Density of states of the Hubbard model supplemented with the quantizing magnetic field

TL;DR

This paper calculates the zero-temperature density of states of electrons in a Hubbard model under a magnetic field, revealing how Landau subbands and Mott gaps evolve with interaction strength and doping.

Contribution

It introduces a strong coupling diagram technique to analyze the density of states in the Hubbard model with magnetic field, highlighting the effects of interaction strength and doping.

Findings

Landau subbands appear for small U at moderate doping

Large U causes subband blurring and Mott gap formation

Density of states shows gaps near Hubbard transfer frequencies

Abstract

Using the strong coupling diagram technique, we calculate the zero-temperature density of states $\rho$ of electrons on a square lattice immersed in a perpendicular uniform magnetic field. The electrons are described by Hubbard Hamiltonian. For moderate doping, Landau subbands are observed for small Hubbard repulsions $U$ only. For larger $U$, the subbands are blurred. Instead, small peaks varying with the field induction $B$ arise by opening the Mott gap in its vicinity. The related variation of $\rho$ with $1/B$ may be connected with the low-frequency quantum oscillations in lightly doped cuprates. For all considered repulsions, $\rho$ has gaps near transfer frequencies of the Hubbard atom, $-\mu$ and $U-\mu$, with $\mu$ the chemical potential. In the heavily underdoped case $\mu<0$, Landau subbands are grouped into the lower and upper Hubbard subbands for moderate and large repulsions. The intensity of the upper Hubbard subband decreases with approaching the Fermi level to the lower edge of the spectrum and finally vanishes.