Generalized Nonequilibrium Quantum Transport of Spin and Pseudospins: Entanglements and Topological Phases

TL;DR

This paper develops a unified framework for nonequilibrium quantum transport involving multiple spins and pseudospins, revealing new insights into topological phases, entanglement, and localization phenomena in quantum materials.

Contribution

It introduces a general formalism for quantum transport equations that incorporate charge, spin, isospin, and pseudospin, applicable to various topological and 2D materials.

Findings

Identification of a characteristic integer $N_{s}$ governing spin transport equations.

Insights into mechanisms of zero modes and edge states in topological insulators.

Proposed new mechanisms for localization, delocalization, and superconductivity emergence.

Abstract

General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins. Limiting cases are obtained for one, two or three different kinds of spin ocurring in a system. We show that a characteristic integer number $N_{s}$ determines the formal form of spin quantum transport equations, irrespective of the type of spins or pseudospins, as well as the maximal entanglement entropy. The results may shed a new perspective on the mechanism leading to zero modes and chiral/helical edge states in topological insulators, integer quantum Hall effect topological insulator (QHE-TI), quantum spin Hall effect topological insulator (QSHE-TI) and Kondo topological insulator (Kondo-TI). It also shed new light in the observed competing weak localization and antilocalization in spin-dependent quantum transport measurements. In particular, a novel mechanism of localization and delocalization, as well as the new mechanism leading to the onset of superconductivity in bilayer systems seems to emerge naturally from torque entanglements in nonequilibrium quantum transport equations of spin and pseudospins. Moreover, the general results may serve as a foundation for engineering approximations of the quantum transport simulations of spintronic devices based on graphene and other 2-D materials such as the transition metal dichalcogenides (TMDs), as well as based on topological materials exhibiting quantum spin Hall effects. The extension of the formalism to spincaloritronics and pseudo-spincaloritronics is straightforward.