Pseudospin, velocity and Berry phase in a bilayer graphene

TL;DR

This paper uses Clifford's geometric algebra to analytically study pseudospin, velocity, and Berry phase in bilayer graphene, especially under external voltage, providing a new mathematical approach to understanding its electronic properties.

Contribution

It introduces a novel application of geometric algebra to analyze bilayer graphene's electronic properties, simplifying calculations of pseudospin, velocity, and Berry phase.

Findings

Analytical expressions for pseudospin, velocity, and Berry phase derived.

External voltage effects on charge carriers characterized.

Geometric algebra approach simplifies complex quantum calculations.

Abstract

Hamiltonian and eigenstate problem is formulated for a bilayer graphene in terms of Clifford's geometric algebra \textit{Cl}$_{3,1}$. It is shown that such approach allows to perform analytical calculations in a simple way if geometrical algebra rotors are used. The measured quantities are express through spectrum and rotation half-angle of the pseudospin that appears in geometric algebra rotors. Properties of free charge carriers -- pseudospin, velocity and Berry phase -- in a bilayer graphene are investigated in the presence of the external voltage applied between the two layers.