scholarly journals Optical spectral weight, phase stiffness, and Tc bounds for trivial and topological flat band superconductors

2021 ◽  
Vol 118 (34) ◽  
pp. e2106744118 ◽  
Author(s):  
Nishchhal Verma ◽  
Tamaghna Hazra ◽  
Mohit Randeria
Keyword(s):  
Quantum Monte Carlo ◽  
Mean Field ◽  
Spectral Weight ◽  
Upper Bounds ◽  
Flat Band ◽  
Wannier Functions ◽  
Flat Bands ◽  
Flux Model ◽  
Lieb Lattice ◽  
Insight Into

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) Tc. We focus on on-site attraction |U| on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight D̃low≤ñ|U|Ω/2 with ñ=minn,2−n , where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for D̃low linear in |U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

scholarly journals Nearest Neighbour Particle-Particle Interaction in Fermionic Quasi One-Dimensional Flat Band Lattices

2020 ◽  
Vol 75 (5) ◽  
pp. 393-402 ◽  
Author(s):  
Simon Tilleke ◽  
Mirko Daumann ◽  
Thomas Dahm
Keyword(s):  
Cold Atoms ◽  
Particle Interaction ◽  
Mean Field ◽  
Finite Size ◽  
Diamond Lattice ◽  
Flat Band ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
Flat Bands ◽  
Triangle Lattice

AbstractIn this paper, we have studied spinless fermions in four specific quasi one-dimensional systems that are known to host flat bands in the noninteracting limit: the triangle lattice, the stub lattice, the diamond lattice, and the diamond lattice with transverse hopping. The influence of the nearest neighbour interaction on the flat bands was investigated. We used exact diagonalization of finite size lattices employing the Lanczos technique and determine the single particle spectral functions of the interacting system. Our results are compared with mean field calculations. In the cases of the triangle lattice and the stub lattice we found that the flat bands become dispersive in the presence of a finite interaction. For the diamond lattice and the diamond lattice with transverse hopping, we demonstrated that the flat bands are robust under the influence of the interaction in certain parameter ranges. Such systems could be realised experimentally with cold atoms in optical lattices.

scholarly journals Towards holographic flat bands

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Nicolás Grandi ◽  
Vladimir Juričić ◽  
Ignacio Salazar Landea ◽  
Rodrigo Soto-Garrido
Keyword(s):  
Chemical Potential ◽  
Condensed Matter ◽  
Anomalous Hall Effect ◽  
Spectral Weight ◽  
Flat Band ◽  
Dirac Fermion ◽  
Holographic Model ◽  
Quantum Phases ◽  
Flat Bands ◽  
Dirac Systems

Abstract Motivated by the phenomenology in the condensed-matter flat-band Dirac systems, we here construct a holographic model that imprints the symmetry breaking pattern of a rather simple Dirac fermion model at zero chemical potential. In the bulk we explicitly include the backreaction to the corresponding Lifshitz geometry and compute the dynamical critical exponent. Most importantly, we find that such a geometry is unstable towards a nematic phase, exhibiting an anomalous Hall effect and featuring a Drude-like shift of its spectral weight. Our findings should motivate further studies of the quantum phases emerging from such holographic models.

scholarly journals Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

2016 ◽  
Vol 117 (4) ◽  
Author(s):  
Aleksi Julku ◽  
Sebastiano Peotta ◽  
Tuomas I. Vanhala ◽  
Dong-Hee Kim ◽  
Päivi Törmä
Keyword(s):  
Flat Band ◽  
Geometric Origin ◽  
Lieb Lattice

scholarly journals Competition between the Soft Gap and the Molecular Kondo Singlets in Flat-band Lattices

2018 ◽  
Vol 28 (4) ◽  
pp. 361 ◽  
Author(s):  
Bo Duong Nguyen ◽  
Son Hong Nguyen ◽  
Tien Minh Tran
Keyword(s):  
Renormalization Group ◽  
Strong Coupling ◽  
Kondo Effect ◽  
Magnetic Impurity ◽  
Local Moment ◽  
Flat Band ◽  
Numerical Renormalization Group ◽  
Kondo Problem ◽  
Conduction Electrons ◽  
Lieb Lattice

The Kondo problem of a magnetic impurity embedded in the Lieb lattice is studied by the numerical renormalization group. The magnetic impurity hybridizes with conduction electrons from both the flat- and the soft-gap bands. We find a competition between the soft gap and the molecular Kondo singlet formations. The molecular Kondo effect occurs only when the magnetic impurity strongly hybridizes with conduction electrons at edge center sites of the Lieb lattice, and at the temperature range between the artificial strong coupling and the local moment regimes.

scholarly journals REALISTIC MODELING OF STRONGLY CORRELATED ELECTRON SYSTEMS: AN INTRODUCTION TO THE LDA+DMFT APPROACH

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2611-2625 ◽  
Author(s):  
K. HELD ◽  
I. A. NEKRASOV ◽  
N. BLÜMER ◽  
V. I. ANISIMOV ◽  
D. VOLLHARDT
Keyword(s):  
Quantum Monte Carlo ◽  
Local Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Structure Theory ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Basic Ideas ◽  
Set Up

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La 1-x Sr x TiO 3, obtained by solving the DMFT equations by quantum Monte Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e. the iterative perturbation theory and the non-crossing approximation.

Sign in / Sign up

Export Citation Format

Share Document