PT-Symmetry Breaking and Catastrophes in Dissipationless Resonant Tunneling Heterostructures

TL;DR

This paper investigates how symmetry breaking and resonance coalescence occur in dissipationless resonant tunneling heterostructures, linking quantum transport phenomena to non-Hermitian Hamiltonian properties and catastrophe theory.

Contribution

It introduces a novel approach using non-Hermitian Hamiltonians to analyze resonance coalescence and symmetry breaking in RTS, including classification via catastrophe theory.

Findings

Resonance peaks coalesce at exceptional points in PT-symmetric Hamiltonians.

Symmetry breaking of electron wavefunctions occurs during resonance coalescence.

The study classifies peak coalescence types and explores effects of dissipation and asymmetry.

Abstract

We study the phenomenon of spontaneous symmetry breaking in dissipationless resonant tunneling heterostructures (RTS). To describe the quantum transport in this system we apply both the nonequilibrium Green function formalism based on a tight-binding model and a numerical solution of the Schroedinger equation within the envelope wavefunction formalism. An auxiliary non-Hermitian Hamiltonian is introduced. Its eigenvalues determine exactly the transparency peak positions. We present a procedure how to construct a family of non-Hermitian Hamiltonians with real eigenvalues. In general these Hamiltonians do not have PT-symmetry. In spatially symmetric RTS the corresponding auxiliary non-Hermitian Hamiltonian becomes PT-symmetric and possesses real eigenvalues, which can coalesce at exceptional points (EP) of Hamiltonian. A coalescence of the auxiliary non-Hermitian Hamiltonian eigenvalues means a coalescence of resonances in RTS, which is accompanied be symmetry breaking of the electron wavefunction probability distribution (at a given direction of the particle flow). We construct a classification of different types of the peak coalescence in terms of the catastrophe theory and investigate the impact of dissipation and asymmetry on these phenomena. Possible applications include sensors and broad-band filters.