Quantum-geometry-enabled Landau-Zener tunneling in singular flat bands

TL;DR

This paper explores how singular flat bands respond to electric fields, revealing that quantum geometry enables Landau-Zener tunneling and nontrivial transport phenomena near band crossing points.

Contribution

It introduces a minimal two-band lattice model showing how quantum geometry influences Landau-Zener tunneling and transport in singular flat bands.

Findings

Wannier-Stark spectrum is well described by intraband Berry phase away from BCP

Near BCP, interband Berry connection induces Landau-Zener tunneling

Quantum distance and geometric phases govern tunneling rate and wavefunction delocalization

Abstract

Flat-band materials have attracted substantial interest for their intriguing quantum geometric effects. Here we investigate how singular flat bands (SFBs) respond to a static, uniform electric field and whether they can support single-particle dc transport. By constructing a minimal two-band lattice model, we show that away from the singular band crossing point (BCP), the Wannier-Stark (WS) spectrum of the flat band is well captured by an intraband Berry phase $\Phi_{\mathrm{B}}$. The associated WS eigenstates are exponentially localized along the field direction, precluding dc transport. In contrast, near the BCP the interband Berry connection becomes prominent and drives Landau-Zener tunneling, which bends the flat-band WS ladder and delocalizes the SFB wavefunctions. Remarkably, this regime is governed solely by the maximal quantum distance $d$ through two geometric phases $(\theta,\varphi)$: $\theta$ characterizes the tunneling rate and $\varphi$ acts as a generalized Berry phase. These results highlight the essential role of quantum geometry in enabling nontrivial transport signatures in SFBs.