A lattice gauge theory model for graphene

TL;DR

This thesis introduces a lattice gauge theory model for graphene with electromagnetic interactions, revealing how these interactions influence electronic properties, response functions, and lattice distortions, and suggesting they promote lattice instability and gap formation.

Contribution

It develops a rigorous lattice gauge theory model for graphene, analyzing electromagnetic effects on electronic properties and lattice distortions with novel renormalization group techniques.

Findings

Interaction-dependent anomalous exponents in Schwinger functions

Wave function renormalization diverges in the infrared

Electromagnetic interactions enhance Kekulé and charge density wave responses

Abstract

In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward identities. In particular, it is shown that, at all orders in renormalized perturbation theory, the Schwinger functions and the response functions decay with interaction dependent anomalous exponents. Regarding the 2-point Schwinger function, the wave function renormalization diverges in the infrared limit, while the effective Fermi velocity flows to the speed of light. Concerning the response functions, those associated to a Kekul\'e distortion of the honeycomb lattice and to a charge density wave instability are enhanced by the electromagnetic electron-electron interactions (their scaling in real space is depressed), while the lowest order correction to the scaling exponent of the density-density response function is vanishing. Then, the model in presence of a fixed Kekul\'e distortion is studied, and it is shown that the interaction strongly renormalizes the effective amplitude of the lattice distortion. Finally, the effect of the electronic repulsion on the Peierls-Kekul\'e instability is discussed by deriving a non-BCS gap equation, from which we find evidence that strong electromagnetic interactions facilitate the spontaneous distortion of the lattice and the opening of a gap. This thesis is based on joint work with A. Giuliani and V. Mastropietro.