Coalescence of resonances in dissipationless resonant tunneling structures and [formula omitted]-symmetry breaking

Abstract

We study the phenomenon of spontaneous symmetry breaking in dissipationless resonant tunneling structures (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 Schrödinger equation within the envelope wavefunction formalism. An auxiliary non-Hermitian Hamiltonian is introduced. Its eigenvalues determine exactly the transparency peak positions. In spatially symmetric RTS the corresponding auxiliary non-Hermitian Hamiltonian becomes PT-symmetric and possesses real eigenvalues, which can coalesce at exceptional points of this Hamiltonian. A coalescence of the auxiliary non-Hermitian Hamiltonian eigenvalues means a coalescence of perfect resonances in RTS, which can be accompanied be symmetry breaking of the electron wavefunction probability distribution (at a given direction of the particle flow). Also we construct a classification of different types of the coalescence of resonances in terms of the catastrophe theory and investigate the impact of small imperfections (scattering and asymmetry) on these phenomena.