Electron-electron interactions, quantum Coulomb gap, and dynamical scaling near integer quantum Hall transitions

Abstract

The effects of electron-electron interactions on the bulk tunneling density of states (TDOS) are studied near the integer quantum Hall transitions (IQHT). Taking into account the dynamical screening of the interactions in the critical conducting state, we show that the behavior of the TDOS is significantly altered from its noninteracting counterpart. For Coulomb interaction, we demonstrate that the TDOS vanishes linearly at the Fermi level according to a quantum Coulomb gap form with a nonuniversal slope. For short-range interactions, the TDOS is found to follow a power-law with an exponent proportional to the interaction strength. Since short-range interactions are known to be irrelevant perturbations at the non-interacting critical point, we predict that upon scaling, the power-law is smeared, leading to a finite zero bias TDOS. However, the approach to the zero-bias value is described by a power-law with a universal exponent determined by the scaling dimension of short-range interactions. We also consider the case of quasi-1D samples with edges and find that the TDOS becomes dependent of the Hall conductance due to an altered boundary condition for diffusion. For short-range interactions, the TDOS of a quasi-1D strip is linear near the Fermi level with a slope inversely proportional to the resistivity in the perturbative limit. These results are in qualitative agreement with the bulk tunneling experiments. We discuss recent developments in understanding the role played by electron-electron interactions at the IQHT and the implications of these results on dynamical scaling of the transition width. We argue that for the long-range Coulomb interaction, the existence of the quantum Coulomb gap in the quantum critical regime of the transition gives rise to the observed dynamical exponent z=1.