Origin of conical dispersion relations

TL;DR

This paper presents a mechanism using a one-dimensional Kronig-Penney model with two delta potentials to produce conical dispersion relations similar to those in graphene, and explores a potential link to string theory via Virasoro algebra.

Contribution

It introduces a simple one-dimensional model that reproduces conical dispersion relations and suggests a novel connection to string theory through local Virasoro invariance.

Findings

The model reproduces gap closure and conical dispersion similar to graphene.

Eigenvalue problem exhibits local Virasoro invariance near conical points.

Potential implications for understanding electronic properties and string theory connections.

Abstract

A mechanism that produces conical dispersion relations is presented. A Kronig Penney one dimensional array with two different strengths delta function potentials gives rise to both the gap closure and the dispersion relation observed in graphene and other materials. The Schr\''odinger eigenvalue problem is locally invariant under the infinite dimensional Virasoro algebra near conical dispersion points in reciprocal space, thus suggesting a possible relation to string theory.