Abstract

We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Using several averaging tecniques we identify the emergent gapless (diffusion) modes which determine the behavior of the conductivity on large scales and study the scaling behaviour of the conductivity which is determined by the presence of an attractive fixed point.

If nodal fermions are coupled to in - plane phonons, a spontaneous transition into the Hall insulating phase occurs. At sufficiently strong electron - phonon interaction a gap appears in the spectrum of fermions, signaling a transition into a phase with spontaneously broken parity symmetry. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern - Simons excitations.
Evaluating the Kubo formula for both models we find quantized Hall plateaux in each case, with conductance of binodal model exactly twice as large as of the mononodal model.

References:
PRB 90, 174207 (2014), arXiv:1405.6191
JPCM 28, 305701 (2016), arXiv:1602.02786 Phil. Mag. 98, 1799 (2018), arXiv:1608.01096 PRB 93, 125112 (2016), arXiv:1505.04194
arXiv:1807.02035