Session S21: Spin-Orbit Coupling and Spin Coherence in Semiconductor Heterostructures

Unusual In-Plane Field Dependence of Spin Resolved Magnetic Focussing in 2D Hole Systems

The need for an all-electrical method of spin control has driven great interest in the spin-orbit interaction. Transverse magnetic focussing provides a method to study spin dynamics by creating spatial separation of spin. We perform magnetic focussing of holes in high symmetry (100) GaAs/AlGaAs heterostructures. We compare focussing in single heterojunction (very strong Rashba) and quantum well (weaker Rashba) structures. While the period of the focussing peaks is the same, we discuss several features that differentiate the spin resolved peaks in these systems. By varying the focussing length we extract the focussing decay length for each spin peak. We also study the dependence of the spin peak separation on the 2D density. Finally, we observe unusual behaviour of the height of the spin peaks with in-plane magnetic fields.   

Spin dynamics in many-electron quantum dots of tunable size

The electron spin coherence time in GaAs-based quantum dots is limited by hyperfine interaction with statistical fluctuations of the nuclear spin polarization. For larger dots in the transition to a 2D system, spin-orbit interaction becomes the dominant dephasing mechanism. In the region in between, a minimum dephasing is expected. Here we investigate the spin coherence time in quantum dots of tunable size obtained from dry etching of a 2D electron gas (2DEG) confined in a GaAs quantum well. Using the pump-probe magneto-optical Kerr rotation technique, electron spin dynamics in ensembles of uniform dots is measured. The spin coherence time increases by two orders of magnitude, from 200 ps in the 2DEG, to more than 20 ns for dots with a diameter of 400 nm. A periodic optical orientation of electron spin polarization at a rate of 80 MHz induces a mode-locking of the spin precession that is enhanced by orientation of nuclear spin polarization, similar to what has been observed for singly charged self-assembled quantum dots but here realized in large many-electron quantum dots with tunable spin-orbit interaction.   

Weak localization magneto-conductivity in quantum wells with Rashba and Dresselhaus spin-orbit interaction - An analytic solution

We formulate an analytic solution to the problem of the weak localization (WL) corrections to the conductivity in the presence of a quantizing magnetic field that incorporates all three spin-orbit terms that are relevant to semiconductors: linear Rashba, linear and cubic Dresselhaus. Our theory produces a complete phenomenological description of the WL contributions that showcases in a direct way the interplay between the Landau level quantization of the electron states and the spin-orbit-driven spin-flip processes. The form of the solution is determined by the relative strengths of the linear couplings, α for Rashba and β for Dresselhaus. Although present throughout the calculation, the cubic Dresselhaus term becomes important only in the α ≈ β case when it acts as a spin-symmetry breaking factor. All the contributions to magnetoconductivity associated with the quantification of the electron orbits are calculated in a Landau level invariant form. The analytic expression obtained for β >> α (or α >> β) becomes an exact solution when α = 0 (or β = 0). A closed-form formula describes the α ≈ β regime, where the result depends only on the difference between the linear Rashba and Dresselhaus terms and the cubic Dresselhaus parameter.   

Stretching and Breaking the Persistent Spin Helix

We introduce the concept of the stretchable persistent spin helix (PSH), i.e. a PSH with gate-adjustable pitch [1]. This opens the door for electrical spin manipulation while spins are protected from the usual Dyakonov-Perel spin decay when propagating through the material. To implement this, a top and back gate is employed to independently tune both the Rashba coefficient α and the effective Dresselhaus coefficient β in-situ. Tunability of β was predicted ca 1990 based a density dependence in the projected 2D term. Here, we demonstrate this in an experiment [1], and we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields. Varying both α and β controllably and continuously with gate voltages, we can demonstrate robust continuous locking at α=β over a wide range, thus stretching the PSH. When combined with numerics, this yields th spin-orbit parameters of the system. Stretchable PSHs could provide the platform for long-distance communication ∼8–25 μm between solid-state spin qubits.

Further, we exploit the high spin-symmetry PSH state to derive a closed-form expression for the weak localization magnetoconductivity -- the paradigmatic signature of spin-orbit coupling in quantum transport. The small parameter of the theory is the deviation from the symmetry state introduced by the mismatch of the linear terms and by the cubic Dresselhaus term. In this regime, we perform quantum transport experiments in GaAs quantum wells. Top and back gates allow independent tuning of the Rashba and Dresselhaus terms in order to explore the broken-symmetry regime where the formula applies. We present a reliable two-step method to extract all parameters from fits to the new expression, obtaining excellent agreement with recent experiments. This provides experimental confirmation of the new theory, and advances spin-orbit coupling towards a powerful resource in emerging quantum technologies.

[1] Dettwiler et al., Phys. Rev. X7, 031010 (2017).   

Spin-orbit coupling effects in nonlinear optical response

We investigate the effects of the spin-obit (SO) coupling in the shift current response of solids within the independent-particle approximation. The SO coupling introduces new terms which depend on Berry connections and strongly modify the optical response to circular polarization. Applications two-dimensional ferroelectrics and single-layer Transitions Metal Dichalcogenides are discussed.   

Surface Berry plasmons in magnetic semiconductors

The concept of ``surface Berry plasmons" is studied in the concrete instance of a magnetic semiconductor in which the Berry curvature, generated by atomic spin-orbit interaction, has opposite signs for carriers spin parallel or antiparallel to the magnetization. By using collisionless hydrodynamic equations with appropriate boundary conditions, we study both the surface plasmons of a three-dimensional magnetic semiconductor and the edge plasmons of a two-dimensional one. In the 3D case we calculate the dependence of the plasmon frequency on the angle between the direction of propagation and the bulk magnetization. In the 2D case we find that the frequency of the plasmon depends on the direction of propagation along the edge. These Berry curvature effects are compared and contrasted with the anisotropies induced in the plasmon dispersion by an external magnetic field in the absence of Berry curvature. We argue that Berry curvature effects may be used to control the direction of propagation of the surface plasmons, and create a link between plasmonics and spintronics.   

Optical Response in Semiconductor Quantum Wells in proximity to Chiral p-wave Supercon- ductor

By using gauge-invariant optical Bloch equation, we investigate the optical response to
the linearly polarized THz pulses in semiconductor quantum wells in proximity to chiral p-wave superconductor, in which time-reversal symmetry is spontaneously broken.
We show that during the optical process, the Higgs mode and quasiparticle charge imbalance
are excited, leading to oscillations of the p-wave gap and effective chemical potential, respectively. Moreover, we study the nonlinear optical conductivity tensor including usual (diagonal) part similar to conventional superconductivity, as well as magneto-optical (off-diagonal) one present in superconductors with spontaneous time-reversal breaking. Finally, we extend the gauge-invariant optical Bloch equation into non-Abelian gauge-invariant one with spatially dependent magnetization. As an application, we also investigate the optical response to linearly polarized THz pulses in chiral p-wave superconducting semiconductor quantum wells in proximity to transverse conical ferromagnets. Besides the Higgs mode,
quasiparticle charge imbalance and nonlinear optical conductivity tensor, the properties of
triplet vector during the optical process are also revealed.   

Coupled Orbital and Spin Dynamics of Particles with Magnetic Moments

We propose a consistent unified framework for describing the coupled dynamics of orbital motion and magnetic moments for generic charge carriers. Our general approach naturally covers phenomena such as spin precession and magnetization transport, including the spin Hall effect and its inverse, but it also applies to apparently unrelated phenomena such as the Aharonov-Casher effect and the Stern-Gerlach effect. We will present selected examples to illustrate the power of our approach.   

Quantum transport theory: numerics and dynamics

In recent years a number of systems have been identified in which momentum-space Berry phases play an important role in determining transport coefficients. Examples include the anomalous and spin Hall effects in spintronics and the negative magnetoresistance of Weyl semimetals. A convenient quantum kinetic formalism has recently been developed which is intended to allow these transport effects to be evaluated in real materials. As discussed in Refs. [1, 2], the formalism treats linear response to static electric field and nonlinear response to static magnetic field in the low-field regime. We present a numerical implementation of this formalism, validated by comparing with analytic results for simple models but applicable to general tight-binding models. We also discuss the extension of this formalism to consider nonlinear response to a time-varying electric field, with potential application to the valley Hall effect.

[1] D. Culcer, A. Sekine, and A. H. MacDonald, Phys. Rev. B 96, 035106 (2017).
[2] A. Sekine, D. Culcer, and A. H. MacDonald, arXiv:1706.01200.   

Strong Influence of Spin-orbit Coupling on Magnetotransport in Two-dimensional Hole Systems

Low-dimensional hole systems have attracted considerable recent attention in the context of nanoelectronics and quantum information. They exhibit strong spin-orbit coupling but a weak hyperfine interaction, which allows fast, low-power electrical spin manipulation and potentially increased coherence times while their effective spin-3/2 is responsible for physics inaccessible in electron systems. However, experimentally measuring, identifying, and quantifying spin-orbit coupling effects in transport, such as electrically-induced spin polarizations and spin Hall currents, are challenging. We show that the magnetotransport properties of two-dimensional hole systems display strong signatures of the spin-orbit interaction. Specifically, the low-magnetic field Hall coefficient and longitudinal conductivity contain a contribution that is second order in the spin-orbit interaction coefficient and is non-linear in the carrier number density. We propose an experimental setup to probe these spin-orbit dependent magnetotransport properties, which will permit one to extract the spin-orbit coefficient directly from the magnetotransport.   

Spin Hall Effect in Ferroelectric Rashba Semiconductors

The coupling of different functionalities in materials has been playing an increasingly significant role in the design and discovery of devices with novel properties. In this work, we study the Spin Hall Effect (SHE) in Ferro-Electric Rashba Semi-Conductors(FERSC) in order to explore the possibility of controlling spin transport via an electric field. This study is motivated by the discovery of the spin-electric coupling effect in FERSC (eg. GeTe) which allows the switch and control of the spin texture via an electric field, and the fact that band splitting together with electric filed could eventually lead to a universal spin hall conductivity. A detailed theoretical investigation of systems such as GeTe, SnTe, and some hexagonal ABC semiconductors (eg. LiBeSb, NaZnSb) will be presented. These results are obtained using the recently developed PAOFLOW package (http://www.aflowlib.org/src/paoflow/) integrated in AFLOWπ high-throughput framework (http://www.aflowlib.org/src/aflowpi/).
  

Anomalous Hall effect in epitaxial spinel NiCo2O4 films

We report the magnetotransport studies of the spinel ferrimagnetic NiCo₂O₄ (NCO) thin films. NCO has an inverse spinel structure with the Neel temperature T_N above room temperature. We deposited epitaxial NCO films as thin as 2 u.c. (~1.6 nm) on (001) MgAl₂O₄ substrates using off-axis magnetron sputtering, with high crystallinity and atomically smooth surface achieved. The NCO films possess an out-of-plane magnetic easy axis. A robust anomalous Hall effect (AHE) has been observed at the temperature range from 2 K to T_N of 330 K, which changes sign at ~190 K. We discuss the possible mechanisms that determine the AHE signal in the NCO films. Our study reveals the complex energy landscape in NCO due to the competition of the crystalline field with the charge and spin degrees of freedom.