One-dimensional transport and the quantisation of the ballistic resistance

Ohm's law lost and regained: observation and impact of transmission and velocity zeros

The quantum conductance and its classical wave analogue, the transmittance, are given by the sum of the eigenvalues of the transmission matrix. However, neither measurements nor theoretical analysis of the transmission eigenchannels have been carried out to explain the dips in conductance found in simulations as new channels are introduced. Here, we measure the microwave transmission matrices of random waveguides and find the spectra of all transmission eigenvalues, even at dips in the lowest transmission eigenchannel that are orders of magnitude below the noise in the transmission matrix. Transmission vanishes both at topological transmission zeros, where the energy density at the sample output vanishes, and at crossovers to new channels, where the longitudinal velocity vanishes. Zeros of transmission pull down all the transmission eigenvalues and thereby produce dips in the transmittance. These dips and the ability to probe the characteristics of even the lowest transmission eigenchannel are due to correlation among the eigenvalues. The precise tracking of dips in the conductance by peaks in the density of states points to a further correlation between zeros and poles of the transmission matrix. The conductance approaches Ohm's law as the sample width increases in accord with the correspondence principle.

Gate-tunable subband degeneracy in semiconductor nanowires

Degeneracy and symmetry have a profound relation in quantum systems. Here, we report gate-tunable subband degeneracy in PbTe nanowires with a nearly symmetric cross-sectional shape. The degeneracy is revealed in electron transport by the absence of a quantized plateau. Utilizing a dual gate design, we can apply an electric field to lift the degeneracy, reflected as emergence of the plateau. This degeneracy and its tunable lifting were challenging to observe in previous nanowire experiments, possibly due to disorder. Numerical simulations can qualitatively capture our observation, shedding light on device parameters for future applications.

Gate-defined quantum point contacts in a germanium quantum well

We report an experimental study of quantum point contacts defined in a high-quality strained germanium quantum well with layered electric gates. At a zero magnetic field, we observed quantized conductance plateaus in units of 2e2/h. Bias-spectroscopy measurements reveal that the energy spacing between successive one-dimensional subbands ranges from 1.5 to 5 meV as a consequence of the small effective mass of the holes and the narrow gate constrictions. At finite magnetic fields perpendicular to the device plane, the edges of the conductance plateaus get split due to the Zeeman effect and Landé g factors were estimated to be ∼6.6 for the holes in the germanium quantum well. We demonstrate that all quantum point contacts in the same device have comparable performances, indicating a reliable and reproducible device fabrication process. Thus, our work lays a foundation for investigating multiple forefronts of physics in germanium-based quantum devices that require quantum point contacts as building blocks.

Electronic Transport and Quantum Phenomena in Nanowires

Nanowires are natural one-dimensional channels and offer new opportunities for advanced electronic quantum transport experiments. We review recent progress on the synthesis of nanowires and methods for the fabrication of hybrid semiconductor/superconductor systems. We discuss methods to characterize their electronic properties in the context of possible future applications such as topological and spin qubits. We focus on group III-V (InAs and InSb) and group IV (Ge/Si) semiconductors, since these are the most developed, and give an outlook on other potential materials.

Fast Fourier-Chebyshev Approach to Real-Space Simulations of the Kubo Formula

The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that are accurate and scalable to large lattice sizes beyond one spatial dimension. Here, we propose a general framework to numerically study large systems, which combines the spectral accuracy of Chebyshev expansions with the efficiency of divide-and-conquer methods. We use the hybrid algorithm to calculate the two-terminal conductance and the bulk conductivity tensor of 2D lattice models with over 10^{7} sites. By efficiently sampling the microscopic information contained in billions of Chebyshev moments, the algorithm is able to accurately resolve the linear-response properties of complex systems in the presence of quenched disorder. Our results lay the groundwork for future studies of transport phenomena in previously inaccessible regimes.

Ballistic PbTe Nanowire Devices

Disorder is the primary obstacle in the current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected, with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown by using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of 2e2/h are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires as most of the previously studied SAG nanowires (InSb or InAs) have not exhibited zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

One-Shot GW Transport Calculations: A Charge-Conserving Solution

Transport measurements are a common method of characterizing small systems in chemistry and physics. When interactions are negligible, the current through submicrometer structures can be obtained using the Landauer formula. Meir and Wingreen derived an exact expression for the current in the presence of interactions. This powerful tool requires knowledge of the exact Green's function. Alternatively, self-consistent approximations for the Green's function are frequently sufficient for calculating the current while crucially satisfying all conservation laws. We provide here yet another alternative, circumventing the high computational cost of these methods. We present expressions for the electric and thermal currents in which the lowest-order self-energy is summed to all orders (one-shot GW approximation). We account for both self-energy and vertex corrections such that current is conserved. Our formulas for the currents capture important features due to interactions and, hence, provide a powerful tool for cases in which the exact solution cannot be found.

Quantum Conductance in Memristive Devices: Fundamentals, Developments, and Applications

Quantum effects in novel functional materials and new device concepts represent a potential breakthrough for the development of new information processing technologies based on quantum phenomena. Among the emerging technologies, memristive elements that exhibit resistive switching, which relies on the electrochemical formation/rupture of conductive nanofilaments, exhibit quantum conductance effects at room temperature. Despite the underlying resistive switching mechanism having been exploited for the realization of next-generation memories and neuromorphic computing architectures, the potentialities of quantum effects in memristive devices are still rather unexplored. Here, a comprehensive review on memristive quantum devices, where quantum conductance effects can be observed by coupling ionics with electronics, is presented. Fundamental electrochemical and physicochemical phenomena underlying device functionalities are introduced, together with fundamentals of electronic ballistic conduction transport in nanofilaments. Quantum conductance effects including quantum mode splitting, stability, and random telegraph noise are analyzed, reporting experimental techniques and challenges of nanoscale metrology for the characterization of memristive phenomena. Finally, potential applications and future perspectives are envisioned, discussing how memristive devices with controllable atomic-sized conductive filaments can represent not only suitable platforms for the investigation of quantum phenomena but also promising building blocks for the realization of integrated quantum systems working in air at room temperature.

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.

Thermoelectric Polarization Transport in Ferroelectric Ballistic Point Contacts

We formulate a scattering theory of polarization and heat transport through a ballistic ferroelectric point contact. We predict a polarization current under either an electric field or a temperature difference that depends strongly on the direction of the ferroelectric order and can be detected by its magnetic stray field and associated thermovoltage and Peltier effect.

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.

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.

Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.

Topology-Changing Broadband Metamaterials Enabled by Closable Nanotrenches

One of the most straightforward methods to actively control optical functionalities of metamaterials is to apply mechanical strain deforming the geometries. These deformations, however, leave symmetries and topologies largely intact, limiting the multifunctional horizon. Here, we present topology manipulation of metamaterials fabricated on flexible substrates by mechanically closing/opening embedded nanotrenches of various geometries. When an inner bending is applied on the substrate, the nanotrench closes and the accompanying topological change results in abrupt switching of metamaterial functionalities such as resonance, chirality, and polarization selectivity. Closable nanotrenches can be embedded in metamaterials of broadband spectrum, ranging from visible to microwave. The 99.9% extinction performance is robust, enduring more than a thousand bending cycles. Our work provides a wafer-scale platform for active quantum plasmonics and photonic application of subnanometer phenomena.

Cryogenic Transport Characteristics of P-Type Gate-All-Around Silicon Nanowire MOSFETs

A 16-nm-L_g p-type Gate-all-around (GAA) silicon nanowire (Si NW) metal oxide semiconductor field effect transistor (MOSFET) was fabricated based on the mainstream bulk fin field-effect transistor (FinFET) technology. The temperature dependence of electrical characteristics for normal MOSFET as well as the quantum transport at cryogenic has been investigated systematically. We demonstrate a good gate-control ability and body effect immunity at cryogenic for the GAA Si NW MOSFETs and observe the transport of two-fold degenerate hole sub-bands in the nanowire (110) channel direction sub-band structure experimentally. In addition, the pronounced ballistic transport characteristics were demonstrated in the GAA Si NW MOSFET. Due to the existence of spacers for the typical MOSFET, the quantum interference was also successfully achieved at lower bias.

New signatures of the spin gap in quantum point contacts

One dimensional semiconductor systems with strong spin-orbit interaction are both of fundamental interest and have potential applications to topological quantum computing. Applying a magnetic field can open a spin gap, a pre-requisite for Majorana zero modes. The spin gap is predicted to manifest as a field dependent dip on the first 1D conductance plateau. However, disorder and interaction effects make identifying spin gap signatures challenging. Here we study experimentally and numerically the 1D channel in a series of low disorder p-type GaAs quantum point contacts, where spin-orbit and hole-hole interactions are strong. We demonstrate an alternative signature for probing spin gaps, which is insensitive to disorder, based on the linear and non-linear response to the orientation of the applied magnetic field, and extract a spin-orbit gap ΔE ≈ 500 μeV. This approach could enable one-dimensional hole systems to be developed as a scalable and reproducible platform for topological quantum applications.

In one-dimensional systems, the combination of a strong spin-orbit interaction and an applied magnetic field can give rise to a spin-gap, however experimental identification is difficult. Here, the authors present new signatures for the spin-gap, and verify these experimentally in hole QPCs.

Robust quantum point contact via trench gate modulation

Quantum point contacts (QPC) are a primary component in mesoscopic physics and have come to serve various purposes in modern quantum devices. However, fabricating a QPC that operates robustly under extreme conditions, such as high bias or magnetic fields, still remains an important challenge. As a solution, we have analyzed the trench-gated QPC (t-QPC) that has a central gate in addition to the split-gate structure used in conventional QPCs (c-QPC). From simulation and modelling, we predicted that the t-QPC has larger and more even subband spacings over a wider range of transmission when compared to the c-QPC. After an experimental verification, the two QPCs were investigated in the quantum Hall regimes as well. At high fields, the maximally available conductance was achievable in the t-QPC due to the local carrier density modulation by the trench gate. Furthermore, the t-QPC presented less anomalies in its DC bias dependence, indicating a possible suppression of impurity effects.

Coherent Electron Optics with Ballistically Coupled Quantum Point Contacts

The realization of integrated quantum circuits requires precise on-chip control of charge carriers. Aiming at the coherent coupling of distant nanostructures at zero magnetic field, here we study the ballistic electron transport through two quantum point contacts (QPCs) in series in a three terminal configuration. We enhance the coupling between the QPCs by electrostatic focusing using a field effect lens. To study the emission and collection properties of QPCs in detail we combine the electrostatic focusing with magnetic deflection. Comparing our measurements with quantum mechanical and classical calculations we discuss generic features of the quantum circuit and demonstrate how the coherent and ballistic dynamics depend on the details of the QPC confinement potentials.

Exploring the limits of sensitivity for strain gauges of graphene and hexagonal boron nitride decorated with metallic nanoislands

The purpose of this work is to clarify the mechanism of piezoresistance in a class of ultra-sensitive strain gauges based on metallic films on 2D substrates ("2D/M" films). The metals used are gold or palladium deposited as ultrathin films (≤16 nm). These films transition from a regime of subcontiguous growth to a percolated morphology with increasing nominal thickness. The 2D substrates are either single-layer graphene or hexagonal boron nitride (hBN). By using either a conductor (graphene) or an insulator (hBN), it is possible to de-couple the relative contributions of the metal and the 2D substrate from the overall piezoresistance of the composite structure. Here, we use a combination of measurements including electron microscopy, automated image analysis, temperature-dependent conductivity, and measurements of gauge factor of the films as they are bent over a 1 μm step edge (0.0001% or 1 ppm). Our observations are enumerated as follows: (1) of the four permutations of metal and 2D substrate, all combinations except hBN/Au are able to resolve 1 ppm strain (considered extraordinary for strain gauges) at some threshold thickness of metal; (2) for non-contiguous (i.e., unpercolated) films of metal on hBN, changes in resistance for these small step strains cannot be detected; (3) for percolated films on hBN, changes in resistance upon strain can be resolved only for palladium and not for gold; (4) graphene does not exhibit detectable changes in resistance when subjected to step strains of either 1 or 10 ppm, but does so upon the deposition of any amount of gold or palladium, even for nominal thicknesses below the threshold for percolation. Our observations reveal unexpected complexity in the properties of these simple composite materials, and ways in which these materials might be combined to exhibit even greater sensitivity.

Dynamical Coulomb Blockade as a Local Probe for Quantum Transport

Quantum fluctuations are imprinted with valuable information about transport processes. Experimental access to this information is possible, but challenging. We introduce the dynamical Coulomb blockade (DCB) as a local probe for fluctuations in a scanning tunneling microscope (STM) and show that it provides information about the conduction channels. In agreement with theoretical predictions, we find that the DCB disappears in a single-channel junction with increasing transmission following the Fano factor, analogous to what happens with shot noise. Furthermore we demonstrate local differences in the DCB expected from changes in the conduction channel configuration. Our experimental results are complemented by ab initio transport calculations that elucidate the microscopic nature of the conduction channels in our atomic-scale contacts. We conclude that probing the DCB by STM provides a technique complementary to shot noise measurements for locally resolving quantum transport characteristics.

A One-Dimensional Effective Model for Nanotransistors in Landauer-Büttiker Formalism

In a series of publications, we developed a compact model for nanotransistors in which quantum transport in a variety of industrial nano-FETs was described quantitatively. The compact nanotransistor model allows for the extraction of important device parameters as the effective height of the source-drain barrier, device heating, and the quality of the coupling between conduction channel and the contacts. Starting from a basic description of quantum transport in a multi-terminal device in Landauer–Büttiker formalism, we give a detailed derivation of all relevant formulas necessary to construct our compact nanotransistor model. Here we make extensive use of the the R-matrix method.

Pascal conductance series in ballistic one-dimensional LaAlO3/SrTiO3 channels

One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate-strontium titanate (LaAlO₃/SrTiO₃) interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: (1, 3, 6, 10, 15, …) ⋅ e ² /h, where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.

Basic modelling of effects of geometry and magnetic field for quantum wires injecting electrons into a two-dimensional electron reservoir

High-mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors has been used experimentally and theoretically to study ballistic electron transport. The present paper is motivated by recent experiments in magnetic electron focusing. The proposed device consists of two quantum point contacts (QPCs) serving as electron injector and collector which are placed in the same semiconductor GaAs/AlGaAs heterostructure. Here we focus on a theoretical study of the injection of electrons via a quantum wire/QPC into an open two-dimensional (2D) reservoir. The transport is considered for non-interacting electrons at different transmission regimes using the mode-matching technique. The proposed mode-matching technique has been implemented numerically. Electron flow through the quantum wire with hard-wall rectangular, conical and rounded openings has been studied. We have found for these three cases that the geometry of the opening does not play a crucial role for the electron propagation. When a perpendicular magnetic field is applied the electron paths in the 2D reservoir are curved. We analyse this case both classically and quantum-mechanically. The effect of spin-splitting due to exchange interactions on the electron flow is also considered. The effect is clearly present for realistic choices of device parameters and consistent with observations. The results of this study may be applied in designing magnetic focusing devices and spin separation.

Exciton Gas Transport through Nanoconstrictions

An indirect exciton is a bound state of an electron and a hole in spatially separated layers. Two-dimensional indirect excitons can be created optically in heterostructures containing double quantum wells or atomically thin semiconductors. We study theoretically the transmission of such bosonic quasiparticles through nanoconstrictions. We show that the quantum transport phenomena, for example, conductance quantization, single-slit diffraction, two-slit interference, and the Talbot effect, are experimentally realizable in systems of indirect excitons. We discuss similarities and differences between these phenomena and their counterparts in electronic devices.

Giant Zero Bias Anomaly due to Coherent Scattering from Frozen Phonon Disorder in Quantum Point Contacts

We demonstrate an unusual manifestation of coherent scattering for electron waves in mesoscopic quantum point contacts, in which fast electron dynamics allows the phonon system to serve as a quasistatic source of disorder. The low-temperature conductance of these devices exhibits a giant (≫2e^{2}/h) zero bias anomaly (ZBA), the features of which are reproduced in a nonequilibrium model for coherent scattering from the "frozen" phonon disorder. According to this model, the ZBA is understood to result from the in situ electrical manipulation of the phonon disorder, a mechanism that could open up a pathway to the on-demand control of coherent scattering in the solid state.

Beyond the State of the Art: Novel Approaches for Thermal and Electrical Transport in Nanoscale Devices

Almost any interaction between two physical entities can be described through the transfer of either charge, spin, momentum, or energy. Therefore, any theory able to describe these transport phenomena can shed light on a variety of physical, chemical, and biological effects, enriching our understanding of complex, yet fundamental, natural processes, e.g., catalysis or photosynthesis. In this review, we will discuss the standard workhorses for transport in nanoscale devices, namely Boltzmann's equation and Landauer's approach. We will emphasize their strengths, but also analyze their limits, proposing theories and models useful to go beyond the state of the art in the investigation of transport in nanoscale devices.

Recent advances in Sb-based III-V nanowires

Owing to the high mobility, narrow bandgap, strong spin-orbit coupling and large g-factor, Sb-based III-V nanowires (NWs) attracted significant interests in high speed electronics, long-wavelength photodetectors and quantum superconductivity in the past decade. In this review, we aim to give an integrated summarization about the recent advances in binary as well as ternary Sb-based III-V NWs, starting from the fundamental properties, NWs growth mechanism, typical synthetic methods to their applications in transistors, photodetectors, and Majorana fermions detection. Up to now, famous NWs growth techniques of solid-source chemical vapor deposition (CVD), molecular beam epitaxy, metal organic vapor phase epitaxy and metal organic CVD etc have been adopted and developed for the controllable growth of Sb-based III-V NWs. Several parameters including heating temperature, III/V ratio of source materials, growth temperature, catalyst size and kinds, and growth substrate play important roles on the morphology, position, diameter distribution, growth orientation and crystal phase of Sb-based III-V NWs. Furthermore, we discuss the photoelectrical applications of Sb-based III-V NWs such as field-effect-transistors, tunnel diode, low-power inverter, and infrared detectors etc. Importantly, due to the strongest spin-orbit interaction and giant g-factor among all III-V semiconductors, InSb with the geometry of one-dimension NW is considered as the most promising candidate for the detection of Majorana fermions. In the end, we also summarize the main challenges remaining in the field and put forward some suggestions for the future development of Sb-based III-V NWs.

Conductance quantisation in patterned gate In0.75Ga0.25As structures up to 6 × (2e 2/h)

We present electrical measurements from In_0.75Ga_0.25As 1D channel devices with Rashba-type, spin-orbit coupling present in the 2D contact regions. Suppressed backscattering as a result of the time-reversal asymmetry at the 1D channel entrance results in enhanced ballistic transport characteristics with clear quantised conductance plateaus up to 6  ×  (2e ²/h). Applying DC voltages between the source and drain ohmic contacts and an in-plane magnetic field confirms a ballistic transport picture. For asymmetric patterned gate biasing, a lateral spin-orbit coupling effect is weak. However, the Rashba-type spin-orbit coupling leads to a g-factor in the 1D channel that is reduced in magnitude from the 2D value of 9 to ~6.5 in the lowest subband when the effective Rashba field and the applied magnetic field are perpendicular.

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.

Low-Magnetic-Field Regime of a Gate-Defined Constriction in High-Mobility Graphene

We report on the evolution of the coherent electronic transport through a gate-defined constriction in a high-mobility graphene device from ballistic transport to quantum Hall regime upon increasing the magnetic field. At a low field, the conductance exhibits Fabry-Pérot resonances resulting from the npn cavities formed beneath the top-gated regions. Above a critical field B* corresponding to the cyclotron radius equal to the npn cavity length, Fabry-Pérot resonances vanish, and snake trajectories are guided through the constriction with a characteristic set of conductance oscillations. Increasing further the magnetic field allows us to probe the Landau level spectrum in the constriction and unveil distortions due to the combination of confinement and deconfinement of Landau levels in a saddle potential. These observations are confirmed by numerical calculations.

Spin-momentum locked spin manipulation in a two-dimensional Rashba system

Spin-momentum locking, which constrains spin orientation perpendicular to electron momentum, is attracting considerable interest for exploring various spin functionalities in semiconductors and topological materials. Efficient spin generation and spin detection have been demonstrated using the induced helical spin texture. Nevertheless, spin manipulation by spin-momentum locking remains a missing piece because, once bias voltage is applied to induce the current flow, the spin orientation must be locked by the electron momentum direction, thereby rendering spin phase control difficult. Herein, we demonstrate the spin-momentum locking-induced spin manipulation for ballistic electrons in a strong Rashba two-dimensional system. Electron spin rotates in a circular orbital motion for ballistically moving electrons, although spin orientation is locked towards the spin-orbit field because of the helical spin texture. This fact demonstrates spin manipulation by control of the electron orbital motion and reveals potential effects of the orbital degree of freedom on the spin phase for future spintronic and topological devices and for the processing of quantum information.

Synaptic dynamics in complex self-assembled nanoparticle networks

We report a detailed study of neuromorphic switching behaviour in inherently complex percolating networks of self-assembled metal nanoparticles. We show that variation of the strength and duration of the electric field applied to this network of synapse-like atomic switches allows us to control the switching dynamics. Switching is observed for voltages above a well-defined threshold, with higher voltages leading to increased switching rates. We demonstrate two behavioral archetypes and show how the switching dynamics change as a function of duration and amplitude of the voltage stimulus. We show that the state of each synapse can influence the activity of the other synapses, leading to complex switching dynamics. We further demonstrate the influence of the morphology of the network on the measured device properties, and the constraints imposed by the overall network conductance. The correlated switching dynamics, device stability over long periods, and the simplicity of the device fabrication provide an attractive pathway to practical implementation of on-chip neuromorphic computing.

Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations.

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.

Quantized Ballistic Transport of Electrons and Electron Pairs in LaAlO3/SrTiO3 Nanowires

SrTiO₃-based heterointerfaces support quasi-two-dimensional (2D) electron systems that are analogous to III-V semiconductor heterostructures, but also possess superconducting, magnetic, spintronic, ferroelectric, and ferroelastic degrees of freedom. Despite these rich properties, the relatively low mobilities of 2D complex-oxide interfaces appear to preclude ballistic transport in 1D. Here we show that the 2D LaAlO₃/SrTiO₃ interface can support quantized ballistic transport of electrons and (nonsuperconducting) electron pairs within quasi-1D structures that are created using a well-established conductive atomic-force microscope (c-AFM) lithography technique. The nature of transport ranges from truly single-mode (1D) to three-dimensional (3D), depending on the applied magnetic field and gate voltage. Quantization of the lowest e²/ h plateau indicate a ballistic mean-free path l_MF ∼ 20 μm, more than 2 orders of magnitude larger than for 2D LaAlO₃/SrTiO₃ heterostructures. Nonsuperconducting electron pairs are found to be stable in magnetic fields as high as B = 11 T and propagate ballistically with conductance quantized at 2 e²/ h. Theories of one-dimensional (1D) transport of interacting electron systems depend crucially on the sign of the electron-electron interaction, which may help explain the highly ballistic transport behavior. The 1D geometry yields new insights into the electronic structure of the LaAlO₃/SrTiO₃ system and offers a new platform for the study of strongly interacting 1D electronic systems.

Transport regimes of a split gate superconducting quantum point contact in the two-dimensional LaAlO3/SrTiO3 superfluid

One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact in GaAs/AlGaAs heterostructures. Being formed with split gate technology, these structures represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel. It has been a long standing goal to achieve similar experimental conditions also in superconductors. Here we demonstrate the formation of a superconducting quantum point contact (SQPC) with split gate technology in a two-dimensional superconductor, utilizing the unique gate tunability of the superfluid at the LaAlO3/SrTiO3 interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: First, SQPC for which the supercurrent is carried only by a few quantum transport channels. Second, superconducting island strongly coupled to the equilibrium reservoirs. Third, charge island with a discrete spectrum weakly coupled to the reservoirs.

Nature of magnetization and lateral spin-orbit interaction in gated semiconductor nanowires

Semiconductor nanowires are interesting candidates for realization of spintronics devices. In this paper we study electronic states and effects of lateral spin-orbit coupling (LSOC) in a one-dimensional asymmetrically biased nanowire using the Hartree-Fock method with Dirac interaction. We have shown that spin polarization can be triggered by LSOC at finite source-drain bias,as a result of numerical noise representing a random magnetic field due to wiring or a random background magnetic field by Earth magnetic field, for instance. The electrons spontaneously arrange into spin rows in the wire due to electron interactions leading to a finite spin polarization. The direction of polarization is, however, random at zero source-drain bias. We have found that LSOC has an effect on orientation of spin rows only in the case when source-drain bias is applied.

Discretization of the total magnetic field by the nuclear spin bath in fluorine-doped ZnSe

The coherent spin dynamics of fluorine donor-bound electrons in ZnSe induced by pulsed optical excitation is studied in a perpendicular applied magnetic field. The Larmor precession frequency serves as a measure for the total magnetic field exerted onto the electron spins and, surprisingly, does not increase linearly with the applied field, but shows a step-like behavior with pronounced plateaus, given by multiples of the laser repetition rate. This discretization occurs by a feedback mechanism in which the electron spins polarize the nuclear spins, which in turn generate a local Overhauser field adjusting the total magnetic field accordingly. Varying the optical excitation power, we can control the plateaus, in agreement with our theoretical model. From this model, we trace the observed discretization to the optically induced Stark field, which causes the dynamic nuclear polarization.

Understanding the electron and nuclear spin interactions is essential to the application of quantum information devices. Here the authors report a step-like electron Larmor frequency versus external magnetic field due to the discretization of the total magnetic field by the nuclear spin bath in ZnSe:F.

Coherent control of single electrons: a review of current progress

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.

Signatures of Wigner localization in one-dimensional systems

We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.

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.

Classification of conductance traces with recurrent neural networks

We present a new automated method for structural classification of the traces obtained in break junction experiments. Using recurrent neural networks trained on the traces of minimal cross-sectional area in molecular dynamics simulations, we successfully separate the traces into two classes: point contact or nanowire. This is done without any assumptions about the expected features of each class. The trained neural network is applied to experimental break junction conductance traces, and it separates the classes as well as the previously used experimental methods. The effect of using partial conductance traces is explored, and we show that the method performs equally well using full or partial traces (as long as the trace just prior to breaking is included). When only the initial part of the trace is included, the results are still better than random chance. Finally, we show that the neural network classification method can be used to classify experimental conductance traces without using simulated results for training, but instead training the network on a few representative experimental traces. This offers a tool to recognize some characteristic motifs of the traces, which can be hard to find by simple data selection algorithms.

Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact

Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from 'electrochemical' to 'mechanical', which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.

Mapping the Coulomb Environment in Interference-Quenched Ballistic Nanowires

The conductance of semiconductor nanowires is strongly dependent on their electrostatic history because of the overwhelming influence of charged surface and interface states on electron confinement and scattering. We show that InAs nanowire field-effect transistor devices can be conditioned to suppress resonances that obscure quantized conduction thereby revealing as many as six sub-bands in the conductance spectra as the Fermi-level is swept across the sub-band energies. The energy level spectra extracted from conductance, coupled with detailed modeling shows the significance of the interface state charge distribution revealing the Coulomb landscape of the nanowire device. Inclusion of self-consistent Coulomb potentials, the measured geometrical shape of the nanowire, the gate geometry and nonparabolicity of the conduction band provide a quantitative and accurate description of the confinement potential and resulting energy level structure. Surfaces of the nanowire terminated by HfO₂ are shown to have their interface donor density reduced by a factor of 30 signifying the passivating role played by HfO₂.

Impact of Mismatch Angle on Electronic Transport Across Grain Boundaries and Interfaces in 2D Materials

We study the impact of grain boundaries (GB) and misorientation angles between grains on electronic transport in 2-dimensional materials. Here we have developed a numerical model based on the first-principles electronic bandstructure calculations in conjunction with a method which computes electron transmission coefficients from simultaneous conservation of energy and momentum at the interface to essentially evaluate GB/interface resistance in a Landauer formalism. We find that the resistance across graphene GBs vary over a wide range depending on misorientation angles and type of GBs, starting from 53 Ω μm for low-mismatch angles in twin (symmetric) GBs to about 10²⁰ Ω μm for 21° mismatch in tilt (asymmetric) GBs. On the other hand, misorientation angles have weak influence on the resistance across MoS₂ GBs, ranging from about 130 Ω μm for low mismatch angles to about 6000 Ω μm for 21°. The interface resistance across graphene-MoS₂ heterojunctions also exhibits a strong dependence on misorientation angles with resistance values ranging from about 100 Ω μm for low-mismatch angles in Class-I (symmetric) interfaces to 10¹⁵ Ω μm for 14° mismatch in Class-II (asymmetric) interfaces. Overall, symmetric homo/heterojunctions exhibit a weak dependence on misorientation angles, while in MoS₂ both symmetric and asymmetric GBs show a gradual dependence on mismatch angles.

Underlying Physics of Conductive Polymer Composites and Force Sensing Resistors (FSRs). A Study on Creep Response and Dynamic Loading

Force Sensing Resistors (FSRs) are manufactured by sandwiching a Conductive Polymer Composite (CPC) between metal electrodes. The piezoresistive property of FSRs has been exploited to perform stress and strain measurements, but the rheological property of polymers has undermined the repeatability of measurements causing creep in the electrical resistance of FSRs. With the aim of understanding the creep phenomenon, the drift response of thirty two specimens of FSRs was studied using a statistical approach. Similarly, a theoretical model for the creep response was developed by combining the Burger's rheological model with the equations for the quantum tunneling conduction through thin insulating films. The proposed model and the experimental observations showed that the sourcing voltage has a strong influence on the creep response; this observation-and the corresponding model-is an important contribution that has not been previously accounted. The phenomenon of sensitivity degradation was also studied. It was found that sensitivity degradation is a voltage-related phenomenon that can be avoided by choosing an appropriate sourcing voltage in the driving circuit. The models and experimental observations from this study are key aspects to enhance the repeatability of measurements and the accuracy of FSRs.

Spin Fluctuations in the 0.7 Anomaly in Quantum Point Contacts

It has been argued that the 0.7 anomaly in quantum point contacts (QPCs) is due to an enhanced density of states at the top of the QPC barrier (the van Hove ridge), which strongly enhances the effects of interactions. Here, we analyze their effect on dynamical quantities. We find that they pin the van Hove ridge to the chemical potential when the QPC is subopen, cause a temperature dependence for the linear conductance that qualitatively agrees with experiments, strongly enhance the magnitude of the dynamical spin susceptibility, and significantly lengthen the QPC traversal time. We conclude that electrons traverse the QPC via a slowly fluctuating spin structure of finite spatial extent.

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.