Non-perturbative dynamics of flat-band systems with correlated disorder

Abstract

We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed correlations. We verify this method with a one-dimensional (1D) cross-stitch model, and find good agreement with analytical results obtained from the disorder-dressed evolution equations. This allows us to reproduce previous findings, that disorder can mobilize 1D flat-band states which would otherwise remain localized. As explained by the corresponding disorder-dressed evolution equations, such mobilization requires an asymmetric disorder-induced coupling to dispersive bands, a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing. We exemplify this with the 1D Lieb lattice. While analytical expressions are not available for the two-dimensional (2D) system due to its complexity, we extend the numerical method to the 2D $\alpha -T_3$ model, and find that the initial flat-band wave packet preserves its localization when $\alpha =0$, regardless of disorder and intersections. However, when $\alpha \ne 0$, the wave packet shifts in real space. We interpret this as a Berry phase controlled, disorder-induced wave-packet mobilization. In addition, we present density functional theory calculations of candidate materials, specifically $\mathrm{H}{\mathrm{g}}_{1-\mathrm{x}}\mathrm{C}{\mathrm{d}}_{\mathrm{x}}\mathrm{Te}$. The flat-band emerges near the $\Gamma$ point ($\mathbf{k}=$0) in the Brillouin zone.

Accepted on Chin. Phys. B

References in corpus (15)

• Nearly-flat bands with nontrivial topology
• Observation of Fractionally Quantized Anomalous Hall Effect
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Flat Bands Under Correlated Perturbations
• Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase
• Zero modes and the edge states of the honeycomb lattice
• Aharonov-Bohm Caging and Inverse Anderson transition in Ultracold Atoms
• Exact many-electron ground states on the diamond Hubbard chain
• Designing Ultra-Flat Bands in Twisted Bilayer Materials at Large Twist Angles without specific degree
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Ground state properties of the Holstein model near the adiabatic limit
• Tunable quantum criticalities in an isospin extended Hubbard model simulator
• Non-perturbative dynamics of flat-band systems with correlated disorder

Cited by in corpus (3)

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• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping