Giant magnetoresistance of edge current between fermion and spin topological systems

TL;DR

This paper investigates the edge current behavior in a topological insulator-fermion junction, revealing how magnetic fields can switch the current on and off through topologically protected chiral edge states.

Contribution

It provides an exact solution for a hybrid topological system, demonstrating how Chern numbers influence edge currents and how magnetic fields can control these currents.

Findings

Edge currents depend on the Chern numbers of subsystems.

Magnetic fields can switch the edge current on or off.

Chiral edge states govern the boundary interactions.

Abstract

A spin-$\frac{1}{2}$ subsystem conjoined along a cut with a subsystem of spinless fermions in the state of topological insulator is studied on a honeycomb lattice. The model describes a junction between a 2D topological insulator and a 2D spin lattice with direction-dependent exchange interactions in topologically trivial and nontrivial phase states. The model Hamiltonian of the complex system is solved exactly by reduction to free Majorana fermions in a static $\mathbb{Z}_2$ gauge field. In contrast to junctions between topologically trivial phases, the junction is defined by chiral edge states and direct interaction between them for topologically nontrivial phases. As a result of the boundary interaction between chiral edge modes, the edge junction is defined by the Chern numbers of the subsystems: such the gapless edge modes with the same (different) chirality switch on (off) the edge current between topological subsystems. The sign of the Chern number of spin subsystem is changed in an external magnetic field, thus the electric current strongly depends both on a direction and a value of an applied weak magnetic field. We have provided a detailed analysis of the edge current and demonstrate how to switch on (off) the electric current in the magnetic field.