Sensitivity of the conductance of a disordered metal to the motion of a single atom: Implications for 1/f noise

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Spontaneous Time-Reversal Symmetry Breaking at Individual Grain Boundaries in Graphene

Graphene grain boundaries (GBs) have attracted interest for their ability to host nearly dispersionless electronic bands and magnetic instabilities. Here, we employ quantum transport and universal conductance fluctuation measurements to experimentally demonstrate a spontaneous breaking of time-reversal symmetry across individual GBs of chemical vapor deposited graphene. While quantum transport across the GBs indicate spin-scattering-induced dephasing and hence formation of local magnetic moments, below T≲4  K we observe complete lifting of time-reversal symmetry at high carrier densities (n≳5×10^{12}  cm^{-2}) and low temperature (T≲2  K). An unprecedented thirtyfold reduction in the universal conductance fluctuation magnitude with increasing doping density further supports the possibility of an emergent frozen magnetic state at the GBs. Our experimental results suggest that realistic GBs of graphene can be a promising resource for new electronic phases and spin-based applications.

Dephasing rates for weak localization and universal conductance fluctuations in two dimensional Si:P and Ge:P δ-layers

We report quantum transport measurements on two dimensional (2D) Si:P and Ge:P δ-layers and compare the inelastic scattering rates relevant for weak localization (WL) and universal conductance fluctuations (UCF) for devices of various doping densities (0.3–2.5 × 10¹⁸ m⁻²) at low temperatures (0.3–4.2 K). The phase breaking rate extracted experimentally from measurements of WL correction to conductivity and UCF agree well with each other within the entire temperature range. This establishes that WL and UCF, being the outcome of quantum interference phenomena, are governed by the same dephasing rate.

Nonequilibrium fluctuations as a distinctive feature of weak localization

Two-dimensional materials, such as graphene, topological insulators, and two-dimensional electron gases, represent a technological playground to develop coherent electronics. In these systems, quantum interference effects, and in particular weak localization, are likely to occur. These coherence effects are usually characterized by well-defined features in dc electrical transport, such as a resistivity increase and negative magnetoresistance below a crossover temperature. Recently, it has been shown that in magnetic and superconducting compounds, undergoing a weak-localization transition, a specific low-frequency 1/f noise occurs. An interpretation in terms of nonequilibrium universal conductance fluctuations has been given. The universality of this unusual electric noise mechanism has been here verified by detailed voltage-spectral density investigations on ultrathin copper films. The reported experimental results validate the proposed theoretical framework, and also provide an alternative methodology to detect weak-localization effects by using electric noise spectroscopy.

Quantum noise and asymmetric scattering of electrons and holes in graphene

We present measurements of quantum interference noise in double-gated single layer graphene devices at low temperatures. The noise characteristics show a nonmonotonic dependence on carrier density, which is related to the interplay between charge inhomogeneity and different scattering mechanisms. Linearly increasing 1/f noise at low carrier densities coincides with the observation of weak localization, suggesting the importance of short-range disorder in this regime. Using perpendicular and parallel p-n junctions, we find that the observed asymmetry of the noise with respect to the Dirac point can be related to asymmetric scattering of electrons and holes on the disorder potential.

Spontaneous breaking of time-reversal symmetry in strongly interacting two-dimensional electron layers in silicon and germanium

We report experimental evidence of a remarkable spontaneous time-reversal symmetry breaking in two-dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time-reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two-dimensional electrons are confined to narrow half-filled impurity bands.

Time-dependent universal conductance fluctuations in IrO2 nanowires

: Single-crystalline iridium dioxide nanowires show the time-dependent universal conductance fluctuations (TUCFs) at cryogenic temperatures. The conductance fluctuations persist up to temperature T as high as nearly 10 K. The root-mean-square TUCF magnitudes increase with decreasing T, reaching approximately 0.1 e2 / h at 1.7 K. We ascribe these conductance fluctuations to originating from the conduction electrons scattering upon mobile defects (moving scattering centers). Our measured TUCF characteristics are satisfactorily explained in terms of the existing TUCF theory in its three-dimensional form. The extracted electron dephasing length Lφ(1.7 K) ≃90 nm is smaller than the diameter (≈ 180 nm) of our nanowires.

Direct observation of valley hybridization and universal symmetry of graphene with mesoscopic conductance fluctuations

In graphene, the valleys represent spinlike quantities and can act as a physical resource in valley-based electronics to produce novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of 4 when valley triplet states are gapped in the presence of short-range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry class that outlines a fundamental feature arising from graphene's unique crystal structure.

Transport properties of graphene functionalized with molecular switches

We provide a theory of the electronic transport properties of a graphene layer functionalized with molecular switches. Our considerations are motivated by the spiropyran-merocyanine system which is non-polar in its ring-closed spiropyran form and zwitterionic in its ring-open merocyanine form. The reversible switching between these two isomers affects the carriers in graphene through the associated change in the molecular dipole moment, turning the graphene layer into a sensor of the molecular switching state. We present results for both the quasiclassical (Boltzmann) and the quantum coherent regimes of transport. Quite generally, we find a linear sensitivity of the conductance on the molecular dipole moment whenever quantum interference effects play an essential role which contrasts with a quadratic (and typically weaker) dependence when quantum interference is absent.

Universal conductance fluctuations in Dirac materials in the presence of long-range disorder

We study quantum transport in Dirac materials with a single fermionic Dirac cone (strong topological insulators and graphene in the absence of intervalley coupling) in the presence of non-Gaussian long-range disorder. We show, by directly calculating numerically the conductance fluctuations, that in the limit of very large system size and disorder strength, quantum transport becomes universal. However, a systematic deviation away from universality is obtained for realistic system parameters. By comparing our results to existing experimental data on 1/f noise, we suggest that many of the graphene samples studied to date are in a nonuniversal crossover regime of conductance fluctuations.

Impact of small-angle scattering on ballistic transport in quantum dots

Disorder increasingly affects performance as electronic devices are reduced in size. The ionized dopants used to populate a device with electrons are particularly problematic, leading to unpredictable changes in the behavior of devices such as quantum dots each time they are cooled for use. We show that a quantum dot can be used as a highly sensitive probe of changes in disorder potential and that, by removing the ionized dopants and populating the dot electrostatically, its electronic properties become reproducible with high fidelity after thermal cycling to room temperature. Our work demonstrates that the disorder potential has a significant, perhaps even dominant, influence on the electron dynamics, with important implications for "ballistic" transport in quantum dots.

Imaging universal conductance fluctuations in graphene

We study conductance fluctuations (CF) and the sensitivity of the conductance to the motion of a single scatterer in two-dimensional massless Dirac systems. Our extensive numerical study finds limits to the predicted universal value of CF. We find that CF are suppressed for ballistic systems near the Dirac point and approach the universal value at sufficiently strong disorder. The conductance of massless Dirac fermions is sensitive to the motion of a single scatterer. CF of order e(2)/h result from the motion of a single impurity by a distance comparable to the Fermi wavelength. This result applies to graphene systems with a broad range of impurity strength and concentration while the dependence on the Fermi wavelength can be explored via gate voltages. Our prediction can be tested by comparing graphene samples with varying amounts of disorder and can be used to understand interference effects in mesoscopic graphene devices.

Imaging coherent transport in graphene. Part I: mapping universal conductance fluctuations

Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales--the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations versus scatterer position. We find that the conductance is highly sensitive to the tip position, producing delta G approximately e(2)/h fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment and demonstrate the value of a cooled SPM for probing coherent transport in graphene.

Imaging coherent transport in graphene. Part II: probing weak localization

Graphene has opened new avenues of research in quantum transport, with potential applications for coherent electronics. Coherent transport depends sensitively on scattering from microscopic disorder present in graphene samples: electron waves traveling along different paths interfere, changing the total conductance. Weak localization is produced by the coherent backscattering of waves, while universal conductance fluctuations are created by summing over all paths. In this work, we obtain conductance images of weak localization with a liquid-He-cooled scanning probe microscope, by using the tip to create a movable scatterer in a graphene device. This technique allows us to investigate coherent transport with a probe of size comparable to the electron wavelength. Images of magnetoconductance versus tip position map the effects of disorder by moving a single scatterer, revealing how electron interference is modified by the tip perturbation. The weak localization dip in conductivity at B = 0 is obtained by averaging magnetoconductance traces at different positions of the tip-created scatterer. The width Delta B(WL) of the dip yields an estimate of the electron coherence length L(phi) at fixed charge density. This 'scanning scatterer' method provides a new way of investigating coherent transport in graphene by directly perturbing the disorder configuration that creates these interferometric effects.

Low- and high-frequency noise from coherent two-level systems

Recent experiments indicate a connection between the low- and high-frequency noises affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g., by sufficiently coherent two-level systems (TLS's). This implies a relation between the noise power in different frequency domains, which depends on the distribution of the parameters of the TLS's. We show that a distribution, natural for tunneling TLS's, with a log-uniform distribution in the tunnel splitting and linear distribution in the bias, accounts for experimental observations.

Resistance noise scaling in a dilute two-dimensional hole system in GaAs

We have measured the resistance noise of a two-dimensional (2D) hole system in a high mobility GaAs quantum well, around the 2D metal-insulator transition (MIT) at zero magnetic field. The normalized noise power S(R)/R(2) increases strongly when the hole density p(s) is decreased, increases slightly with temperature (T) at the largest densities, and decreases strongly with T at low p(s). The noise scales with the resistance, S(R)/R(2) approximately R2.4, as for a second order phase transition such as a percolation transition. The p(s) dependence of the conductivity is consistent with a critical behavior for such a transition, near a density p(*) which is lower than the observed MIT critical density p(c).

Sensitivity of wave field evolution and manifold stability in chaotic systems

The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes and give a simple expression for the crossover time between the regimes. The wave field's evolution is considerably more stable than the exponential instability of chaotic trajectories seems to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.

Universal conductance fluctuations in three dimensional metallic single crystals of Si

In this paper we report the measurement of conductance fluctuations in 3D crystals of Si made metallic by heavy doping. ( L/L(straight phi) approximately 10(3), where L(straight phi) is the phase coherence length.) Temperature and magnetic field dependence of noise strongly indicate the universal conductance fluctuations as a predominant source of the observed magnitude of noise. Conductance fluctuations within a single phase coherent region of L(3)(straight phi) were found to be saturated at <(deltaG(straight phi))(2)> approximately (e(2)/h)(2). An accurate knowledge of the level of disorder enables us to calculate the change in conductance deltaG1 due to movement of a single scatterer as <(deltaG1)(2)> approximately (e(2)/h)(2), which is approximately 2 orders of magnitude higher than its theoretically expected value in 3D systems.

Mesoscopic sensitivity of speckles in disordered nonlinear media to changes of the scattering potential

We show that the sensitivity of wave speckle patterns in disordered nonlinear media to changes of scattering potential increases with sample size. For large sizes the sensitivity diverges, which implies that for a given coherent wave incident on a sample there are multiple solutions for the spatial distribution of the wave density. The number of solutions increases exponentially with the sample size.