U. Zülicke

Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling

The presence of spin-orbit coupling affects the spontaneously flowing persistent currents in mesoscopic conducting rings. Here we analyze their dependence on magnetic flux with emphasis on identifying possibilities to prove the presence and extract the strength of Rashba spin splitting in low-dimensional systems. Effects of disorder and mixing between quasi-one-dimensional ring subbands are considered. The spin-orbit coupling strength can be inferred from the values of flux where sign changes occur in the persistent charge current. As an important consequence of the presence of spin splitting, we identify a nontrivial persistent spin current that is not simply proportional to the charge current. The different flux dependences of persistent charge and spin currents are a unique signature of spin-orbit coupling affecting the electronic structure of the ring.

Spin accumulation in quantum wires with strong Rashba spin-orbit coupling

We present analytical and numerical results for the effect of Rashba spin-orbit coupling on band structure, transport, and interaction effects in quantum wires when the spin precession length is comparable to the wire width. The situation with only the lowest spin-split subbands occupied is particularly interesting because electrons close to Fermi points of the same chirality can have approximately parallel spins. We discuss consequences for spin-dependent transport and effective Tomonaga-Luttinger descriptions of interactions in the quantum wire.

Filtering spin with tunnel-coupled electron wave guides

We show how momentum-resolved tunneling between parallel electron wave guides can be used to observe and exploit lifting of spin degeneracy due to Rashba spin-orbit coupling. A device is proposed that achieves spin filtering without using ferromagnets or the Zeeman effect.

Zeeman splitting in ballistic hole quantum wires

We have studied the Zeeman splitting in ballistic hole quantum wires formed in a (311)A quantum well by surface gate confinement. Transport measurements clearly show lifting of the spin degeneracy and crossings of the subbands when an in-plane magnetic field B is applied parallel to the wire. When B is oriented perpendicular to the wire, no spin splitting is discernible up to B = 8.8 T. The observed large Zeeman splitting anisotropy in our hole quantum wires demonstrates the importance of quantum confinement for spin splitting in nanostructures with strong spin-orbit coupling.

Andreev reflection in strong magnetic fields

We have studied the interplay of Andreev reflection and cyclotron motion of quasiparticles at a superconductor-normal-metal interface with a strong magnetic field applied parallel to the interface. Bound states are formed due to the confinement introduced by both the external magnetic field and the superconducting gap. These bound states are a coherent superposition of electron and hole edge excitations similar to those realized in finite quantum-Hall samples. We find the energy spectrum for these Andreev edge states and calculate transport properties.

Universal Rashba spin precession of two-dimensional electrons and holes

We study spin precession due to Rashba spin splitting of electrons and holes in semiconductor quantum wells. Based on a simple analytical expression that we derive for the current modulation in a broad class of experimental situations of ferromagnet/nonmagnetic semiconductor/ferromagnet hybrid structures, we conclude that the Datta-Das spin transistor i) is feasible with holes and ii) its functionality is not affected by integration over injection angles. The current modulation shows a universal oscillation period, irrespective of the different forms of the Rashba Hamiltonian for electrons and holes. The analytic formulas approximate extremely well exact numerical calculations of a more elaborate Kohn-Luttinger model.

Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects

In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian, describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.

Rashba spin splitting in quantum wires

Abstract This article presents an overview of results pertaining to electronic structure, transport properties, and interaction effects in ballistic quantum wires with Rashba spin splitting. Limits of weak and strong spin–orbit coupling are distinguished, and spin properties of the electronic states elucidated. The case of strong Rashba spin splitting where the spin-precession length is comparable to the wire width turns out to be particularly interesting. Hybridization of spin-split quantum-wire subbands leads to an unusual spin structure where the direction of motion for electrons can fix their spin state. This peculiar property has important ramifications for linear transport in the quantum wire, giving rise to spin accumulation without magnetic fields or ferromagnetic contacts. A description for interacting Rashba-split quantum wires is developed, which is based on a generalization of the Tomonaga–Luttinger model.

Mesoscopic effects in tunneling between parallel quantum wires

We consider a phase-coherent system of two parallel quantum wires that are coupled via a tunneling barrier of finite length. The usual perturbative treatment of tunneling fails in this case, even in the diffusive limit, once the length L of the coupling region exceeds a characteristic length scale

Periphery deformations and tunneling at correlated quantum Hall edges

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