Diamagnetism of nodal fermions

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 $\mathrm{B}{\mathrm{i}}_{1-\mathrm{x}}\mathrm{S}{\mathrm{b}}_{\mathrm{x}}$ ($x=0.04$), 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.

arXiv comment11 pages, 2 eps figures

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