# Surface state transport in double-gated and magnetized topological insulators with hexagonal warping effects

## TL;DR

This paper investigates how magnetic fields, gate voltages, and hexagonal warping influence electron transport on the surface of topological insulators, revealing controllable conductance and magnetoresistance effects.

## Contribution

It introduces a detailed analysis of surface state transport in double-gated, magnetized topological insulators considering hexagonal warping effects, highlighting tunable electronic properties.

## Key findings

- Magnetic fields shift Dirac cones and open gaps depending on magnetization orientation.
- Hexagonal warping enhances high-energy transport with snowflake-shaped contours.
- Resonant tunnelling states cause oscillations in conductance and magnetoresistance.

## Abstract

We explore the scattering of Dirac electrons in a double-gated topological insulator in the presence of magnetic proximity effects and warped surface states. It is found that a magnetic field can shift the Dirac cone in momentum space and deform the constant-energy contour, or opens up a band gap at the Dirac point, depending on the magnetization orientation. The double gate voltage induces quantum wells and/or quantum barriers on the surface of topological insulators, generating surface resonant tunnelling states. It is found that the hexagonal warping effect can increase the electronic transport at high energies when the constant-energy contour exhibits a snowflake shape. The energy-dependent conductances in the parallel and antiparallel magnetic configurations exhibit out-of-phase oscillations due to the quantum interference of propagating waves in the region between the two magnetized segments. Although the conductance spectrum of the double-well structure is higher than that of the double-barrier structure, the magnetoresistance ratio versus the separation distance between the two magnetized barriers exhibits pronounced oscillations due to the resonant tunnelling states. We show that the surface state transport can be controlled by the exchange field and gate voltage without breaking time reversal symmetry, suggesting that the double gated and magnetized topological insulators can be utilized to achieve a large magnetoresistance ratio with a tunable sign.