In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

New perspectives for Rashba spin–orbit coupling

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.

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One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.

Keldysh technique and non-linear σ-model: basic principles and applications

Two quantum point contacts are used to respectively inject and detect spins by purely electrical means in an all-semiconductor spin transistor. The spin field-effect transistor envisioned by Datta and Das1 opens a gateway to spin information processing2,3. Although the coherent manipulation of electron spins in semiconductors is now possible4,5,6,7,8, the realization of a functional spin field-effect transistor for information processing has yet to be achieved, owing to several fundamental challenges such as the low spin-injection efficiency due to resistance mismatch9, spin relaxation and the spread of spin precession angles. Alternative spin transistor designs have therefore been proposed10,11, but these differ from the field-effect transistor concept and require the use of optical or magnetic elements, which pose difficulties for incorporation into integrated circuits. Here, we present an all-electric and all-semiconductor spin field-effect transistor in which these obstacles are overcome by using two quantum point contacts as spin injectors and detectors. Distinct engineering architectures of spin–orbit coupling are exploited for the quantum point contacts and the central semiconductor channel to achieve complete control of the electron spins (spin injection, manipulation and detection) in a purely electrical manner. Such a device is compatible with large-scale integration and holds promise for future spintronic devices for information processing.

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All-electric all-semiconductor spin field-effect transistors

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

https://iopscience.iop.org/article/10.1088/1361-6633/aaa98a/pdf

Coherent control of single electrons: a review of current progress.

Experimental evidence is presented showing that strong spin polarization in side-gated quantum point contacts can be achieved electrically, making these structures attractive for future spintronic applications.

All-electric quantum point contact spin-polarizer

The controlled creation, manipulation and detection of spin-polarized currents by purely electrical means remains a central challenge of spintronics. Efforts to meet this challenge by exploiting the coupling of the electron orbital motion to its spin, in particular Rashba spin-orbit coupling, have so far been unsuccessful. Recently, it has been shown theoretically that the confining potential of a small current-carrying wire with high intrinsic spin-orbit coupling leads to the accumulation of opposite spins at opposite edges of the wire, though not to a spin-polarized current. Here, we present experimental evidence that a quantum point contact -- a short wire -- made from a semiconductor with high intrinsic spin-orbit coupling can generate a completely spin-polarized current when its lateral confinement is made highly asymmetric. By avoiding the use of ferromagnetic contacts or external magnetic fields, such quantum point contacts may make feasible the development of a variety of semiconductor spintronic devices.

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All-Electric Quantum Point Contact Spin Polarizer

The Coulomb drag between two spatially separated one-dimensional (1D) electron systems in lithographically fabricated 2??m long quantum wires is studied experimentally. The drag voltage VD shows peaks as a function of a gate voltage which shifts the position of the Fermi level relative to the 1D subbands. The maximum in VD and the drag resistance RD occurs when the 1D subbands of the wires are aligned and the Fermi wave vector is small. The drag resistance is found to decrease exponentially with interwire separation. In the temperature region 0.2?K?T?1?K, RD decreases with increasing temperature in a power-law fashion RDTx with x ranging from -0.6 to -0.77 depending on the gate voltage. We interpret our data in terms of the Tomonaga-Luttinger liquid theory.

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Experimental studies of Coulomb drag between ballistic quantum wires

A nonequilibrium Green's function formalism is used to study the conductance of a side-gated quantum point contact (QPC) in the presence of the lateral spin-orbit coupling (LSOC). A small difference of bias voltage between the two side gates (SGs) leads to an inversion asymmetry in the LSOC between the opposite edges of the channel. In the single-electron modeling of transport, this triggers a spontaneous but insignificant spin polarization in the QPC. However, the spin polarization of the QPC is enhanced substantially when the effect of electron-electron interaction is included. The spin polarization is strong enough to result in the occurrence of a conductance plateau at $0.5{G}_{0}$ $({G}_{0}=2{e}^{2}/h)$ in the absence of any external magnetic field. In our simulations of a model QPC device, the 0.5 plateau is found to be quite robust and survives up to a temperature of 40 K. The spontaneous spin polarization and the resulting magnetization of the QPC can be reversed by flipping the polarity of the source to drain bias or the potential difference between the two SGs. These numerical simulations are in good agreement with recent experimental results for side-gated QPCs made from the low band-gap semiconductor InAs.

Possible origin of the 0.5 plateau in the ballistic conductance of quantum point contacts

The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. In this review, we review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, also known as quantum wires, in the absence of inter-wire tunnelling, to focus on these features and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum drag resistance RD when the one-dimensional subbands of the two quantum wires are aligned and the Fermi wave vector kF is small, and also an exponential decay of RD with increasing inter-wire separation, both features confirmed by experimental observations. A crucial difference between the two theoretical models emerges in the temperature dependence of the drag effect. Although the FL theory predicts a linear temperature dependence, the LL theory promises a rich and varied dependence on temperature depending on the relative magnitudes of the energy and length scales of the systems. At very low temperatures, the drag resistance may diverge due to the formation of locked charge density waves. At higher temperatures, it should show a power-law dependence on temperature, RD Tx, experimentally confirmed in a narrow temperature range, where x is determined by the Luttinger liquid parameters. The spin degree of freedom plays an important role in the LL theory in predicting the features of the drag effect and is crucial for the interpretation of experimental results. Substantial experimental and theoretical work remains to be done for a comprehensive understanding of one-dimensional Coulomb drag.

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P. Debray

Papers

All-electric quantum point contact spin-polarizer

All-Electric Quantum Point Contact Spin Polarizer

Experimental studies of Coulomb drag between ballistic quantum wires

Possible origin of the 0.5 plateau in the ballistic conductance of quantum point contacts

Coulomb drag between ballistic one-dimensional electron systems