Anomalous Bilayer Quantum Hall Effect

TL;DR

This paper proposes that bilayer flat band lattices can realize an anomalous bilayer quantum Hall effect without magnetic fields, demonstrating various topological phases and phase transitions through exact diagonalization.

Contribution

It introduces bilayer flat band lattices as solid-state analogues of bilayer quantum Hall systems, revealing new topological states and phase transitions in this setting.

Findings

Stabilization of excitonic condensate Halperin's (1,1,1) state at total filling v_T=1

Observation of phase transitions among Halperin's (3,3,0), (1,1,2), and Laughlin states at v_T=2/3

Demonstration of potential for realizing non-Abelian anyons in bilayer flat band materials

Abstract

In parallel to the condensed-matter realization of quantum Hall (Chern insulators), quantum spin Hall (topological insulators), and fractional quantum Hall (fractional Chern insulators) effects, we propose that bilayer flat band (FB) lattices with one FB in each layer constitute solid-state analogues of bilayer quantum Hall (BQH) system, leading to anomalous BQH (ABQH) effect, without magnetic field. By exact diagonalization of a bilayer Kagome lattice Hamiltonian, as a prototypical example, we demonstrate the stabilization of excitonic condensate Halperin's (1,1,1) state at the total filling $v_T=1$ of the two Fbs. Furthermore, by tuning the inter-layer tunneling and distance between the Kagome layers at $v_T=2/3$, we show phase transitions among Halperin's (3,3,0), spin-singlet (1,1,2), and particle-hole conjugate of Laughlin's 1/3 states, as previously observed in BQH systems. Our work opens a new research direction in the field of FB physics by demonstrating bilayer FB materials as an attractive avenue for realizing exotic ABQH states including non-Abelian anyons.