# NON-ABELIAN GEOMETRIC PHASES AND CONDUCTANCE OF SPIN-3/2 HOLES

@article{Arovas1998NONABELIANGP, title={NON-ABELIAN GEOMETRIC PHASES AND CONDUCTANCE OF SPIN-3/2 HOLES}, author={Daniel P. Arovas and Yu. B. Lyanda-Geller}, journal={Physical Review B}, year={1998}, volume={57}, pages={12302-12305} }

Angular momentum J= (3) /(2) holes in semiconductor heterostructures are shown to accumulate non-Abelian geometric phases as a consequence of their motion. We provide a general framework for analyzing such a system and compute conductance oscillations for a simple ring geometry. We also analyze a figure-eight geometry that captures intrinsically non-Abelian interference effects. {copyright} {ital 1998} {ital The American Physical Society}

## 13 Citations

Effective geometric phases and topological transitions in SO(3) and SU(2) rotations.

- Physics, MedicineJournal of physics. Condensed matter : an Institute of Physics journal
- 2016

It is shown that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology, associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry.

Intrinsic spin Hall effect in the two-dimensional hole gas.

- Physics, MedicinePhysical review letters
- 2005

We show that two types of spin-orbit coupling in the 2 dimensional hole gas, with and without inversion symmetry breaking, contribute to the intrinsic spin-Hall effect. Furthermore, the vertex…

Geometric Phase through Spatial Potential Engineering.

- Physics, MedicinePhysical review letters
- 2020

A spatial analog of the Berry's phase mechanism for the coherent manipulation of states of nonrelativistic massive particles moving in a two-dimensional landscape using a Wilczek-Zee non-Abelian phase shift contribution that is intrinsically geometrical, hence insensitive to the specific details of the potential landscape.

Coriolis force, geometric phase, and spin-electric coupling in semiconductors

- Physics
- 2006

We consider the response of the effective spin of a charge carrier in semiconducting systems to an adiabatic rotation of its crystal momentum induced by an electric field. We demonstrate that the…

Dirac electrons in quantum rings

- Physics
- 2018

We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband…

Resonant tunneling anisotropic magnetoresistance induced by magnetic proximity

- PhysicsPhysical Review B
- 2020

We reveal that the interplay between Rashba spin-orbit coupling and proximity-induced magnetization in a two-dimensional electron gas leads to peculiar transport properties and large anisotropy of…

Noncyclic geometric changes of quantum states

- Physics
- 2006

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the…

Dissipationless Quantum Spin Current at Room Temperature

- Physics, MedicineScience
- 2003

Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this…

Spin precession in an adiabatically rotating electric field

- Physics
- 2004

Due to spin-orbit coupling, the adiabatic perturbation of an electron’s orbital motion induced by a revolvingexternal electric ﬁeld lead to the electron spin-precession. The obtained results describe…

## References

Geometric Phases in Physics

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During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a…