High Resolution Spectroscopy of Two-Dimensional Electron Systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the "single particle" density of states (SPDOS) spectrum of a system. The SPDOS is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proven difficult to probe spectroscopically. Here we present an improved version of time domain capacitance spectroscopy (TDCS) that now allows us to measure the SPDOS of a 2DES with unprecedented fidelity and resolution. Using TDCS, we perform measurements of a cold 2DES, providing the first direct measurements of the single-particle exchange-enhanced spin gap and single particle lifetimes in the quantum Hall system, as well as the first observations of exchange splitting of Landau levels not at the Fermi surface. The measurements reveal the difficult to reach and beautiful structure present in this highly correlated system far from the Fermi surface.Comment: There are formatting and minor textual differences between this version and the published version in Nature (follow the DOI link below

Finite temperature phase transition for disordered weakly interacting bosons in one dimension

It is commonly accepted that there are no phase transitions in one-dimensional (1D) systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we demonstrate that the 1D gas of short-range interacting bosons in the presence of disorder can undergo a finite temperature phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition because transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. We thus reveal how the interaction between disordered bosons influences their Anderson localization. This key question, first raised for electrons in solids, is now crucial for the studies of atomic bosons where recent experiments have demonstrated Anderson localization in expanding very dilute quasi-1D clouds.Comment: 8 pages, 5 figure

Probing interactions in mesoscopic gold wires

We have measured in gold wires the energy exchange rate between quasiparticles, the phase coherence time of quasiparticles and the resistance vs. temperature, in order to probe the interaction processes which are relevant at low temperatures. We find that the energy exchange rate is higher than expected from the theory of electron-electron interactions, and that it has a different energy dependence. The dephasing time is constant at temperatures between 8 K and 0.5 K, and it increases below 0.5 K. The magnetoresistance is negative at large field scales, and the resistance decreases logarithmically with increasing temperatures, indicating the presence of magnetic impurities, probably Fe. Whereas resistivity and phase coherence measurements can be attributed to magnetic impurities, the question is raised whether these magnetic impurities could also mediate energy exchanges between quasiparticles.Comment: latex pothier.tex, 12 files, 15 pages in: Proceedings of the NATO Advanced Research Workshop on Size Dependent Magnetic Scattering, Pesc, Hungary, May 28 - June 1st, 2000 Chandrasekhar V., Van Haesendonck C. eds (Kluwer, 2001) [SPEC-S00/083

Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization - asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases - a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M. Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and Experiment, Springer Proceedings in Physics 173. arXiv admin note: text overlap with arXiv:1405.112

Controlled Dephasing of Electrons by Non-Gaussian Shot Noise

In a 'controlled dephasing' experiment [1-3], an interferometer loses its coherence due to entanglement with a controlled quantum system ('which path' detector). In experiments that were conducted thus far in mesoscopic systems only partial dephasing was achieved. This was due to weak interactions between many detector electrons and the interfering electron, resulting in a Gaussian phase randomizing process [4-10]. Here, we report the opposite extreme: a complete destruction of the interference via strong phase randomization only by a few electrons in the detector. The realization was based on interfering edge channels (in the integer quantum Hall effect regime, filling factor 2) in a Mach-Zehnder electronic interferometer, with an inner edge channel serving as a detector. Unexpectedly, the visibility quenched in a periodic lobe-type form as the detector current increased; namely, it periodically decreased as the detector current, and thus the detector's efficiency, increased. Moreover, the visibility had a V-shape dependence on the partitioning of the detector current, and not the expected dependence on the second moment of the shot noise, T(1-T), with T the partitioning. We ascribe these unexpected features to the strong detector-interferometer coupling, allowing only 1-3 electrons in the detector to fully dephase the interfering electron. Consequently, in this work we explored the non-Gaussian nature of noise [11], namely, the direct effect of the shot noise full counting statistics [12-15].Comment: 14 pages, 4 figure

Bipolar supercurrent in graphene

Graphene -a recently discovered one-atom-thick layer of graphite- constitutes a new model system in condensed matter physics, because it is the first material in which charge carriers behave as massless chiral relativistic particles. The anomalous quantization of the Hall conductance, which is now understood theoretically, is one of the experimental signatures of the peculiar transport properties of relativistic electrons in graphene. Other unusual phenomena, like the finite conductivity of order 4e^2/h at the charge neutrality (or Dirac) point, have come as a surprise and remain to be explained. Here, we study the Josephson effect in graphene. Our experiments rely on mesoscopic superconducting junctions consisting of a graphene layer contacted by two closely spaced superconducting electrodes, where the charge density can be controlled by means of a gate electrode. We observe a supercurrent that, depending on the gate voltage, is carried by either electrons in the conduction band or by holes in the valence band. More importantly, we find that not only the normal state conductance of graphene is finite, but also a finite supercurrent can flow at zero charge density. Our observations shed light on the special role of time reversal symmetry in graphene and constitute the first demonstration of phase coherent electronic transport at the Dirac point.Comment: Under review, 12 pages, 4 Figs., suppl. info (v2 identical, resolved file problems

Non-Equilibrium Edge Channel Spectroscopy in the Integer Quantum Hall Regime

Heat transport has large potentialities to unveil new physics in mesoscopic systems. A striking illustration is the integer quantum Hall regime, where the robustness of Hall currents limits information accessible from charge transport. Consequently, the gapless edge excitations are incompletely understood. The effective edge states theory describes them as prototypal one-dimensional chiral fermions - a simple picture that explains a large body of observations and calls for quantum information experiments with quantum point contacts in the role of beam splitters. However, it is in ostensible disagreement with the prevailing theoretical framework that predicts, in most situations, additional gapless edge modes. Here, we present a setup which gives access to the energy distribution, and consequently to the energy current, in an edge channel brought out-of-equilibrium. This provides a stringent test of whether the additional states capture part of the injected energy. Our results show it is not the case and thereby demonstrate regarding energy transport, the quantum optics analogy of quantum point contacts and beam splitters. Beyond the quantum Hall regime, this novel spectroscopy technique opens a new window for heat transport and out-of-equilibrium experiments.Comment: 13 pages including supplementary information, Nature Physics in prin

Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.Comment: 13 pages, 5 figure

Universal Resistances of the Quantum RC circuit

We examine the concept of universal quantized resistance in the AC regime through the fully coherent quantum RC circuit comprising a cavity (dot) capacitively coupled to a gate and connected via a single spin-polarized channel to a reservoir lead. As a result of quantum effects such as the Coulomb interaction in the cavity and global phase coherence, we show that the charge relaxation resistance $R_q$ is identical for weak and large transmissions and it changes from $h/2e^2$ to $h/e^2$ when the frequency (times $\hbar$) exceeds the level spacing of the cavity; $h$ is the Planck constant and $e$ the electron charge. For large cavities, we formulate a correspondence between the charge relaxation resistance $h/e^2$ and the Korringa-Shiba relation of the Kondo model. Furthermore, we introduce a general class of models, for which the charge relaxation resistance is universal. Our results emphasize that the charge relaxation resistance is a key observable to understand the dynamics of strongly correlated systems.Comment: 12 pages, 3 figure

Spin and valley quantum Hall ferromagnetism in graphene

In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can spontaneously break this symmetry, manifesting as additional integer quantum Hall plateaus outside the normal sequence. Here we report the observation of a large number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using temperature-dependent tilted field magnetotransport. The large measured activation gaps confirm the Coulomb origin of the broken symmetry states, but the order is strongly dependent on LL index. In the high energy LLs, the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets with Skyrmionic excitations at half filling, whereas in the `relativistic' zero energy LL, lattice scale anisotropies drive the system to a spin unpolarized state, likely a charge- or spin-density wave.Comment: Supplementary information available at http://pico.phys.columbia.ed