Model of phase fluctuations in a lattice<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave superconductor: Application to the Cooper-pair charge-density wave in underdoped cuprates

Melikyan, Ashot; Tešanović, Zlatko

doi:10.1103/physrevb.71.214511

Cited by 54 publications

(45 citation statements)

References 45 publications

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“…This implies that, as x falls below x c at low T and in zero field, superconductivity is destroyed by the spontaneous appearance of free (anti) vortices engendered by increased charge localization and strong phase fluctuation 3,4,6 . In zero field, superconductivity first transforms to a vortex-liquid state with strong phase disordering.…”

Section: Of the Orbital Term χ Orb (T )Hmentioning

confidence: 99%

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Low-temperature vortex liquid in La2−xSrxCuO4

Checkelsky

Komiya

et al. 2007

Nature Phys

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In copper oxide superconductors, the lightly doped (small dopant concentration, x) region is of major interest 1,2 because superconductivity, antiferromagnetism and the pseudogap state come together near a critical doping value, x c . But the way in which superconductivity is destroyed as x is decreased at very low temperatures, T , is not clear [3][4][5][6][7] . Does the pair condensate vanish abruptly at a critical value, x c ? Or is phase coherence of the condensate destroyed by spontaneous vortices-as is the case at elevated T (refs 8-10)? So far, magnetization data at low T are very sparse in this region of the phase diagram. Here, we report torque magnetometry measurements on La 2−x Sr x CuO 4 , which show that, in zero magnetic field, quantum phase fluctuations destroy superconductivity at x c ≈ 0.055. The phase-disordered condensate survives to x = 0.03. In finite field H, the vortex solidto-liquid transition occurs at H lower than the depairing field, H c2 . The resulting phase diagram reveals the large fraction of the x-H plane occupied by the quantum vortex liquid.In underdoped La 2−x Sr x CuO 4 (LSCO), the magnetic susceptibility is dominated by the Curie-like spin susceptibility and the van Vleck orbital susceptibility [11][12][13] . These strongly T-dependent terms render weak diamagnetic signals difficult to detect using standard magnetometry. However, because the spin susceptibility is nearly isotropic 13 whereas the incipient diamagnetism is anisotropic, torque magnetometry has proved to be effective in resolving the diamagnetic signal [14][15][16][17] (the resistivity anisotropy is 6,000-8,000 below 40 K, so the supercurrent is predominantly in-plane; see Supplementary Information). With H tilted at a slight angle, φ, to the crystal c axis, the torque, τ, may be expressed as an effective magnetization, M obs ≡ τ/μ 0 H x V , where V is the sample volume, μ 0 is the permeability and H x = H sin φ (we take z c). In cuprates, M obs comprises three terms 14,15M s is the anisotropy of the spin local moments and χ orb is the anisotropy of the van Vleck orbital susceptibility (see the Supplementary Information).We label the seven samples studied as 03 (with = 0.030), 04 (0.040), 05 (0.050), 055 (0.055), 06 (0.060), 07 (0.070) and 09 (0.090). To start, we confirmed that, above ∼25 K, M obs derived from the torque experiment in sample 03 is in good, quantitative agreement with the anisotropy inferred from previous bulk susceptibility measurements 13 on a large crystal of LSCO (x = 0.03) (see the Supplementary Information). In Fig. 1b, the evolution is similar, except that the larger diamagnetism forces M obs to negative values at low H. As mentioned, the spin contribution, M s , is unresolved above ∼40 K in both panels. To magnify the diamagnetic signal, we subtract the orbital term, χ orb H (the three terms are also apparent in the total observed susceptibility χ obs = M obs /H; see the Supplementary Information).The resulting curves, M obs (T , H ) ≡ M obs − χ orb H, are shown for sample 05 in Fig. 1c...

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Section: Of the Orbital Term χ Orb (T )Hmentioning

confidence: 99%

“…But the way in which superconductivity is destroyed as x is decreased at very low temperatures, T , is not clear [3][4][5][6][7] . Does the pair condensate vanish abruptly at a critical value, x c ?…”

mentioning

confidence: 99%

Low-temperature vortex liquid in La2−xSrxCuO4

Checkelsky

Komiya

et al. 2007

Nature Phys

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“…In this region, a variety of spin-density [25,43,45,46,49,[83][84][85], charge-density [25,[86][87][88], pair-density wave [88][89][90][91], and stripe orders [30,32,51,52,85,[92][93][94][95] have been posited in both the Hubbard model and the simpler t-J model, with different types of orders seen in different simulation methods. These inhomogeneous phases are proposed to be relevant in the pseudogap physics [89,90,[96][97][98][99][100].…”

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confidence: 99%

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

2016

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We compute the ground-state phase diagram of the Hubbard and frustrated Hubbard models on the square lattice with density matrix embedding theory using clusters of up to 16 sites. We provide an error model to estimate the reliability of the computations and complexity of the physics at different points in the diagram. We find superconductivity in the ground state as well as competition between inhomogeneous charge, spin, and pairing states at low doping. The estimated errors in the study are below T c in the cuprates and on the scale of contributions in real materials that are neglected in the Hubbard model. DOI: 10.1103/PhysRevB.93.035126 The Hubbard model [1][2][3] is one of the simplest quantum lattice models of correlated electron materials. Its one-band realization on the square lattice plays a central role in understanding the essential physics of high-temperature superconductivity [4,5]. Rigorous, near-exact results are available in certain limits [6]: at high temperatures from series expansions [7][8][9][10], in infinite dimensions from converged dynamical mean-field theory [11][12][13][14], and at weak coupling from perturbation theory [15] and renormalization group analysis [16,17]. Further, at half filling, the model has no fermion sign problem, and unbiased determinantal quantum Monte Carlo simulations can be converged [18]. Away from these limits, however, approximations are necessary. Many numerical methods have been applied to the model at both finite and zero temperatures, including fixed-node, constrained path, determinantal, and variational quantum Monte Carlo (QMC) [19][20][21][22][23][24][25][26][27][28][29], density matrix renormalization group (DMRG) [30][31][32], dynamical cluster (DCA) [33,34], (cluster) dynamical mean-field theories (CDMFT) [35,36], and variational cluster approximations (VCA) [37,38]. (We refer to DCA/CDMFT/VCA collectively as Green's function cluster theories.) These pioneering works have suggested rich phenomenology in the phase diagram including metallic, antiferromagnetic, and d-wave (and other kinds of) superconducting phases, a pseudogap regime, inhomogeneous orders such as stripes, and charge, spin, and pairdensity waves, as well as phase separation [6,19,20,24,25,[27][28][29]32,35,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. However, as different numerical methods have yielded different pictures of the ground-state phase diagram, a precise quantitative picture of the ground-state phase diagram has yet to emerge.It is the goal of this paper to produce such a quantitative picture as best as possible across the full Hubbard model phase diagram below U = 8. Our method of choice is density matrix embedding theory (DMET), which is very accurate in this regime [59][60][61][62][63][64][65][66], employed together with clusters of up to 16 sites and thermodynamic extrapolation. We carefully calibrate errors in our calculations, giving error bars to quantify the remaining uncertainty in our phase diagram. These error bars also serve,...

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“…45 In addition, there have been theoretical studies of the SC quantum phase fluctuations using the QED 3 effective theory of the HTS in relation with the inhomogeneous pattern formation in cuprates from the STM experimental results. 46,47 While DMRG treatments 24 provide detailed information on the real space charge, spin, and pairing orders, the precise nature of the interplay, and whether the dif-ferent orders compete or cooperate, remains unclear. In addition, the enhancement of the superconducting transition temperature T c by local inhomogeneity has been demonstrated by Martin et al in Ref.…”

Section: 20mentioning

confidence: 99%

s-wave superconductivity phase diagram in the inhomogeneous two-dimensional attractive Hubbard model

et al. 2007

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We study s-wave superconductivity in the two-dimensional square lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction Ui between the electrons takes on two values, Ui = 0 and −U/(1 − f ) (with f the concentration of non-interacting sites) as a function of average electron occupation per site n, and study the evolution of the phase diagram as f varies. In certain regions of the phase diagram, inhomogeneity results in a larger zero temperature average pairing amplitude (order parameter) and also a higher superconducting (SC) critical temperature Tc, relative to a uniform system with the same mean interaction strength (Ui = −U on all sites). These effects are observed for stripes, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. The phase diagrams also include regions where superconductivity is obliterated due to the formation of various charge ordered phases. The enhancement of Tc due to inhomogeneity is robust as long as the electron doping per site n is less than twice the fraction of interacting sites [2(1 − f )] regardless of the pattern. We also show that for certain inhomogeneous patterns, when n = 2(1 − f ), increasing temperature can work against the stability of existing charge ordered phases for large f and as a result, enhance Tc. PACS numbers:I. MOTIVATION Fascination with inhomogeneous superconducting (SC) phases extends back several decades, with many conferences and monographs having been devoted to the subject.1,2,3 For conventional superconductors, the inhomogeneities were extrinsic, arising from a granular nature of samples or due to the deliberate synthesis of disordered built materials or films. The high temperature superconductors (HTS) introduced new aspects into this area of study. First, inhomogeneous states (normal and SC) seem to be intrinsic to HTS, at least in the underdoped regime, similar to quenched disorder in the metalinsulator transition in two dimensions.4,5 Secondly, the inhomogeneity occurs on a smaller length scale of just a few lattice constants as evidenced by scanning tunneling spectroscopy (STS) at the nanoscale. 6,7,8,9 In addition, the strong electronic correlation in HTS cuprates plays a major role in the elucidation of the inhomogeneous SC state; indeed the inhomogeneity is widely believed to arise from the strong intra-atomic interactions that tend to frustrate bandlike conduction, to induce local magnetic moments, and to drive charge and spin order on a few lattice constant scale. The study of the doped Mott insulating phase has been one of the most active areas of theoretical study of HTS, one that has proven to be unexpectedly complex and rich and which is still under intense exploration and debate. Surprisingly, holes doped into the high temperature superconductors tend to arrange themse...

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Model of phase fluctuations in a latticed-wave superconductor: Application to the Cooper-pair charge-density wave in underdoped cuprates

Cited by 54 publications

References 45 publications

Low-temperature vortex liquid in La2−xSrxCuO4

Low-temperature vortex liquid in La2−xSrxCuO4

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

s-wave superconductivity phase diagram in the inhomogeneous two-dimensional attractive Hubbard model

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