Diamagnetism of nodal fermions

TL;DR

This paper derives the scaling form of diamagnetic susceptibility for nodal fermions at quantum criticality, with implications for measurements in graphene and high-temperature superconductors.

Contribution

It provides a theoretical framework for understanding the diamagnetic response of nodal fermions at quantum critical points, connecting it to experimental observables.

Findings

Derived the scaling form of diamagnetic susceptibility at finite temperature and chemical potential.

Predicted measurable Landau diamagnetic susceptibility in graphene and related materials.

Analyzed the crossover behavior from high-temperature to quantum critical regimes.

Abstract

Free nodal fermionic excitations are simple but interesting examples of fermionic quantum criticality in which the dynamic critical exponent $z=1$, and the quasiparticles are well defined. They arise in a number of physical contexts. We derive the scaling form of the diamagnetic susceptibility, $\chi$, at finite temperatures and for finite chemical potential. From measurements in graphene, or in $\mathrm{Bi_{1-x}Sb_{x}}$ ($x=0.04$), one may be able to infer the striking Landau diamagnetic susceptibility of the system at the quantum critical point. Although the quasiparticles in the mean field description of the proposed $d$-density wave (DDW) condensate in high temperature superconductors is another example of nodal quasiparticles, the crossover from the high temperature behavior to the quantum critical behavior takes place at a far lower temperature due to the reduction of the velocity scale from the fermi velocity $v_{F}$ in graphene to $\sqrt{v_{F}v_{\mathrm{DDW}}}$, where $v_{\mathrm{DDW}}$ is the velocity in the direction orthogonal to the nodal direction at the Fermi point of the spectra of the DDW condensate.