Density of states of a two-dimensional electron gas in a long-range random potential

A Flexible Design Platform for Si/SiGe Exchange-Only Qubits with Low Disorder

Spin-based silicon quantum dots are an attractive qubit technology for quantum information processing with respect to coherence time, control, and engineering. Here we present an exchange-only Si qubit device platform that combines the throughput of CMOS-like wafer processing with the versatility of direct-write lithography. The technology, which we coin "SLEDGE", features dot-shaped gates that are patterned simultaneously on one topographical plane and subsequently connected by vias to interconnect metal lines. The process design enables nontrivial layouts as well as flexibility in gate dimensions, material selection, and additional device features such as for rf qubit control. We show that the SLEDGE process has reduced electrostatic disorder with respect to traditional overlapping gate devices with lift-off metallization, and we present spin coherent exchange oscillations and single qubit blind randomized benchmarking data.

Local, global, and nonlinear screening in twisted double-layer graphene

One-atom-thick crystalline layers and their vertical heterostructures carry the promise of designer electronic materials that are unattainable by standard growth techniques. To realize their potential it is necessary to isolate them from environmental disturbances, in particular those introduced by the substrate. However, finding and characterizing suitable substrates, and minimizing the random potential fluctuations they introduce, has been a persistent challenge in this emerging field. Here we show that Landau-level (LL) spectroscopy offers the unique capability to quantify both the reduction of the quasiparticles' lifetime and the long-range inhomogeneity due to random potential fluctuations. Harnessing this technique together with direct scanning tunneling microscopy and numerical simulations we demonstrate that the insertion of a graphene buffer layer with a large twist angle is a very effective method to shield a 2D system from substrate interference that has the additional desirable property of preserving the electronic structure of the system under study. We further show that owing to its remarkable nonlinear screening capability a single graphene buffer layer provides better shielding than either increasing the distance to the substrate or doubling the carrier density and reduces the amplitude of the potential fluctuations in graphene to values even lower than the ones in AB-stacked bilayer graphene.

Influence of Coulomb interaction of tunable shapes on the collective transport of ultradilute two-dimensional holes

In high quality updoped GaAs field-effect transistors, the two-dimensional charge carrier concentrations can be tuned to very low values similar to the density of electrons on helium surfaces. An important interaction effect, screening of the Coulomb interaction by the gate, rises as a result of the large charge spacing comparable to the distance between the channel and the gate. Based on the results of the temperature (T) dependence of the resistivity from measuring four different samples, a power-law characteristic is found for charge densities ≤2×10(9)  cm(-2). Moreover, the exponent exhibits a universal dependence on a single dimensionless parameter, the ratio between the mean carrier separation and the distance to the metallic gate that screens the Coulomb interaction. Thus, the electronic properties are tuned through varying the shape of the interaction potential.

Direct imaging of charged impurity density in common graphene substrates

Kelvin probe microscopy in ultrahigh vacuum is used to image the local electrostatic potential fluctuations above hexagonal boron nitride (h-BN) and SiO2, common substrates for graphene. Results are compared to a model of randomly distributed charges in a two-dimensional (2D) plane. For SiO2, the results are well modeled by 2D charge densities ranging from 0.24 to 2.7 × 10(11) cm(-2), while h-BN displays potential fluctuations 1-2 orders of magnitude lower than SiO2, consistent with the improvement in charge carrier mobility for graphene on h-BN compared to SiO2. Electron beam exposure of SiO2 increases the charge density fluctuations, creating long-lived metastable charge populations of ~2 × 10(11) cm(-2) at room temperature, which can be reversed by heating.

Helical edge resistance introduced by charge puddles

We study the influence of electron puddles created by doping of a 2D topological insulator on its helical edge conductance. A single puddle is modeled by a quantum dot tunnel coupled to the helical edge. It may lead to significant inelastic backscattering within the edge because of the long electron dwelling time in the dot. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on the temperature and doping level and compare it with recent experimental data.

Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene

The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene, we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap Δ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential Δ(cr), separating the insulating regime from a percolative regime in which less than half of the area of the bilayer graphene sample is insulating. We find that most of the current experiments are in the percolative regime with Δ(cr)≪Δ. The huge suppression of Δ(cr) compared with Δ provides a possible explanation for the large difference between the theoretical band gap Δ and the experimentally extracted transport gap.

A bioelectronic platform using a graphene-lipid bilayer interface

The electronic properties of graphene can be modulated by charged lipid bilayer adsorbing on the surface. Biorecognition events which lead to changes in membrane integrity can be monitored electrically using an electrolyte-gated biomimetic membrane-graphene transistor. Here, we demonstrate that the bactericidal activity of antimicrobial peptides can be sensed electrically by graphene based on a complex interplay of biomolecular doping and ionic screening effect.

Observation of reentrant phases induced by short-range disorder in the lowest Landau level of Al{x}Ga{1-x}As/Al{0.32}Ga{0.68}as heterostructures

We report the observation of a reentrant quantum Hall effect in the lowest Landau level between filling factors of 2/3 and 3/5 in a Al{x}Ga{1-x}As/Al{0.32}Ga{0.68}As heterostructure sample with x=0.85%. A reentrant insulating phase is also observed between filling factors of 2/5 and 1/3, demonstrating particle-hole symmetry between these phases. A sample with x=0.21% shows much weaker reentrant features, indicating that increased short-range scattering, due to the Al alloy in the conduction channel, aids in the formation of these phases.

Neutrality point of graphene with coplanar charged impurities

The ground state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on alpha, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when alpha is small, which is the case for graphene on a substrate with a high dielectric constant.

Hamiltonian theory of disorder at nu = 1/3

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Quantum Hall to insulator transition in the bilayer quantum Hall ferromagnet

We describe a phase transition of the bilayer quantum Hall ferromagnet at nu=1. In the presence of static disorder (modeled by a periodic potential), bosonic S=1/2 spinons undergo a superfluid-insulator transition while preserving ferromagnetism. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Consequences for charge and counterflow conductivity and for interlayer tunneling conductance are discussed.

Evidence of a transition from nonlinear to linear screening of a two-dimensional electron system detected by photoluminescence spectroscopy

We clearly identify single-electron-localization (SEL), nonlinear screening (NLS), and linear screening (LS) regimes of gate induced electrons in a GaAs quantum well from photoluminescence spectra and intergate capacitance. Neutral and charged excitons observed in the SEL regime rapidly lose their oscillator strength when electron puddles are formed, which mark the onset of NLS. A further increase in the density of the electrons induces the transition from the NLS to LS, where the emission of a charged exciton changes to the recombination of two-dimensional electron gas and a hole.

Theory of activated transport in bilayer quantum Hall systems

We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.

A self-consistent theory for graphene transport

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities n(imp). For dirty samples (250 x 10(10) cm(-2) < n(imp) < 400 x 10(10) cm(-2)), the value of the minimum conductivity at low carrier density is indeed 4e(2)/h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on n(imp), increasing to 8e(2)/h for n(imp) approximately 20 x 10(10) cm(-2). A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.

Thermodynamic density of states of two-dimensional GaAs systems near the apparent metal-insulator transition

We perform combined resistivity and compressibility studies of two-dimensional hole and electron systems which show the apparent metal-insulator transition--a crossover in the sign of deltaR/deltaT with changing density. No thermodynamic anomalies have been detected in the crossover region. Instead, despite a tenfold difference in r(s), the compressibility of both electrons and holes is well described by the theory of nonlinear screening of the random potential. We show that the resistivity exhibits a scaling behavior near the percolation threshold found from analysis of the compressibility. Notably, the percolation transition occurs at a much lower density than the crossover.

Coherence network in the quantum Hall bilayer

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a coherence network induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.

The microscopic nature of localization in the quantum Hall effect

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.

Unexpected behavior of the local compressibility near the B = 0 metal-insulator transition

We have measured the local electronic compressibility of a two-dimensional hole gas as it crosses the B = 0 metal-insulator transition. In the metallic phase, the compressibility follows the mean-field Hartree-Fock (HF) theory and is found to be spatially homogeneous. In the insulating phase it deviates by more than an order of magnitude from the HF predictions and is spatially inhomogeneous. The crossover density between the two types of behavior agrees quantitatively with the transport critical density, suggesting that the system undergoes a thermodynamic change at the transition.