Filling up complex spectral regions through non-Hermitian disordered chains

Eigenspectra that fill regions in the complex plane have been intriguing to many,inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices.In this work,we propose a simple and robust ansatz for constructing models whose eigenspectra fill up generic prescribed regions.Our approach utilizes specially designed non-Hermitian random couplings that allow the co-existence of eigenstates with a continuum of localization lengths,mathematically emulating the effects of semi-infinite boundaries.While some of these couplings are necessarily long-ranged,they are still far more local than what is possible with known random matrix ensembles.Our ansatz can be feasibly implemented in physical platforms such as classical and quantum circuits,and harbors very high tolerance to imperfections due to its stochastic nature.

Anderson Localization in the Induced Disorder System

We propose a coherently prepared three-level atomic medium that can provide a flexible disordered scheme for realizing the Anderson localization. Different disorder levels can be attained by modulating the intensity ratio between the two control beams. Due to the real-time tunability, the localization of the signal beam is observable and controllable. The influences of the induced disorder level, atomic density and the initial waist radius of the signal beam on the Anderson localization in the medium are also discussed.

Transport properties of a random binary side-coupled chain

We investigate the transport properties of a random binary side-coupled chain by using the transfer-matrix technique. It is found that there are resonant states in the systems with short-range correlations between the host chain atoms and the side-coupled atoms. The analytic expressions for the extended states are also presented in the systems with the side couplings between like atoms and between unlike atoms.

Transport properties of a ladder with two random dimer chains

We investigate the transport properties of a ladder with two random dimer （RD） chains. It is found that there are two extended states in the ladder with identical RD chains and a critical state regarded as an extended state in the ladder with pairing RD chains. Such a critical state is caused by the chiral symmetry. The ladder with identical RD chains can be decoupled into two isolated RD chains and the ladder with pairing RD chains can not. The analytic expressions of the extended states are presented for the ladder with identical RD chains.

Weak antilocalization and interaction-induced localization of Dirac and Weyl Fermions in topological insulators and semimetals

Weak localization and antilocalization are quantum transport phenomena that arise from the quantum interference in disordered metals.At low temperatures,they can give distinct temperature and magnetic field dependences in conductivity,allowing the symmetry of the system to be explored.In the past few years,they have also been observed in newly emergent topological materials,including topological insulators and topological semimetals.In contrast from the conventional electrons,in these new materials the quasiparticles are described as Dirac or Weyl fermions.In this article,we review our recent efforts on the theories of weak antilocalization and interaction-induced localization for Dirac and Weyl fermions in topological insulators and topological semimetals.