Diamagnetism of nodal fermions

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 Bi1-xSbx (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 are 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 root v(F)v(DDW), where v(DDW) is the velocity in the direction orthogonal to the nodal direction at the Fermi point of the spectra of the DDW condensate.