Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\cal{PT}$-symmetric flat band lattice

TL;DR

This paper investigates stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $ ext{PT}$-symmetric flat band lattice, revealing conditions for persistent oscillations and potential control of transport in such systems.

Contribution

It demonstrates the existence of stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $ ext{PT}$-symmetric lattice, especially in the broken phase with isolated complex bands.

Findings

Large, persistent Bloch oscillations observed in broken $ ext{PT}$ phase.

Landau-Zener tunneling enables super Bloch oscillations.

Control of transport phenomena in non-Hermitian systems demonstrated.

Abstract

This article aims to study the existence of stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian system when exposed to external fields. We investigate a non-Hermitian $\cal{PT}$-symmetric diamond chain network and its transport dynamics in two different situations, namely in a flat band case and a non-flat band case. The considered system does not support unbroken-$\cal{PT}$ phase or completely real eigenspectra in any of the parametric regions in both the flat and non-flat band cases. In the flat band case, up to a critical value of the gain-loss parameter, the bands are found to be gapless or inseparable, and for other values the bands are isolated. Considering the non-flat band case, all the bands are found to be complex dispersive and are also isolated. In the case of completely broken $\cal{PT}$ phase, we look upon the possibility to have stable dynamics or Bloch oscillations upon the application of external fields like synthetic electric field. In particular, when the complex bands are isolated, we point out that the Landau-Zener tunneling induced by the synthetic electric field can enable Bloch oscillations. The amplitude of these Bloch oscillations is large and persists for a long propagation distance which reveals that super Bloch oscillations can be observed in the broken $\cal{PT}$ phase of the system. We also report the amplified Bloch oscillations which pave the way towards controlling transport phenomena in non-Hermitian systems.