Abstract For the first time, basing both on experimental facts and our theoretical consideration, we show that Fermi systems with flat bands should be tuned with the superconducting state. Experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity V F as a function of the temperature T c of superconduction phase transition have revealed , where N s (0) is the density of states at the Fermi level. We show that the high- T c compounds exhibit the same behavior. Such observation is a challenge to theories of high- T c superconductivity, since V F is negatively correlated with T c , for . We show that the theoretical idea of forming flat bands in strongly correlated Fermi systems can explain this behavior and other experimental data collected on both and twisted bilayer graphene. Our findings place stringent constraints on theories describing the nature of high- T c superconductivity and the deformation of flat band by the superconducting phase transition.
Abstract For the first time, basing both on experimental facts and our theoretical consideration, we show that Fermi systems with flat bands should be tuned with the superconducting state. Experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity V F as a function of the temperature T c of superconduction phase transition have revealed , where N s (0) is the density of states at the Fermi level. We show that the high- T c compounds exhibit the same behavior. Such observation is a challenge to theories of high- T c superconductivity, since V F is negatively correlated with T c , for . We show that the theoretical idea of forming flat bands in strongly correlated Fermi systems can explain this behavior and other experimental data collected on both and twisted bilayer graphene. Our findings place stringent constraints on theories describing the nature of high- T c superconductivity and the deformation of flat band by the superconducting phase transition.
Abstract The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence of resistivity in a large number of strongly correlated Fermi systems as well as normal metals. We show that the observed scattering rate is explained by the emergence of flat bands, while the so-called Planckian limit occurs accidentally since the normal metals exhibit the same scattering rate behavior. We also analyze recent challenging experimental data on tunneling differential conductivity collected under the application of magnetic field on the twisted graphene and the archetypical heavy fermion metal YbRh 2 Si 2 . Also we describe recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that these observations support the fermion condensation theory. Our theoretical results are in good agreement with corps of different and seemingly unrelated experimental facts. They show that the fermion-condensation quantum phase transition is an intrinsic property of strongly correlated Fermi systems and can be viewed as the universal agent explaining their core physics.
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.
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.
Abstract Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high- T c superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal ( T ) and particle-hole ( C ) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity d I /d V , where I is the current and V the bias voltage, is a symmetric function of V . Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn 5 and YbRh 2 Si 2 . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition . An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T - and C -invariance, with the differential conductivity again becoming a symmetric function of V . This behavior has been observed in recent measurements of tunneling conductivity in both YbRh 2 Si 2 and graphene. Also within the FC framework, we describe and explain recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that the observed scaling is explained by the emergence of flat bands formed by fermion condensation.
In this thesis, superconductivity of fermions in two-dimensional Hubbard lattice models is theoretically studied. Each of the studied lattice structures features intriguing properties that provide valuable insight to understand superconductivity in general. While real condensed matter systems are too complicated to tackle with theoretical tools, the Hubbard model is one of the simplest quantum many-body models to possess a wide spectrum of physically relevant phenomena, from superconductivity to magnetism and topological order. Hubbard models are also interesting as they can be experimentally realized and accurately controlled by utilizing ultracold gases.
The first part of the thesis explains the required theoretical background of superconductivity in the level of mean-field and linear response theories. Specifically, we primarily focus on the superfluid weight which implies the existence of the Meissner effect and dissipationless current, defining properties of superconductors. We further discuss how the Berezinskii-Kosterlitz-Thouless (BKT) transition, related to the loss of superconductivity due to the thermal fluctuations of the superconducting order parameter in high enough temperatures, can be accessed via the superfluid weight.
In the second part, the main results are discussed. We show how the superconductivity of lattice models featuring dispersionless Bloch bands, so-called flat bands, can be large and originating from the quantum geometric properties of the Bloch states of the flat bands. This is in contrast to conventional dispersive bands where superconductivity is determined by the effective mass of the particles, i.e. by the dispersion relation of the Bloch bands alone and not by the Bloch states. This is well demonstrated in the Lieb lattice geometry, studied in Publication I, which features both a strictly flat and two dispersive Bloch bands, allowing direct comparison of superconductivity in dispersive and flat bands. We show how the superconductivity of the flat band is more robust than that of the dispersive bands and how the superfluid weight behaves non-monotonically as a function of the interaction strength. This non-monotonic behavior should be experimentally accessible. Flat band superconductivity is also the topic of Publication III, where the experimentally realized twisted bilayer graphene (TBG) is studied with local and non-local attractive interactions. We predict qualitative differences between local and non-local interaction schemes which could be distinguished experimentally and reveal the quantum geometric origin of superconductivity in TBG systems in case of both the assumed interaction schemes.
Exotic Fulde-Ferrell (FF) superfluid phases, characterized by the non-zero momentum of Cooper pairs, were explored in Publication II. We show how the FF phases can be stabilized against thermal fluctuations in the presence of spin-orbit coupling (SOC) and that topologically non-trivial FF states, created with SOC and Zeeman fields, can be found at finite temperatures.; Tassa…
We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.