## Spontaneous spin polarisations in hole systems induced by spin-orbit coupling

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Holes are the absence of electrons in a semiconductor, and have very different spin properties than electrons. Recent studies show that holes have extremely attractive properties for spintronics and quantum information, for example they have a strongly suppressed hyperfine interaction, so quantum information can be preserved for long times. Holes experience a very strong spin-orbit interaction, and the hole-hole Coulomb interaction is also strong. Hole-based systems are studied intensively at UNSW experimentally.

In an electric field certain spin-orbit coupled systems acquire a spin polarisation. In the case of heavy hole systems, this spin polarisation stems from the Dresselhaus spin-orbit interaction. The interplay between spin-orbit and hole-hole interactions is highly nontrivial, and is receiving growing attention. Our group has demonstrated that this current-induced spin polarisation is enhanced by hole-hole interactions, and that this enhancement may diverge, signifying a transition to a state in which there is a spontaneous spin polarisation induced by spin-orbit interactions.

The aim of this half-year project is to understand under what circumstances such a state can exist, how it may be detected, and what practical applications it may have. To achieve this, the student will learn a form of quantum transport theory based on the quantum Liouville equation, followed by the random phase approximation to describe screening, and the Hartree-Fock approximation for hole-hole interactions. They will use this to evaluate both the bare spin polarisation induced by an electric field in a non-interacting system, and the corrections due to interactions to all orders in perturbation theory. They will determine when this response can diverge, the critical temperature at which this happens, and the effect of quantum mechanical fluctuations on this transition.

It is expected that the spin polarisation will have a feedback effect on the current, potentially enabling an electrical measurement of a spin phenomenon, as well as a direct measurement of the spin-orbit parameters of the material under study. The student will calculate this feedback effect, and determine a way to measure it experimentally.

Electric fields in spin-orbit coupled systems are usually accompanied by spin Hall currents, and these in turn are affected by interactions. If time allows, the student will determine the interaction correction to the spin-Hall current, and whether this interferes with the current-induced spin polarisation.