Physical dipoles and second order perturbation theory for dipolar fermions in two dimensions

TL;DR

This paper investigates the effects of finite-sized physical dipoles on the second order perturbation theory of two-dimensional dipolar fermions, resolving divergences and analyzing resulting Fermi liquid properties.

Contribution

It introduces a regularization method for dipolar interactions considering finite dipole size, enabling finite second order calculations in 2D dipolar fermions.

Findings

Second order corrections weaken first order effects in the Fermi liquid phase.

Regularization removes ultraviolet divergence in self-energy calculations.

Calculated renormalized chemical potential and Fermi surface.

Abstract

In two dimensions the Fourier transform of the interaction between two point dipoles has a term which grows linearly in the modulus $| \mathbf{\textit{q}} |$ of the momentum . As a consequence, in second order perturbation theory the self-energy of two-dimensional dipolar fermions is ultraviolet divergent. We show that for electric dipoles this divergence can be avoided if one takes into account that physical dipoles consist of two opposite charges which are separated by a finite distance. Using this regularization, we calculate the self-energy, the renormalized chemical potential, and the renormalized Fermi surface of dipolar fermions in two dimensions in second order perturbation theory. We find that in the Fermi liquid phase the second order corrections weaken first order effects.