Superconductivity, superfluidity and quantum geometry in twisted multilayer systems

Törmä, Païvi; Peotta, Sebastiano; Bernevig, B. Andrei

doi:10.1038/s42254-022-00466-y

Cited by 145 publications

(57 citation statements)

References 153 publications

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“…This is the case regardless of the diverse microscopic details characterizing these substances, such as crystal symmetry and structure defects. The explanation of this finding rests on the fact that the fermion condensation most readily occurs in substances hosting flat bands, see, e.g., [1,[5][6][7][8][9][10][11][12]. Experimental manifestations of the fermion condensation phenomena are varied, implying that different experimental techniques are most suitable for detecting and analyzing them.…”

Section: Discussionmentioning

confidence: 99%

“…Shown that the transition temperature T c is proportional to the Fermi velocity V F , V F ∝ T c , rather than N s (0) ∝ 1/V F ∝ T c ; Demonstrated that flat bands make T c ∝ g, with g being the coupling constant. It is of crucial importance to note that the flat band superconductivity has already been observed in twisted bilayer graphene, where due to the flat band, the transition temperature T c highly exceeds the limit dictated by the conventional BCS theory [5][6][7][8][9][10][11][12]. Thus, the basic task now is to attract more experimental groups to search for the room-T c superconductivity in graphite and other perspective materials.…”

Section: Discussionmentioning

confidence: 99%

“…As a result, M * N becomes a function of the only variable T N ∝ T/B, as seen from Figure 3b. In the vicinity of the FCQPT, the normalized effective mass M * N (T N ) can be well approximated by a certain universal function [15,19], interpolating the solutions of Equation ( 3) between the LFL state, given by Equation (11), and the NFL one, given by Equation (10) [15]…”

Section: Internal Variables Revealing the Scaling Behaviormentioning

confidence: 99%

“…Strongly correlated Fermi systems such as heavy-fermion metals, graphene, and high-T c superconductors exhibit the non-Fermi-liquid (NFL) behavior. Theoretical predictions [1][2][3][4] and experimental data collected on many of these systems show that at low temperatures a portion of their excitation spectrum becomes approximately dispersionless, giving rise to so-called flat bands and high-T c superconductivity, see, e.g., [1,[5][6][7][8][9][10][11][12]. The emergence of flat bands at low T indicates that the system is close to a special quantum critical point, namely a topological fermion condensation quantum phase transition (FCQPT), leading to the formation of flat bands dubbed the fermion condensation (FC).…”

Section: Introductionmentioning

confidence: 99%

“…This fact, see Equation (2), leads to creating high-T c superconductors [1,[5][6][7][8][9][10][11][12]. This observation is supported by special features of high-T c superconductivity based on flat bands, namely that T c is proportional to the Fermi velocity V F ∝ 1/N s (0) V F ∝ T c , rather than N s (0) ∝ 1/V F ∝ T c as stated in standard BCS-like theories [13,16] as predicted [17].…”

Section: Introductionmentioning

confidence: 99%

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Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

Shaginyan

Msezane

Japaridze

2022

Atoms

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This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Internal Variables Revealing the Scaling Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

Shaginyan

Msezane

Japaridze

2022

Atoms

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Implementation and Characterization of the Dice Lattice in the Electron Quantum Simulator

Tassi,

Bercioux

2024

Advanced Physics Research

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Materials featuring touching points, localized states, and flat bands are of great interest in condensed matter and artificial systems due to their implications in topology, quantum geometry, superconductivity, and interactions. In this theoretical study, the experimental realization of the dice lattice with adjustable parameters is proposed by arranging carbon monoxide molecules on a two‐dimensional (2D) electron system at a (111) copper surface. First, a theoretical framework is developed to obtain the spectral properties within a nearly free electron approximation and then compare them with tight‐binding calculations. This investigation reveals that the high mobility of Shockley state electrons enables an accurate theoretical description of the artificial lattice using a next‐nearest‐neighbor tight‐binding model, resulting in the emergence of a touching point, a quasi‐flat band, and localized lattice site behavior in the local density of states. Additionally, theoretical results for a long‐wavelength low‐energy model that accounts for next‐nearest‐neighbor hopping terms are presented. Furthermore, the model's behavior under an external magnetic field is theoretically examined by employing Peierl's substitution, a commonly used technique in theoretical physics to incorporate magnetic fields into lattice models. The theoretical findings suggest that, owing to the exceptional electron mobility, the highly degenerate eigenenergy associated with the Aharonov‐Bohm caging mechanism may not manifest in the proposed experiment.

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Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Martínez‐Strasser,

Herrera,

García‐Etxarri

et al. 2023

Adv Quantum Tech

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The spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems.

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Superconductivity, superfluidity and quantum geometry in twisted multilayer systems

Cited by 145 publications

References 153 publications

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

Implementation and Characterization of the Dice Lattice in the Electron Quantum Simulator

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

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