Wigner crystal physics in quantum wires

Suspended semiconductor nanostructures: physics and technology

The current state of research on quantum and ballistic electron transport in semiconductor nanostructures with a two-dimensional electron gas separated from the substrate and nanoelectromechanical systems is reviewed. These nanostructures fabricated using the surface nanomachining technique have certain unexpected features in comparison to their non-suspended counterparts, such as additional mechanical degrees of freedom, enhanced electron-electron interaction and weak heat sink. Moreover, their mechanical functionality can be used as an additional tool for studying the electron transport, complementary to the ordinary electrical measurements. The article includes a comprehensive review of spin-dependent electron transport and multichannel effects in suspended quantum point contacts, ballistic and adiabatic transport in suspended nanostructures, as well as investigations on nanoelectromechanical systems. We aim to provide an overview of the state-of-the-art in suspended semiconductor nanostructures and their applications in nanoelectronics, spintronics and emerging quantum technologies.

Electronic properties of semiconductor quantum wires for shallow symmetric and asymmetric confinements

Quantum wires (QWs) and quantum point contacts (QPCs) have been realized in GaAs/AlGaAs heterostructures in which a two-dimensional electron gas resides at the interface between GaAs and AlGaAs layered semiconductors. The electron transport in these structures has previously been studied experimentally and theoretically, and a 0.7 conductance anomaly has been discovered. The present paper is motivated by experiments with a QW in shallow symmetric and asymmetric confinements that have shown additional conductance anomalies at zero magnetic field. The proposed device consists of a QPC that is formed by split gates and a top gate between two large electron reservoirs. This paper is focussed on the theoretical study of electron transport through a wide top-gated QPC in a low-density regime and is based on density functional theory. The electron-electron interaction and shallow confinement make the splitting of the conduction channel into two channels possible. Each of them becomes spin-polarized at certain split and top gates voltages and may contribute to conductance giving rise to additional conductance anomalies. For symmetrically loaded split gates two conduction channels contribute equally to conductance. For the case of asymmetrically applied voltage between split gates conductance anomalies may occur between values of 0.25(2e²/h) and 0.7(2e²/h) depending on the increased asymmetry in split gates voltages. This corresponds to different degrees of spin-polarization in the two conduction channels that contribute differently to conductance. In the case of a strong asymmetry in split gates voltages one channel of conduction is pinched off and just the one remaining channel contributes to conductance. We have found that on the perimeter of the anti-dot there are spin-polarized states. These states may also contribute to conductance if the radius of the anti-dot is small enough and tunneling between these states may occur. The spin-polarized states in the QPC with shallow confinement tuned by electric means may be used for the purposes of quantum technology.

Interactions and non-magnetic fractional quantization in one-dimension

In this Perspective article, we present recent developments on interaction effects on the carrier transport properties of one-dimensional (1D) semiconductor quantum wires fabricated using the GaAs/AlGaAs system, particularly the emergence of the long predicted fractional quantization of conductance in the absence of a magnetic field. Over three decades ago, it was shown that transport through a 1D system leads to integer quantized conductance given by N·2e2/h, where N is the number of allowed energy levels (N = 1, 2, 3, …). Recent experiments have shown that a weaker confinement potential and low carrier concentration provide a testbed for electrons strongly interacting. The consequence leads to a reconfiguration of the electron distribution into a zigzag assembly which, unexpectedly, was found to exhibit quantization of conductance predominantly at 1/6, 2/5, 1/4, and 1/2 in units of e2/h. These fractional states may appear similar to the fractional states seen in the Fractional Quantum Hall Effect; however, the system does not possess a filling factor and they differ in the nature of their physical causes. The states may have promise for the emergent topological quantum computing schemes as they are controllable by gate voltages with a distinct identity.

A Short Review of One-Dimensional Wigner Crystallization

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

Fractional Conductance in Strongly Interacting 1D Systems

We study one-dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time-reversal symmetry holds, they may lead to two-terminal fractional quantized conductance and fractional shot noise. The condition on the commensurability of the Fermi momenta of the different channels and the strength of the interactions resulting in such remarkable phenomena are explored using Abelian bosonization. Finite temperature and length effects are accounted for by a generalization of the Luther-Emery refermionization at specific values of the interaction strength, in the strongly interacting regime. We discuss the connection of our model to recent experiments in a confined two-dimensional electron gas, featuring possible fractional conductance plateaus, including situations with a zero magnetic field, when time-reversal symmetry is conserved. One of the most dominant observed fractions, with two-terminal conductance equal to 2/5(e^{2}/h), is found in several scenarios of our model. Finally, we discuss how at very small energy scales the conductance returns to an integer value and the role of disorder.

Zero-Magnetic Field Fractional Quantum States

Since the discovery of the fractional quantum Hall effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing magnetic field. Although various situations have been theoretically envisaged, particularly lattice models in which band flattening resembles Landau levels, the predicted fractions have never been observed. In this Letter, we show that odd and even denominator fractions can be observed, and manipulated, in the absence of a quantizing magnetic field, when a low-density electron system in a GaAs based one-dimensional quantum wire is allowed to relax in the second dimension. It is suggested that such a relaxation results in formation of a zigzag array of electrons with ring paths which establish a cyclic current and a resultant lowering of energy. The behavior has been observed for both symmetric and asymmetric confinement but increasing the asymmetry of the confinement potential, to result in a flattening of confinement, enhances the appearance of new fractional states. We find that an in-plane magnetic field induces new even denominator fractions possibly indicative of electron pairing. The new quantum states described here have implications both for the physics of low dimensional electron systems and also for quantum technologies. This work will enable further development of structures which are designed to electrostatically manipulate the electrons for the formation of particular configurations. In turn, this could result in a designer tailoring of fractional states to amplify particular properties of importance in future quantum computation.

Imaging the Zigzag Wigner Crystal in Confinement-Tunable Quantum Wires

The existence of Wigner crystallization, one of the most significant hallmarks of strong electron correlations, has to date only been definitively observed in two-dimensional systems. In one-dimensional (1D) quantum wires Wigner crystals correspond to regularly spaced electrons; however, weakening the confinement and allowing the electrons to relax in a second dimension is predicted to lead to the formation of a new ground state constituting a zigzag chain with nontrivial spin phases and properties. Here we report the observation of such zigzag Wigner crystals by use of on-chip charge and spin detectors employing electron focusing to image the charge density distribution and probe their spin properties. This experiment demonstrates both the structural and spin phase diagrams of the 1D Wigner crystallization. The existence of zigzag spin chains and phases which can be electrically controlled in semiconductor systems may open avenues for experimental studies of Wigner crystals and their technological applications in spintronics and quantum information.

Temperature Dependence of Spin-Split Peaks in Transverse Electron Focusing

We present experimental results of transverse electron-focusing measurements performed using n-type GaAs. In the presence of a small transverse magnetic field (B_⊥), electrons are focused from the injector to detector leading to focusing peaks periodic in B_⊥. We show that the odd-focusing peaks exhibit a split, where each sub-peak represents a population of a particular spin branch emanating from the injector. The temperature dependence reveals that the peak splitting is well defined at low temperature whereas it smears out at high temperature indicating the exchange-driven spin polarisation in the injector is dominant at low temperatures.

True Bilayer Exciton Condensate of One-Dimensional Electrons

We theoretically predict that a true bilayer exciton condensate, characterized by off-diagonal long-range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin-Wagner theorem. Electron-hole interactions then amplify this tendency towards off-diagonal long-range order, enhancing the condensate properties by more than an order of magnitude over the noninteracting limit. We show that the temperatures below which a substantial condensate fraction would form could reach hundreds of Kelvin, a benefit of the weak screening in one-dimensional systems.

Self-Assembled Wigner Crystals as Mediators of Spin Currents and Quantum Information

Technological applications of many-body structures that emerge in gated devices under minimal control are largely unexplored. Here we show how emergent Wigner crystals in a semiconductor quantum wire can facilitate a pivotal requirement for a scalable quantum computer, namely, transmitting quantum information encoded in spins faithfully over a distance of micrometers. The fidelity of the transmission is remarkably high, faster than the relevant decohering effects, independent of the details of the spatial charge configuration in the wire, and realizable in dilution refrigerator temperatures. The transfer can evidence near unitary many-body nonequilibrium dynamics hitherto unseen in a solid-state device. It could also be useful in spintronics as a method for pure spin current over a distance without charge movement.

Thermally enhanced Wigner oscillations in two-electron 1D quantum dots

Motivated by a recent experiment (Pecker et al 2013 Nat. Phys. 9 576), we study the stability, with respect to thermal effects, of Friedel and Wigner density fluctuations for two electrons trapped in a one-dimensional quantum dot. Diagonalizing the system exactly, the finite-temperature average electron density is computed. While the weak and strong interaction regimes display a Friedel oscillation or a Wigner molecule state at zero temperature, which as expected smear and melt as the temperature increases, a peculiar thermal enhancement of Wigner correlations in the intermediate interaction regime is found. We demonstrate that this effect is due to the presence of two different characteristic temperature scales: T(F), dictating the smearing of Friedel oscillations, and T(W), smoothing Wigner oscillations. In the early Wigner molecule regime, for intermediate interactions, T(F) < T(W) leading to the enhancement of the visibility of Wigner oscillations. These results complement those obtained within the Luttinger liquid picture, valid for larger numbers of particles.

Probing Wigner correlations in a suspended carbon nanotube

The influence of electron–vibron coupling on the transport properties of a strongly interacting quantum dot built in a suspended carbon nanotube (CNT) is analyzed. The latter is probed by a charged atomic force microscope tip scanned along the axis of the CNT which induces oscillations of the chemical potential and of the linear conductance. These oscillations are due to the competition between finite-size effects and the formation of a Wigner molecule for strong interactions. Such oscillations are shown to be suppressed by the electron–vibron coupling. The suppression is more pronounced in the regime of weak Coulomb interactions, which ensures that probing Wigner correlations in such a system is in principle possible.

Zigzag phase transition in quantum wires

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with a linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.

Intersubband edge singularity in metallic nanotubes

The tunneling density of states of both the massless and massive (gapped) particles in metallic carbon nanotubes is known to have an anomalous energy dependence. This is the result of coupling to multiple low-energy bosonic excitation (plasmons). For both kinds of particles the ensuing effect is the suppression of the density of states by electron-electron interactions. We demonstrate that the optical absorption between gapless and gapped states is affected by the many-body effects in the opposite way. The absorption probability is enhanced compared with the noninteracting value and develops a power-law frequency dependence, A(ω) ∝ (ω - Δ)(-γ), where γ≈0.2 for typical nanotubes.

Equilibration of Luttinger liquid and conductance of quantum wires

Luttinger liquid theory describes one-dimensional electron systems in terms of noninteracting bosonic excitations. In this approximation thermal excitations are decoupled from the current flowing through a quantum wire, and the conductance is quantized. We show that relaxation processes not captured by the Luttinger liquid theory lead to equilibration of the excitations with the current and give rise to a temperature-dependent correction to the conductance. In long wires, the magnitude of the correction is expressed in terms of the velocities of bosonic excitations. In shorter wires it is controlled by the relaxation rate.

Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with Yukawa interactions

We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.

Dirac's method for constraints: an application to quantum wires

We investigate the Hubbard model in the limit U = ∞, which is equivalent to the statistical condition of exclusion of double occupancy. We solve this problem using Dirac's method for constraints. The constraints are solved within the bosonization method. We find that the constraints modify the anomalous commutator. We apply this theory to quantum wires at finite temperatures where the Hubbard interaction is U = ∞. We find that the anomalous commutator induced by the constraints gives rise to the 0.7 anomalous conductance.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) ≥ 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

Equilibration of a one-dimensional Wigner crystal

Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.

A scaling approach for interacting quantum wires--a possible explanation for the 0.7 anomalous conductance

We consider a weakly interacting finite wire with short and long range interactions. The long range interactions enhance the 4k(F) scattering and renormalize the wire to a strongly interacting limit. For large screening lengths, the renormalized charge stiffness Luttinger parameter K(eff) decreases to [Formula: see text], giving rise to a Wigner crystal at T=0 with an anomalous conductance at finite temperatures. For short screening lengths, the renormalized Luttinger parameter K(eff) is restricted to ½≤K(eff)≤1. As a result, at temperatures larger than the magnetic exchange energy we find an interacting metal which, for K(eff)≈½, is equivalent to the Hubbard U−>∞ model, with the anomalous conductance G≈e(2)/h.

Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire

We consider a quantum wire with two subbands of spin-polarized electrons in the presence of strong interactions. We focus on the quantum phase transition when the second subband starts to get filled as a function of gate voltage. Performing a one-loop renormalization group analysis of the effective Hamiltonian, we identify the critical fixed-point theory as a conformal field theory having an enhanced SU(2) symmetry and central charge 3/2. While the fixed point is Lorentz invariant, the effective "speed of light" nevertheless vanishes at low energies due to marginally irrelevant operators leading to a diverging critical specific heat coefficient.