The stabilizer group of honeycomb lattices and its application to deformed monolayers

TL;DR

This paper investigates the stability group of the Dirac algebra in honeycomb lattices, leading to new crystalline structures with Dirac points and applications to materials like MoS2, combining algebraic transformations with physical properties.

Contribution

It introduces a novel analysis of the stability group of the Dirac algebra in honeycomb lattices and applies it to model and understand properties of 2D materials such as MoS2.

Findings

New crystalline arrays with Dirac points are constructed.

Unitary and non-unitary transformations reveal symmetry properties and Hamiltonian behaviors.

Application to MoS2 explains invariant bandgaps and dispersion relations.

Abstract

Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing graphene or boron nitride. New crystalline arrays with conical (Dirac) points are obtained; in particular, a model for dichalcogenide monolayers is proposed and analyzed. In our studies we encounter unitary and non-unitary transformations. We show that the latter give rise to $\mbox{$\cal P\,$}\mbox{$\cal T\,$}$-symmetric Hamiltonians, in compliance with known results in the context of boosted Dirac equations. The results of the unitary part are applied to the description of invariant bandgaps and dispersion relations in materials such as MoS$_2$. A careful construction based on atomic orbitals is proposed and the resulting dispersion relation is compared with previous results obtained through DFT.