Stretching and breaking symmetry of the persistent spin helix in quantum transport

As a result of relativistic transformation, electrons moving through an electric field, experience an effective magnetic field, the spin orbit (SO) field, whose direction depends on the momentum and couples to the electron spin. The SO interaction has become a versatile resource in fundamental semiconductor research and is at the heart of semiconductor spintronics. In two dimensional zinc blende structures, the Rashba and Dresselhaus SO field, are the two dominant contributions. While both are linear in momentum, the Dresselhaus SO field also possesses a cubic contribution in momentum. In this thesis, the persistent spin helix (PSH) state is investigated in transport measurements. The PSH results from balancing the strengths of the two dominant contributions to SO coupling, the Rashba parameter alpha and the renormalized Dresselhaus parameter beta. In this case the SO field is uniaxial and spins are robust against momentum scattering. Quantum corrections to conductivity serve as a convenient tool to detect this symmetry, which exhibits weak localization at the PSH symmetry point and weak antilocalization, if the PSH symmetry is broken. In the first part of this thesis we use the transition from weak antilocaliztion to weak localization to detect the PSH state. Using a top gate and back gate we demonstrate control of the Rashba SO coupling and, for the first time, tuning of the renormalized linear Dresselhaus term beta, independently of each other. This allows us to find the PSH state not just for one particular gate configuration but for a continuous set of gate configurations, where the ratio alpha/beta remains to unity but their overall strength varies. This enables a new concept, the stretchable PSH, where the length for a 2pi rotation of the spins becomes tunable. We combine the transport data with numerical self-consistent simulations and can determine all SO coefficients. Stretching of the PSH allows to convey spin polarizations over long distances of up to 25 mum, before their spin gets randomized by the cubic Dresselhaus term. Furthermore, the stretchable PSH allows to coherently control spin rotations at a fixed position. In the second part of this thesis, we break the PSH symmetry to extract the SO coefficients purely from transport experiments. We first derive a closed-form expression for the quantum corrections to the conductivity, in the vicinity of the PSH state, which includes the Rashba and linear, as well as the cubic Dresselhaus term. In symmetrically doped wafers with higher density the cubic Dresselhaus term is strong and breaks the PSH symmetry, which is characterized by the reappearance of weak antilocalization. This allows us to determine the cubic Dresselhaus term from fits to the new expression. In the second stage we tune away from the PSH symmetry and are able to extract the linear SO terms by keeping the cubic term fixed. We are thus able to unambiguously determine fundamental band structure parameters that define the Rashba and Dresselhaus SO strength. The obtained results between the two experiments are in very good agreement and compare very well with recent optical studies

Closed-form weak localization magnetoconductivity in quantum wells with arbitrary Rashba and Dresselhaus spin-orbit interactions

We derive a closed-form expression for the weak localization (WL) corrections to the magnetoconductivity of a 2D electron system with arbitrary Rashba $\alpha$ and Dresselhaus $\beta$ (linear) and $\beta_3$ (cubic) spin-orbit interaction couplings, in a perpendicular magnetic field geometry. In a system of reference with an in-plane $\hat{z}$ axis chosen as the high spin-symmetry direction at $\alpha = \beta$, we formulate a new algorithm to calculate the three independent contributions that lead to WL. The antilocalization is counterbalanced by the term associated with the spin-relaxation along $\hat{z}$, dependent only on $\alpha - \beta$. The other term is generated by two identical scattering modes characterized by spin-relaxation rates which are explicit functions of the orientation of the scattered momentum. Excellent agreement is found with data from GaAs quantum wells, where in particular our theory correctly captures the shift of the minima of the WL curves as a function of $\alpha/\beta$. This suggests that the anisotropy of the effective spin relaxation rates is fundamental to understanding the effect of the SO coupling in transport.Comment: 5 pages, 2 figure

Stretchable persistent spin helices in GaAs quantum wells

The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly-oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba $\alpha$ and Dresselhaus $\beta$ couplings to equal $\it{fixed}$ strengths $\alpha=\beta$, the total SO field becomes unidirectional thus rendering the electron spins immune to dephasing due to momentum scattering. A robust persistent spin helix (PSH) has already been experimentally realized at this singular point $\alpha=\beta$. Here we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with a technique that allows for independent electrical control over the SO couplings via top gate voltage $V_T$ and back gate voltage $V_B$. We demonstrate for the first time the gate control of $\beta$ and the $\it{continuous\,locking}$ of the SO fields at $\alpha=\beta$, i.e., we are able to vary both $\alpha$ and $\beta$ controllably and continuously with $V_T$ and $V_B$, while keeping them locked at equal strengths. This makes possible a new concept: "stretchable PSHs", i.e., helical spin patterns with continuously variable pitches $P$ over a wide parameter range. The extracted spin-diffusion lengths and decay times as a function of $\alpha/\beta$ show a significant enhancement near $\alpha/\beta=1$. Since within the continuous-locking regime quantum transport is diffusive (2D) for charge while ballistic (1D) for spin and thus amenable to coherent spin control, stretchable PSHs could provide the platform for the much heralded long-distance communication $\sim 8 - 25$ $\mu$m between solid-state spin qubits.Comment: 5 color figures, with supplementary info available on arXiv. arXiv admin note: substantial text overlap with arXiv:1403.351

Template-Assisted Scalable Nanowire Networks

This is an open access article published under an ACS AuthorChoice License. See Standard ACS AuthorChoice/Editors' Choice Usage Agreement - https://pubs.acs.org/page/policy/authorchoice_termsofuse.htmlTopological qubits based on Majorana Fermions have the potential to revolutionize the emerging field of quantum computing by making information processing significantly more robust to decoherence. Nanowires are a promising medium for hosting these kinds of qubits, though branched nanowires are needed to perform qubit manipulations. Here we report a gold-free templated growth of III-V nanowires by molecular beam epitaxy using an approach that enables patternable and highly regular branched nanowire arrays on a far greater scale than what has been reported thus far. Our approach relies on the lattice-mismatched growth of InAs on top of defect-free GaAs nanomembranes yielding laterally oriented, low-defect InAs and InGaAs nanowires whose shapes are determined by surface and strain energy minimization. By controlling nanomembrane width and growth time, we demonstrate the formation of compositionally graded nanowires with cross-sections less than 50 nm. Scaling the nanowires below 20 nm leads to the formation of homogeneous InGaAs nanowires, which exhibit phase-coherent, quasi-1D quantum transport as shown by magnetoconductance measurements. These results are an important advance toward scalable topological quantum computing

Stretchable persistent spin helices in GaAs quantum wells

The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba α and renormalized Dresselhaus β couplings to equal fixed strengths α = β, the total SO field becomes unidirectional, thus rendering the electron spins immune to decay due to momentum scattering. A robust persistent spin helix (PSH), i.e., a helical spin-density wave excitation with constant pitch P = 2 π / Q , Q = 4 m α / ℏ2, has already been experimentally realized at this singular point α = β, enhancing the spin lifetime by up to 2 orders of magnitude. Here, we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with independent electrical control over the SO couplings via top gate voltage VT and back gate voltage VB to extract all SO couplings when combined with detailed numerical simulations. We demonstrate for the first time the gate control of the renormalized β and the continuous locking of the SO fields at α = β i.e., we are able to vary both α and β controllably and continuously with VT and VB, while keeping them locked at equal strengths. This makes possible a new concept: "stretchable PSHs," i.e., helical spin patterns with continuously variable pitches P over a wide parameter range. Stretching the PSH, i.e., gate controlling P while staying locked in the PSH regime, provides protection from spin decay at the symmetry point α = β, thus offering an important advantage over other methods. This protection is limited mainly by the cubic Dresselhaus term, which breaks the unidirectionality of the total SO field and causes spin decay at higher electron densities. We quantify the cubic term, and find it to be sufficiently weak so that the extracted spin-diffusion lengths and decay times show a significant enhancement near α = β. Since within the continuous-locking regime quantum transport is diffusive (2D) for charge while ballistic (1D) for spin and thus amenable to coherent spin control, stretchable PSHs could provide the platform for the much heralded long-distance communication ~8-25 μm between solid-state spin qubits, where the spin diffusion length for α ≠ β is an order of magnitude smaller

Symmetry breaking of the persistent spin helix in quantum transport

We exploit the high-symmetry persistent spin helix state obtained for similar Rashba and linear Dresselhaus interactions in a quantum well to revisit the weak localization problem within a perturbative approach in a Landau level formulation. We define the small parameter of the theory as the deviation from the symmetry state introduced by the mismatch of the linear terms and by the strength of the cubic Dresselhaus term. In the vicinity of the helix state, the SO field becomes uniaxial, offering a natural direction of spin quantization, thus defining the z axis within the 2D plane. In contrast to previous theories, this reveals a full decoupling of the Cooperon triplet scattering modes as well as decoupled Landau levels, to lowest order in the small parameter. This makes it possible to derive a closed-form expression for the weak localization magnetoconductivity, thus providing a new paradigm of localization in the weakly-broken spin symmetry regime. We perform quantum transport experiments in GaAs quantum wells, finding very good agreement with the new theory. We present a reliable two-step method to extract the SO and transport parameters from fits of the new expression, obtaining excellen tagreement with recent experiments. This is an important step towards engineering and controlling the spin-orbit interaction as a powerful resource in emerging quantum technologies