801.15.4a CM1 channel model is simulated with where F = 8 GHz with T = 200 ns, N = 1 and B = 4 GHz. s f s   We set T = 1 ns, thus resulting sampling rate of the 1 0 b energy detector is 1/8-th the Nyquist rate. We use WMESS 1 0   algorithm discussed in the previous section to arrive at TOA H[n] =  .. .. , (38)  . . estimates from the energy samples. We employ similar fusion 1 0 and tracking strategy using the Kalman ﬁlter described in the previous section for the dynamic TOA model. The prior state ∼ N w[n] (0, diag(σ2, . . . σ2 )). N denotes the number information, covariance of prior state and other initialization · 1 N of detectors and diag( ) indicates the diagonal matrix with parameters of the Kalman ﬁlter are kept same as in the diagonal elements represented inside the brackets. previous section. Figure ??, shows the variation of MSE The Kalman ﬁlter based fusion of dynamic TOA from with time at SNR of 20 dB for different number of energy multiple energy detector estimates, y[n], is as shown in detectors. As expected the steady state variance decrease with Algorithm ??. At each iteration, the Kalman ﬁlter yields the increase in the number of detectors. Figure ??, shows the fused TOA estimate, τˆtoa[n], and its variance, σˆt2oa[n], from variation of steady state MSE with number of sub-Nyquist multiple energy detector estimates, y[n]. In our analysis, we energy detectors, as discussed earlier a single energy detector have used same kind of detectors and also the reliability with WMESS selection criteria outperforms the matched ﬁlter or importance of each of the detectors are assumed same. at low SNRs, however, at high SNRs more energy detectors By appropriately selecting the measurement matrix H and are need to match the matched ﬁlter performance. Figure covariance of the measurements, we can extend the Kalman ??, also illustrates that fusing two energy detector estimates

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Variation of MSE with time for digital matched ﬁlter and fusion of multiple sub-Nyquist energy detectors using Kalman ﬁlter at different SNRs 9 10−1 8 7 6 10−2 5 4 3 NED =1 NED =4 2 10−3 NED =10 1 Matched ﬁlter (NMF =1) 0 0 5 10 15 20 25 2 4 6 8 10 12 14 16 18 20 22 24 SNR SNR Fig. 10. Steady state MSE verses time, for multiple energy detectors and Fig. 11. Number of sub-Nyquist energy detectors need to match the digital matched ﬁlter. performance of matched ﬁlter operating at Nyquist rate. (NED = 2) can match the matched ﬁler performance across large bandwidth can yield high precision ranging as evident the SNR region. from CRLB Equation (??). For AWGN channel, matched VIII. CONCLUSION AND DISCUSSION ﬁlter based estimation yields optimum performance at high Estimating TOA with good accuracy is very important for SNRs. However, matched ﬁlter requires Nyquist-rate sampling localization and several other applications. 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text: estimation

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text: transceiver

text: types,”

text: Microwave

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text: Techniques,

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text: Transactions

text: on,

text: vol.

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text: pp.

text: June

text: S.M.

text: Kay,

text: Fundamentals

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text: Theory,

text: Fundamentals

text: of

text: Statistical

text: Signal

text: Processing.

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text: Athanasios

text: Papoulis

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text: Unnikrishna

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text: Cassioli,

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text: Emami,

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text: . . . . . . FUSION ALGORITHM Analog Frontend Digital Baseband Processing Block d 1 Detector-1 d 2 Detector-2 RF BPF LNA ADC dfused Ts d L Detector-L d = [d1,d2···,dL] and dfused ∈ {H0,H1} Fig. 1. Depiction of direct sampling receiver architecture with multi detector fusion. The (Detector-1,...,Detector-L), are the different detector types available in the transceiver. The di,i ∈ [1,...,L], indicates the binary decisions made by the different detectors[??] with regard to hypothesis. The dfused, indicates the fused binary decision for the chosen hypothesis. better, and since every detector decision is new information TABLE I about the signaled hypothesis, it should yield better reliability PARAMETERS ON WHICH DETECTORS PERFORMANCE DEPENDS. and improved performance. Parameter Description The proposed transceiver structure shown in Fig. ??, is ap- PFA Probability of false alarm SNR Signal to noise ratio plicable to the future evolution of our in-house ﬂexible UWB hardware platform [?], [?]. This platform can be used for joint NEpp NEnuemrgbyerooffthUeWUBWpBulpsueslseussed in detection ranging and communication applications. The platform has a s(t) Shape of the UWB pulses digital processing section comprising of an FPGA, where the proposed techniques of this paper can be implemented. Even and amplitude detector for multi-pulse IR-UWB signal. In though the applicability of the techniques are demonstrated in Section ??, we will evaluate the performance of the different simulation, the results provide an early insight in to achievable fusion strategies. Finally in Section ??, we will discuss the performance. The variant of the proposed structure in Fig. ?? conclusions. for hypotheses testing are also employed in [?] and [?]. In [?], the authors discuss the UWB hypothesis testing for a bank of II. SYSTEM MODEL similar analog detectors, where as in [?], authors proposes a We consider a binary hypothesis for detection, with H 0 distributed fusion of results from multiple UWB sensors, by representing signal is absent and H representing signal is 1 allocating the different number of pulses to each sensor, under present. Each of the different types of detectors like MF, ED, the constraint of maximum number of allocated pulses, such etc., in the UWB transceiver constructs a test statistic from that the error is minimized. Thus, both are different from the the received samples, based on which inference is made about proposed application of this paper. H or H by comparing the test statistic to some threshold, γ. 0 1 In this paper, we formulate a binary hypothesis problem Different detector types have different ways to construct the of IR-UWB pulse detection, where decisions from different test statistic, and thus have varying degrees of performance like types of detectors are fused using different fusion methods probability of detection, PD, probability of error, Pe, etc. Apart before deciding on the hypothesis as shown in Fig. ??. We from the chosen test statistic, the performance of the particular demonstrate the methods using three commonly employed detector also depends on all or few of the parameters listed in UWB detector-types (L = 3 in Fig. ??), having energy the Table ??. detector (ED), matched ﬁlter (MF), and amplitude detector The transmitted signal under hypothesis H consists of N 1 T (AD) for Detector-1, Detector-2 and Detector-3 respectively. frames, such that The binary decisions signaling the hypothesis from these three N ≥ Ni ∀i ∈ [1, 2, . . . , L], detectors d = [d , d , d ] are fed to the fusion algorithm to T p 1 2 3 arrive at the binary decision regarding the hypothesis, dfused. where, Npi, denotes the number of frames used by Detector-i in The rest of the paper is organized as follows. In Section the hypothesis test. Each frame consists of one IR-UWB pulse, ??, we will discuss the system model. Here, we will deﬁne and during hypothesis H nothing is transmitted (N empty 0 T the signal model which will be used in the rest of the paper. frames). Each UWB pulse is of ﬁxed duration, T, represented Section ??, discusses different fusion strategies. In Section by s(t), sampled at the rate, 1/Ts, and has Ns = T/Ts, sam- ??, we will discuss the analytical expression for PD as a ples. Thus, both hypotheses can be mathematically expressed function of PFA, and SNR for matched ﬁlter, energy detector as ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: P P P P D e D e TABLE II (a) Probability of detection 1 CONFIGURATION OF PARAMETERS FOR DIFFERENT DETECTORS USED IN THE FUSION. 0.8 Detector Type PF−A Np 0.6 Matched Filter 10−7 100 0.4 OR fusion Energy Detector 10 1 1000 AND fusion Amplitude Detector 10−4 100 0.2 Majority-Voting fusion 0 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 (b) Probability of error V. PERFORMANCE EVALUATION OF FUSION METHODS 0.6 OR fusion For counting rule based fusion discussed in Section ??, with AND fusion L = 3, having MF, ED and AD as detectors for “AND”, 0.4 Majority-Voting fusion “OR” and “Majority-Voting” fusion, we should have k = 3, 0.2 k = 1 and k > 2 respectively. We performed Monte-Carlo simulations with similar signal conﬁgurations described in 0 Section ??. We generated 1000 random signals corresponding -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 SNR [dB] to hypotheses, H and H as deﬁned in (??). The probability 1 0 of correct detection of hypothesis, H , when H was indeed Fig. 5. Probability of detection and error performance for various fusion 1 1 signaled, PD, and the probability of mis-classiﬁcation of techniques using the conﬁguration deﬁned in Table ??. hypotheses, Pe, was evaluated using the fusion rules discussed in Section ??. The false alarm, PFA, and number of frames 1 (a) Probability of detection employed, N , for each detector type are taken from Table ??. p 0.8 Results for fused probability of detection, PD, and probability of error, Pe, are as shown in Fig. ??a and Fig. ??b respectively. 0.6 No fusion (ED decision alone) Notice that for a ﬁxed SNR, the probability of detection is high 0.4 OR fusion for the “OR” fusion, however, the probability of error is also 0.2 MAP fusion Majority-Voting fusion high due to the higher false alarm rate. 0 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 The performance is also evaluated using the MAP fusion (b) Probability of error rule (??), for a detector set, (MF, ED, AD), yielding decision 0.6 vector, d (refer to Fig. ??), with the conﬁguration taken from No fusion (ED decision alone) OR fusion Table ??. The probability of detection and probability of error 0.4 Majority-Voting fusion are as shown in Fig. ??a and Fig. ??b, respectively. Notice that MAP fusion the MAP fusion method (deﬁned by (??)) is close to “OR” 0.2 fusion in detection performance, with superior probability 0 of error performance as shown in Fig. ??b. Comparing the -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 SNR [dB] performance of energy detector alone with the MAP fusion rule for multiple detectors in Fig. ??a and Fig. ??b, indicates Fig. 6. Probability of detection and error performance using the fusion rule that a gain of 4 dB in terms of signal to noise ratio (SNR) can deﬁned in (??) (MAP fusion), OR Fusion and ED decision alone without any fusion using the conﬁguration deﬁned in Table ??. be achieved for probability of detection greater than 95% with low probability of error (< 5%). VI. CONCLUSION errors (due to false alarms, refer to Fig. ??b). If the error performance is critical for the UWB application, then MAP In this paper, we analyzed the UWB detection performance fusion formulation gives superior performance in terms of of matched ﬁlter, energy detector and amplitude detector. errors as shown in Fig. ??b. In general, if there are multiple We utilized the performance equations of individual detectors (??), (??) and (??) for analyzing the fusion performance. We detectors available in the UWB transceiver platform, then decision information from these detectors can be concurrently analyzed the performance in terms of detection probability and utilized and intelligently fused based on the application criteria probability of error for different fusion methods like “AND”, “OR” and “Majority-Voting”. This is shown in Fig. ??a to make a more informed decision on the hypothesis. and Fig. ??b. Using the Bayes rule, we derived an optimal REFERENCES fusion rule (??) for UWB detection, which is optimal in the [1] M.Z. Win and R.A. Scholtz, “Impulse radio: how it works,” Communi- probability of error sense and compared its performance. This cations Letters, IEEE, vol. 2, no. 2, pp. 36 –38, feb. 1998. is shown in Fig. ??a and Fig. ??b. [2] “First report and order, revision of part 15 of the commision’s rules regarding ultra-wideband transmission systems,” Tech. Rep., Results indicate that by making a suitable choice of fusion FCC,Washington DC, ET Docket 98-153, 2002. rule, a trade-off between detection and false alarm can be [3] V. Yajnanarayana, S. Dwivedi, A. De Angelis, and P. Ha¨ndel, “Spec- achieved. For example, Fig. ??a, shows that OR fusion is tral efﬁcient IR-UWB communication design for low complexity transceivers,” EURASIP Journal on Wireless Communications and more biased toward detection, however, it also results in higher Networking, vol. 2014, no. 1, pp. 158, 2014. ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: optimal

text: REFERENCES

text: fusion

text: rule

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text: however,

text: it

text: also

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text: in

text: higher

text: Networking,

text: vol.

text: no.

text: pp.

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text: Magnetism in Quasi-One-Dimensional A Cr As (A=K,Rb) superconductors 2 3 3 ∗ Xianxin Wu ,1 Congcong Le,1 Jing Yuan,1 Heng Fan,1,2 and Jiangping Hu1,3,2, 1 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2Collaborative Innovation Center of Quantum Matter, Beijing, China 3Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA (Dated: May 27, 2020) We predict that the recently discovered quasi-one dimensional superconductors, A Cr As (A=K,Rb), pos- 2 3 3 sess strong frustrated magnetic ﬂuctuations and are nearby a novel in-out co-planar magnetic ground state. The frustrated magnetism is very sensitive to c-axis lattice constant and can thus be suppressed by increasing pres- sure. Our results qualitatively explain strong non-Fermi liquid behaviors observed in the normal state of the superconductors as the intertwining between the magnetism and superconductivity can create a large quantum critical region in quasi-one dimensional systems and also suggest that the materials share similar phase diagrams and superconducting mechanism with other unconventional superconductors, such as cuprates and iron-based superconductors. PACS numbers: 74.70.-b, 74.25.Ha, 74.20.Pq, 74.20.Rp One of major challenges in condensed matter physics is to ical representative of Q1D unconventional superconductors understand the role of electron-electron correlation in uncon- where the superconductivity emerges in a vicinity to a novel ventional superconductors. The effect of electron-electron in- magnetically ordered state. We predict that the materials are teraction becomes more important as the dimension of a sys- characterized by strong frustrated magnetic ﬂuctuations and tem is lowered. Indeed, many unconventional superconduc- are nearby a novel in-out co-planar(IOP) magnetic ground tors discovered in the past are quasi-two dimensional(Q2D) state. The magnetism can be described by a minimum effec- electron systems. The superconductivity in these unconven- tive model with three magnetic exchange parameters: the anti- (cid:48) tional superconductors appears in a vicinity to a magneti- ferromagnetic J and J between two nearest-neighbor (NN) 1 1 cally ordered state. Magnetic ﬂuctuations which are caused Cr atoms and the ferromagnetic J between two next NN Cr 2 by electron-electron interaction have been widely considered atoms along c-axis. The frustrated magnetism is very sensi- to be responsible for superconductivity and many non-Fermi tive to c-axis lattice constant and can thus be suppressed by in- liquid behaviors in normal states. creasing pressure. The results suggest that the materials host a typical phase diagram similar to those of the Q2D unconven- While there are many representatives of Q2D unconven- tional superconductors, such as cuprates[10] and iron-based tional superconductors, it has been difﬁcult to ﬁnd one superconductors[11]. The new materials can be ideal systems in quasi-one dimensional(Q1D) systems even if the effect to study the intimate relations between magnetism and super- of the electron-electron correlation is expected to be en- conductivity since a Q1D model can be solved theoretically hanced further. The Q1D superconductors discovered pre- with high controllability. viously, including Bechgaard salts[1, 2] , Tl Mo Se [3] and 2 6 6 Li Mo O [4–7], are not attributed to 3d-orbital electrons 0.9 6 17 It is known that calculations based on the Density Func- which can exhibt strong electron-electron interaction. tional Theory (DFT) can successfully identify the possible Very recently, two novel Q1D materials K Cr As [8] and magnetic ground state in some correlated electron systems. 2 3 3 Rb Cr As [9] have been synthesized and found to be super- Typical examples are the iron-based superconductors where 2 3 3 conducting below the transition temperature 6.1 K and 4.8 K theoretical calculations consistently agree well with experi- respectively. The structure of A Cr As (A=K,Rb) is charac- mental measurements[12–18] even if the magnetic origin is 2 3 3 terized by one-dimensional (Cr As ) chains (Fig.1(a)), which still debatable[19]. Here, we deploy similar DFT calculations. 3 3 contain Cr distorted octahedral clusters. The alkali metal Our DFT calculations employ the projector augmented wave 6 ions are intercalated between the (Cr As ) chains. Both new (PAW) method encoded in Vienna ab initio simulation pack- 3 3 materials show strong non-fermi liquid behaviors in normal age(VASP) [20–22], and generalized-gradient approximation states, as well as unconventional superconducting properties (GGA)[23] for the exchange correlation functional is used. in superconducting (SC) states. Moreover, just like cuprates Throughout this work, the cutoff energy of 450 eV is taken and iron-based superconductors, the electronic physics in for expanding the wave functions into plane-wave basis. The × × these new materials are likely attributed to 3d-oribtals of Cr number of these k points are 6 6 13 for K Cr As and 2 3 3 atoms. Therefore the material may exhibit strong magnetism Rb Cr As [24]. The GGA plus on-site repulsion U method 2 3 3 and electron-electron interaction. (GGA+U) in the formulation of Dudarev et al.[25] is em- In this paper, we show that the new materials can be a crit- ployed to describe the electron correlation effect associated with the Cr 3d states by an effective parameter U . The val- eff ues of U=2.3 eV and J=0.96 eV on Cr are adopted for our GGA+U calculations[26]. We relax the lattice constants and ∗Electronic address: jphu@iphy.ac.cn internal atomic positions, where the plane wave cutoff energy ##LTLine##

text: Magnetism

label: title

text: in

text: Quasi-One-Dimensional

text: A

text: Cr

text: As

text: (A=K,Rb)

text: superconductors

text: Xianxin

label: author

text: Wu

text: Congcong

text: Jing

text: Heng

text: and

text: Jiangping

text: Institute

text: of

text: Physics,

text: Chinese

text: Academy

text: of

text: Sciences,

text: Beijing

text: China

text: Innovation

text: Center

text: of

text: Quantum

text: Matter,

text: Beijing,

text: China

text: of

text: Physics,

text: Purdue

text: University,

text: West

text: Lafayette,

text: Indiana

text: USA

text: (Dated:

text: May

label: date

text: We

label: abstract

text: predict

text: that

text: the

text: recently

text: discovered

text: quasi-one

text: dimensional

text: superconductors,

text: A

text: Cr

text: As

text: (A=K,Rb),

text: pos-

text: sess

text: strong

text: frustrated

text: magnetic

text: ﬂuctuations

text: and

text: are

text: nearby

text: a

text: novel

text: in-out

text: co-planar

text: magnetic

text: ground

text: state.

text: The

text: frustrated

text: magnetism

text: is

text: very

text: sensitive

text: to

text: c-axis

text: lattice

text: constant

text: and

text: can

text: thus

text: be

text: suppressed

text: by

text: increasing

text: pres-

text: sure.

text: Our

text: results

text: qualitatively

text: explain

text: strong

text: non-Fermi

text: liquid

text: behaviors

text: observed

text: in

text: the

text: normal

text: state

text: of

text: the

text: superconductors

text: as

text: the

text: intertwining

text: between

text: the

text: magnetism

text: and

text: superconductivity

text: can

text: create

text: a

text: large

text: quantum

text: critical

text: region

text: in

text: quasi-one

text: dimensional

text: systems

text: and

text: also

text: suggest

text: that

text: the

text: materials

text: share

text: similar

text: phase

text: diagrams

text: and

text: superconducting

text: mechanism

text: with

text: other

text: unconventional

text: superconductors,

text: such

text: as

text: cuprates

text: and

text: iron-based

text: superconductors.

text: PACS

text: numbers:

text: One

text: of

text: major

text: challenges

text: in

text: condensed

text: matter

text: physics

text: is

text: to

text: ical

text: representative

text: of

text: unconventional

text: superconductors

text: understand

text: the

text: role

text: of

text: electron-electron

text: correlation

text: in

text: uncon-

text: where

text: the

text: superconductivity

text: emerges

text: in

text: a

text: vicinity

text: to

text: a

text: novel

text: ventional

text: superconductors.

text: The

text: effect

text: of

text: electron-electron

text: in-

text: magnetically

text: ordered

text: state.

text: We

text: predict

text: that

text: the

text: materials

text: are

text: teraction

text: becomes

text: more

text: important

text: as

text: the

text: dimension

text: of

text: a

text: sys-

text: characterized

text: by

text: strong

text: frustrated

text: magnetic

text: ﬂuctuations

text: and

text: tem

text: is

text: lowered.

text: Indeed,

text: many

text: unconventional

text: superconduc-

text: are

text: nearby

text: a

text: novel

text: in-out

text: co-planar(IOP)

text: magnetic

text: ground

text: tors

text: discovered

text: in

text: the

text: past

text: are

text: quasi-two

text: state.

text: The

text: magnetism

text: can

text: be

text: described

text: by

text: a

text: minimum

text: effec-

text: electron

text: systems.

text: The

text: superconductivity

text: in

text: these

text: unconven-

text: tive

text: model

text: with

text: three

text: magnetic

text: exchange

text: parameters:

text: the

text: anti-

text: tional

text: superconductors

text: appears

text: in

text: a

text: vicinity

text: to

text: a

text: magneti-

text: ferromagnetic

text: J

text: and

text: J

text: between

text: two

text: nearest-neighbor

text: (NN)

text: cally

text: ordered

text: state.

text: Magnetic

text: ﬂuctuations

text: which

text: are

text: caused

text: Cr

text: atoms

text: and

text: the

text: ferromagnetic

text: J

text: between

text: two

text: next

text: NN

text: Cr

text: by

text: electron-electron

text: interaction

text: have

text: been

text: widely

text: considered

text: atoms

text: along

text: c-axis.

text: The

text: frustrated

text: magnetism

text: is

text: very

text: sensi-

text: to

text: be

text: responsible

text: for

text: superconductivity

text: and

text: many

text: non-Fermi

text: tive

text: to

text: c-axis

text: lattice

text: constant

text: and

text: can

text: thus

text: be

text: suppressed

text: by

text: in-

text: liquid

text: behaviors

text: in

text: normal

text: states.

text: creasing

text: pressure.

text: The

text: results

text: suggest

text: that

text: the

text: materials

text: host

text: a

text: typical

text: phase

text: diagram

text: similar

text: to

text: those

text: of

text: the

text: unconven-

text: While

text: there

text: are

text: many

text: representatives

text: of

text: unconven-

text: tional

text: superconductors,

text: such

text: as

text: and

text: iron-based

text: tional

text: superconductors,

text: it

text: has

text: been

text: difﬁcult

text: to

text: ﬁnd

text: one

text: The

text: new

text: materials

text: can

text: be

text: ideal

text: systems

text: in

text: quasi-one

text: systems

text: even

text: if

text: the

text: effect

text: to

text: study

text: the

text: intimate

text: relations

text: between

text: magnetism

text: and

text: super-

text: of

text: the

text: electron-electron

text: correlation

text: is

text: expected

text: to

text: be

text: en-

text: conductivity

text: since

text: a

text: model

text: can

text: be

text: solved

text: theoretically

text: hanced

text: further.

text: The

text: superconductors

text: discovered

text: pre-

text: with

text: high

text: controllability.

text: viously,

text: including

text: Bechgaard

text: Tl

text: Mo

text: Se

text: and

text: Li

text: Mo

text: O

text: are

text: not

text: attributed

text: to

text: electrons

text: It

text: is

text: known

text: that

text: calculations

text: based

text: on

text: the

text: Density

text: Func-

text: which

text: can

text: exhibt

text: strong

text: electron-electron

text: interaction.

text: tional

text: Theory

text: (DFT)

text: can

text: successfully

text: identify

text: the

text: possible

text: Very

text: recently,

text: two

text: novel

text: materials

text: K

text: Cr

text: As

text: and

text: magnetic

text: ground

text: state

text: in

text: some

text: correlated

text: electron

text: systems.

text: Rb

text: Cr

text: As

text: have

text: been

text: synthesized

text: and

text: found

text: to

text: be

text: super-

text: Typical

text: examples

text: are

text: the

text: iron-based

text: superconductors

text: where

text: conducting

text: below

text: the

text: transition

text: temperature

text: K

text: and

text: K

text: theoretical

text: calculations

text: consistently

text: agree

text: well

text: with

text: experi-

text: respectively.

text: The

text: structure

text: of

text: A

text: Cr

text: As

text: (A=K,Rb)

text: is

text: charac-

text: mental

text: even

text: if

text: the

text: magnetic

text: origin

text: is

text: terized

text: by

text: one-dimensional

text: (Cr

text: As

text: chains

text: which

text: still

text: Here,

text: we

text: deploy

text: similar

text: DFT

text: calculations.

text: contain

text: Cr

text: distorted

text: octahedral

text: clusters.

text: The

text: alkali

text: metal

text: Our

text: DFT

text: calculations

text: employ

text: the

text: projector

text: augmented

text: wave

text: ions

text: are

text: intercalated

text: between

text: the

text: (Cr

text: As

text: chains.

text: Both

text: new

text: (PAW)

text: method

text: encoded

text: in

text: Vienna

text: ab

text: initio

text: simulation

text: pack-

text: materials

text: show

text: strong

text: non-fermi

text: liquid

text: behaviors

text: in

text: normal

text: age(VASP)

text: and

text: generalized-gradient

text: approximation

text: states,

text: as

text: well

text: as

text: unconventional

text: superconducting

text: properties

text: for

text: the

text: exchange

text: correlation

text: functional

text: is

text: used.

text: in

text: superconducting

text: (SC)

text: states.

text: Moreover,

text: just

text: like

text: cuprates

text: Throughout

text: this

text: work,

text: the

text: cutoff

text: energy

text: of

text: eV

text: is

text: taken

text: and

text: iron-based

text: superconductors,

text: the

text: electronic

text: physics

text: in

text: for

text: expanding

text: the

text: wave

text: functions

text: into

text: plane-wave

text: basis.

text: The

text: these

text: new

text: materials

text: are

text: likely

text: attributed

text: to

text: of

text: Cr

text: number

text: of

text: these

text: k

text: points

text: are

text: for

text: K

text: Cr

text: As

text: and

text: atoms.

text: Therefore

text: the

text: material

text: may

text: exhibit

text: strong

text: magnetism

text: Rb

text: Cr

text: As

text: The

text: GGA

text: plus

text: on-site

text: repulsion

text: U

text: method

text: and

text: electron-electron

text: interaction.

text: (GGA+U)

text: in

text: the

text: formulation

text: of

text: Dudarev

text: et

text: is

text: em-

text: In

text: this

text: paper,

text: we

text: show

text: that

text: the

text: new

text: materials

text: can

text: be

text: a

text: crit-

text: ployed

text: to

text: describe

text: the

text: electron

text: correlation

text: effect

text: associated

text: with

text: the

text: Cr

text: states

text: by

text: an

text: effective

text: parameter

text: U

text: The

text: val-

text: eff

text: ues

text: of

text: eV

text: and

text: eV

text: on

text: Cr

text: are

text: adopted

text: for

text: our

text: GGA+U

text: We

text: relax

text: the

text: lattice

text: constants

text: and

text: ∗Electronic

text: address:

text: jphu@iphy.ac.cn

text: internal

text: atomic

text: positions,

text: where

text: the

text: plane

text: wave

text: cutoff

text: energy

text: ##LTLine##