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arXiv:2401.02990

Quantum Geometry, Anomalous Scaling, and Strong Pseudogap Superfluidity in a Flat-Band Lieb Lattice

Lin Sun, Hao Deng, Yuxuan Wu, Chuping Li, Junru Wu, Kaichao Zhang, Pengyi Chen, Yuan, Dingli, Qijin Chen

Published Jan 3, 2024• 0 citations
arXivHTMLPDF

Abstract

Flat-band systems such as magic-angle twisted bilayer graphene host strong-correlation superconductivity at vanishingly weak coupling, yet how quantum geometry and pairing fluctuations conspire to drive this phenomenon remains an open question. We investigate finite-temperature superfluidity in a quasi-two-dimensional Lieb lattice using a pairing fluctuation theory with a band-uniform attractive interaction $g<0$ that isolates the intrinsic quantum geometric contributions. Quantum geometry significantly amplifies superfluidity; the geometric pair hopping integral surpasses its conventional counterpart, and the geometric superfluid density becomes the dominant in-plane transport component. When the Fermi level enters the flat band, the BCS paradigm breaks down entirely; the pairing gap and $T_\text{c}$ shift from exponential to anomalous power-law scaling $Δ, T_\text{c} \propto |g|^ν$ ($ν>1$), and the superfluid density inherits an unconventional power-law temperature dependence at low temperatures. In the 2D limit ($t_z=0$), the pseudogap at $T_\text{c}$ nearly saturates the zero-temperature gap even at $|g|/t=0.001$, placing the system in a strong-pseudogap regime that would otherwise require unitary or BEC-scale interactions. These findings establish a microscopic mechanism for flat-band enhanced superfluidity and offer testable predictions for ultracold atom experiments.

DOI
10.48550/arxiv.2401.02990

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Flat-band systems such as magic-angle twisted bilayer graphene host strong-correlation superconductivity at vanishingly weak coupling, yet how quantum geometry and pairing fluctuations conspire to drive this phenomenon remains an open question. We investigate finite-temperature superfluidity in a quasi-two-dimensional Lieb lattice using a pairing fluctuation theory with a band-uniform attractive interaction g<0g<0g<0 that isolates the intrinsic quantum geometric contributions. Quantum geometry significantly amplifies superfluidity; the geometric pair hopping integral surpasses its conventional counterpart, and the geometric superfluid density becomes the dominant in-plane transport component. When the Fermi level enters the flat band, the BCS paradigm breaks down entirely; the pairing gap and TcT_\text{c}Tc​ shift from exponential to anomalous power-law scaling Δ,Tc∝∣g∣νΔ, T_\text{c} \propto |g|^νΔ,Tc​∝∣g∣ν (ν>1ν>1ν>1), and the superfluid density inherits an unconventional power-law temperature dependence at low temperatures. In the 2D limit (tz=0t_z=0tz​=0), the pseudogap at TcT_\text{c}Tc​ nearly saturates the zero-temperature gap even at ∣g∣/t=0.001|g|/t=0.001∣g∣/t=0.001, placing the system in a strong-pseudogap regime that would otherwise require unitary or BEC-scale interactions. These findings establish a microscopic mechanism for flat-band enhanced superfluidity and offer testable predictions for ultracold atom experiments.
Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
Stacking two layers of graphene with a relative twist angle gives rise to Moir\'e patterns, which can strongly modify electronic behavior and may lead to unconventional superconductivity. A synthetic version of twisted bilayers can be engineered with cold atoms in optical lattices. Here, the bilayer structure is mimicked through coupling between atomic sublevels, and the twist is achieved by a spatial modulation of this coupling. In the present paper, we investigate the superconducting behavior of fermionic atoms in such a synthetic twisted bilayer lattice. Attractive interactions between the atoms are treated on the mean-field level, and the superconducting behavior is analyzed via the self-consistently determined pairing gap. A strong enhancement of the pairing gap is found when a quasi-flat band structure occurs at the Fermi surface, reflecting the prominent role played by the twist on the superconductivity. The tunability of interactions allows for the switching of superconducting correlations from intra (synthetic) layer to inter (synthetic) layer. This includes also the intermediate scenario, in which the competition between inter- and intra-layer coupling completely destroys the superconducting behavior, resulting in re-entrant superconductivity upon tuning of the interactions.
We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless (BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T c superconductors. However, unlike the exponential dependence of T c on the electron–electron interaction strength in the conventional high-T c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T c superconductors.
We use stochastic expansion and exact diagonalization to study magic-angle twisted bilayer graphene (TBG) on a disordered substrate. We show that the substrate-induced strong Coulomb disorder in TBG with the chemical potential at the level of the flat bands drives the system to a network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of TBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates TBG's long-time chaotic dynamics at strong disorder, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder, gapped phases of TBG exhibit exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators (OTOCs). This is the system behavior in correlated insulator and superconducting phases, in agreement with the corresponding Larkin-Ovchinnikov result for correlators. The result suggests a low-temperature transition from the superconducting and correlated insulating phases into the strange metal upon increasing the disorder strength. We propose a finite-temperature phase diagram for Coulomb-disordered TBG and discuss the experimental consequences of the emergent SM phase.
Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance.In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude.We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension.This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry.Our bound is particularly useful for the strongly correlated regime of low-density and narrowband systems, where mean-field theory fails.For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases.Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value.Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.
Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, Tc(U)=c∣U∣T_c(U) = c|U|Tc​(U)=c∣U∣. However, the value of ccc and the full nonlinear Tc(U)T_c(U)Tc​(U) curve---with a maximum at large ∣U∣|U|∣U∣---are known beyond mean-field and quantum geometry estimates only for systems with isolated flat bands. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and BEC (preformed Cooper pair) scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of UUU, leading to a sharp crossover to long-range correlations at a characteristic temperature T∗T_*T∗​, which provides a controlled upper bound on TcT_cTc​. The highest T∗T_*T∗​ occurs when all three bands touch at a single momentum point, potentially corresponding to high TcT_cTc​ values.