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The effects of electron-electron interactions on the bulk tunneling densityof states (TDOS) are studied near the integer quantum Hall transitions (IQHT).Taking into account the dynamical screening of the interactions in the criticalconducting state, we show that the behavior of the TDOS is significantlyaltered from its noninteracting counterpart. For Coulomb interaction, wedemonstrate that the TDOS vanishes linearly at the Fermi level according to aquantum Coulomb gap form with a nonuniversal slope. For short-rangeinteractions, the TDOS is found to follow a power-law with an exponentproportional to the interaction strength. Since short-range interactions areknown to be irrelevant perturbations at the non-interacting critical point, wepredict that upon scaling, the power-law is smeared, leading to a finite zerobias TDOS. However, the approach to the zero-bias value is described by apower-law with a universal exponent determined by the scaling dimension ofshort-range interactions. We also consider the case of quasi-1D samples withedges and find that the TDOS becomes dependent of the Hall conductance due toan altered boundary condition for diffusion. For short-range interactions, theTDOS of a quasi-1D strip is linear near the Fermi level with a slope inverselyproportional to the resistivity in the perturbative limit. These results are inqualitative agreement with the bulk tunneling experiments. We discuss recentdevelopments in understanding the role played by electron-electron interactionsat the IQHT and the implications of these results on dynamical scaling of thetransition width. We argue that for the long-range Coulomb interaction, theexistence of the quantum Coulomb gap in the quantum critical regime of thetransition gives rise to the observed dynamical exponent z=1.Comment: 33 pages, 6 figures, revised version to be published in Phys. Rev.

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