Spin Density Matrix of Spin-3/2 Hole Systems

TL;DR

This paper introduces an invariant multipole expansion of the spin density matrix for spin-3/2 hole systems, revealing how magnetic fields induce higher-order moments like octupoles, which are unique to these systems.

Contribution

It provides a novel invariant decomposition of the spin density matrix for spin-3/2 holes, linking multipole moments to physical phenomena like magnetic field effects.

Findings

Charge density as monopole moment

Magnetic field induces octupole moments

Spin polarization remains small despite depopulation

Abstract

For hole systems with an effective spin j=3/2, we present an invariant decomposition of the spin density matrix that can be interpreted as a multipole expansion. The charge density corresponds to the monopole moment and the spin polarization due to a magnetic field corresponds to a dipole moment while heavy hole-light hole splitting can be interpreted as a quadrupole moment. For quasi two-dimensional hole systems in the presence of an in-plane magnetic field B the spin polarization is a higher-order effect that is typically much smaller than one even if the minority spin subband is completely depopulated. On the other hand, the field B can induce a substantial octupole moment which is a unique feature of j=3/2 hole systems.