Introducing Spin in 2D Quantum Tunneling

TL;DR

This paper explores how electron spin affects quantum tunneling in 2D systems using the Levy-Leblond equation, deriving transmission and reflection coefficients for spin states, aligning with known semiconductor results.

Contribution

It introduces a method to incorporate electron spin into 2D tunneling analysis using the Levy-Leblond equation, providing new insights into spin-dependent tunneling phenomena.

Findings

Derived spin-dependent transmission and reflection coefficients.

Confirmed consistency with known results for gapless semiconductors.

Demonstrated the role of spin in 2D quantum tunneling.

Abstract

We study the quantum tunneling of non-relativistic electrons for two dimensional condensed matter systems. We employ the Levy-Leblond equation (which is the analogue of the Dirac equation for non-relativistic fermions) and show that the spin of the particle can be incorporated in the 2D tunneling problem. We derive the transmission and reflection coefficients of spin up and down electrons and show that the sum of these coefficients are consistent with the known results for gapless semiconductors.