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Spin Transport in Interacting Spin-Orbit Coupled Systems

Periodic Reporting for period 1 - SPINSOCS (Spin Transport in Interacting Spin-Orbit Coupled Systems)

Reporting period: 2016-03-01 to 2018-02-28

Our modern civilization is enabled partly by efficient information processing technology. Up to now, most of the information processing has occurred by moving electrons around, hence the name electronics. Despite constant incremental improvement in this technology, it is plausible that a different approach would allow to tackle certain tasks more elegantly and efficiently.

One of these different approaches is spintronics, where spin rather than charge is used to encode, transport and process information. This project has dealt with the intersection of electronics and spintronics, that is, coupling between the motion and spin, also known as the spin-orbit coupling.

During the project we have been able to better understand and explain how motion relates to spin in various circumstances. In particular, we have explored collective behaviour of many particles, and have been able to describe situations, where this novel behavior can be observed experimentally. We hope that our analysis will stimulate experimental work that will in turn lead to practically useful discoveries in the long term.
Four main results have been achieved during the execution of the action.

First, we have put forward a framework that allows to coherently understand how particles behave in the presence of position-space, momentum-space, and phase-space Berry curvatures. In deriving this framework, we have clearly separated the adiabatic transformation, and the semiclassical approximation. This has allowed for an elegant understanding of the spin-orbit coupling problem in general.

Second, we have described a non-Abelian counterpart of the universal intrinsic spin Hall effect. Loosely speaking, this means that particles move as if the magnetic field was pointing in all directions at once. We have quantified the strength of such an omnidirectional spin Hall effect by calculating the corresponding conductivity for fermions and non-condensed bosons, showing the viability of the observation of this effect.

Third, we have reported a system where two qualitatively different kinds of superfluidity are present. In particular, spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity. As an illustration, we have proposed an experimentally accessible stationary state, where the two types of supercurrents counterflow and cancel each other, thus resulting in no mass transport. We have verified the robustness of these findings, and have found that the time scale for coherent (superfluid) dynamics is separated from that of the slower incoherent dynamics by one order of magnitude.

Finally, we have discovered a collective mode corresponding to the spin Hall effect. In particular, in response to a displacement of the center of mass of a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling, spin-dipole moment oscillations occur. We have determined the properties of these oscillations exactly and have found that their amplitude strongly depends on the spin-orbit-coupling strength and the quantum statistics of the particles.

All these results have been disseminated through peer-reviewed publications and presented at international conferences and seminars. These publications are also freely accessible on the arXiv repository.

Popularizing these results and science in general has resulted in multiple articles in the local press, several national radio appearances, as well as an international workshop Ultracold@Vilnius with a popular science talk attended by several hundred students.
We have made several contributions to the state-of-the-art including: deriving quantum Heisenberg equations of motion for momentum and position operators, explicitly containing position-space, momentum-space, and phase-space Berry curvature terms; showing that the effective mass of the equal Rashba-Dresselhaus spin-orbit coupled system can be viewed as a direct effect of the phase-space Berry curvature; showing that in the presence of a three-dimensional (Weyl) spin-orbit coupling, a transverse spin current is generated in response to either a constant spin-independent force or a time-dependent Zeeman field in an arbitrary direction; showing that spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity; illustrating that the basic principles governing these two types of superfluidity are the same by their dynamics in a single framework; showing that a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling exhibits a spin Hall mode.

This project has deepened the fundamental understanding of spin transport in certain circumstances. Therefore, it can have a societal impact by stimulating spin transport experiments, and hence enabling new spintronic devices in the future.
Illustration of two types of superfluidity (indicated by arrows and colors) in the same system