Spin texture and spin current in excitonic phases of the two-band Hubbard model

TL;DR

This study explores spin textures and local spin currents in excitonic insulator states of a two-band Hubbard model, revealing how excitonic symmetry breaking induces spin textures and local spin currents without global spin flow.

Contribution

It introduces a mean-field analysis of spin textures and local spin currents in excitonic phases with various cross-hopping symmetries in the two-band Hubbard model.

Findings

Spin textures emerge on Fermi surfaces due to excitonic symmetry breaking.

Local spin currents can be spontaneously induced without global spin flow.

The presence of spin textures depends on the phase of the excitonic order parameter.

Abstract

Using the mean-field approximation, we study the $k$-space spin textures and local spin currents emerged in the spin-triplet excitonic insulator states of the two-band Hubbard model defined on the square and triangular lattices. We assume a noninteracting band structure with a direct band gap and introduce $s$-, $p$-, $d$-, and $f$-type cross-hopping integrals, i.e., the hopping of electrons between different orbitals on adjacent sites with four different symmetries. First, we calculate the ground-state phase diagrams in the parameter space of the band filling and interaction strengths, whereby we present the filling dependence of the amplitude and phase of the excitonic order parameters. Then, we demonstrate that the spin textures (or asymmetric band structures) are emerged in the Fermi surfaces by the excitonic symmetry breaking when particular phases of the order parameter are stabilized. Moreover, in case of the $p$-type cross-hopping integrals, we find that the local spin current can be induced spontaneously in the system, which does not contradict the Bloch theorem for the absence of the global spin current. The proofs of the absence of the global spin current and the possible presence of the local spin currents are given on the basis of the Bloch theorem and symmetry arguments.