Incipient formation of an electron lattice in a weakly confined quantum wire

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.

Two-dimensional supersolidity in a dipolar quantum gas

Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties^1-5. Although supersolidity has not been observed in solid helium (despite much effort)⁶, ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms^7-16. However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains^17-20, quantum wires^21,22 and theoretically in chains of individual dipolar particles^23,24. This opens the possibility of studying rich excitation properties^25-28, including vortex formation^29-31, and ground-state phases with varied geometrical structure^7,32 in a highly flexible and controllable system.

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.

Valley Subband Splitting in Bilayer Graphene Quantum Point Contacts

We report a study of one-dimensional subband splitting in a bilayer graphene quantum point contact in which quantized conductance in steps of 4e^{2}/h is clearly defined down to the lowest subband. While our source-drain bias spectroscopy measurements reveal an unconventional confinement, we observe a full lifting of the valley degeneracy at high magnetic fields perpendicular to the bilayer graphene plane for the first two lowest subbands where confinement and Coulomb interactions are the strongest and a peculiar merging or mixing of K and K^{'} valleys from two nonadjacent subbands with indices (N,N+2), which are well described by our semiphenomenological model.

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.

Self-organised fractional quantisation in a hole quantum wire

We have investigated hole transport in quantum wires formed by electrostatic confinement in strained germanium two-dimensional layers. The ballistic conductance characteristics show the regular staircase of quantum levels with plateaux at n2e ²/h, where n is an integer, e is the fundamental unit of charge and h is Planck's constant. However as the carrier concentration is reduced, the quantised levels show a behaviour that is indicative of the formation of a zig-zag structure and new quantised plateaux appear at low temperatures. In units of 2e ²/h the new quantised levels correspond to values of n  =  1/4 reducing to 1/8 in the presence of a strong parallel magnetic field which lifts the spin degeneracy but does not quantise the wavefunction. A further plateau is observed corresponding to n  =  1/32 which does not change in the presence of a parallel magnetic field. These values indicate that the system is behaving as if charge was fractionalised with values e/2 and e/4, possible mechanisms are discussed.

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.

Probing dopants in wide semiconductor quantum point contacts

Effects of randomly distributed impurities on conductance, spin polarization and electron localization in realistic gated semiconductor quantum point contacts (QPCs) have been simulated numerically. To this end density functional theory in the local spin-density approximation has been used. In the case when the donor layer is embedded far from the two-dimensional electron gas (2DEG) the electrostatic confinement potential exhibits the conventional parabolic form, and thus the usual ballistic transport phenomena take place both in the devices with split gates alone and with an additional metallic gate on the top. In the opposite case, i.e. when the randomly distributed donors are placed not far away from the 2DEG layer, there are drastic changes like the localization of electrons in the vicinity of confinement potential minima which give rise to fluctuations in conductance and resonances. The conductance as a function of the voltage applied to the top gate for asymmetrically charged split gates has been calculated. In this case resonances in conductance caused by randomly distributed donors are shifted and decrease in amplitude while the anomalies caused by interaction effects remain unmodified. It has been also shown that for a wide QPC the polarization can appear in the form of stripes. The importance of partial ionization of the random donors and the possibility of short range order among the ionized donors are emphasized. The motivation for this work is to critically evaluate the nature of impurities and how to guide the design of high-mobility devices.

Coherent terahertz photonics

We present a review of recent developments in THz coherent systems based on photonic local oscillators. We show that such techniques can enable the creation of highly coherent, thus highly sensitive, systems for frequencies ranging from 100 GHz to 5 THz, within an energy efficient integrated platform. We suggest that such systems could enable the THz spectrum to realize its full applications potential. To demonstrate how photonics-enabled THz systems can be realized, we review the performance of key components, show recent demonstrations of integrated platforms, and give examples of applications.

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.

Bound states, electron localization and spin correlations in low-dimensional GaAs/AlGaAs quantum constrictions

We analyze the occurrence of local magnetization and the effects of electron localization in different models of quantum point contacts (QPCs) using spin-relaxed density functional theory (DFT/LSDA) by means of numerical simulations. In the case of soft confinement potentials the degree of localization is weak and we therefore observe only traces of partial electron localization in the middle of the QPC. In the pinch-off regime there is, however, distinct accumulation at the QPC edges. At the other end, strong confinement potential, low-electron density in the leads and top or implant gates favor electron localization. In such cases one may create a variety of electron configurations from a single localized electron to more complex structures with multiple rows and Wigner lattices.

Evidence for reentrant melting in a quasi-one-dimensional Wigner crystal

We demonstrate, for the first time, that a quasi-one-dimensional Wigner crystal formed on superfluid (4)He with only a few electrons in the confined direction shows reentrant melting. By transport measurements, we find oscillations in current as a function of linear density measured at a fixed driving voltage at high temperatures, and detailed analyses of transport data reveal that the oscillations originate from the periodic reduction of the melting temperature as a function of linear density. Comparison with the structural phase diagram suggests that the reduction of the melting temperature occurs at the boundaries between the different structures as the structure evolves from a single, double, followed by a triple chain.

Commensurability-dependent transport of a Wigner crystal in a nanoconstriction

We present the first transport measurements of a classical Wigner crystal through a constriction formed by a split-gate electrode. The Wigner crystal is formed on the surface of superfluid helium confined in a microchannel. At low temperatures, the current is periodically suppressed with increasing split-gate voltage, resulting in peaklike transport features. We also present the results of molecular dynamics simulations that reproduce this phenomenon. We demonstrate that, at the split-gate voltages for which the current is suppressed, the electron lattice is arranged such that the stability of particle positions against thermal fluctuations is enhanced. In these configurations, the suppression of transport due to interelectron Coulomb forces becomes important.

What lurks below the last plateau: experimental studies of the 0.7 × 2e(2)/h conductance anomaly in one-dimensional systems

The integer quantised conductance of one-dimensional electron systems is a well-understood effect of quantum confinement. A number of fractionally quantised plateaus are also commonly observed. They are attributed to many-body effects, but their precise origin is still a matter of debate, having attracted considerable interest over the past 15 years. This review reports on experimental studies of fractionally quantised plateaus in semiconductor quantum point contacts and quantum wires, focusing on the 0.7 × 2e(2)/h conductance anomaly, its analogues at higher conductances and the zero-bias peak observed in the dc source-drain bias for conductances less than 2e(2)/h.

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.

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.

Electrons in one dimension

In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs-AlGaAs heterostructures. By means of suitably located gates and application of a voltage to 'electrostatically squeeze' the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimensional transport. If the length of the electron channel is sufficiently short, then transport is ballistic and the quantized subbands each have a conductance equal to the fundamental quantum value 2e(2)/h, where the factor of 2 arises from the spin degeneracy. This mode of conduction is discussed, and it is shown that a number of many-body effects can be observed. These effects are discussed as in the spin-incoherent regime, which is entered when the separation of the electrons is increased and the exchange energy is less than kT. Finally, results are presented in the regime where the confinement potential is decreased and the electron configuration relaxes to minimize the electron-electron repulsion to move towards a two-dimensional array. It is shown that the ground state is no longer a line determined by the size quantization alone, but becomes two distinct rows arising from minimization of the electrostatic energy and is the precursor of a two-dimensional Wigner lattice.