Person:

Halperin, Bertrand

We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the buildup of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called ‘‘dark states’’, and the elimination of the difference field. We show that in the case of unequal dots, buildup of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, buildup of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process.

In this pedagogical review, we discuss how electrical resistance can arise in superconductors. Starting with the idea of the superconducting order parameter as a condensate wave function, we introduce vortices as topological excitations with quantized phase winding, and we show how phase slips occur when vortices cross the sample. Superconductors exhibit non-zero electrical resistance under circumstances where phase slips occur at a finite rate. For one-dimensional superconductors or Josephson junctions, phase slips can occur at isolated points in space-time. Phase slip rates may be controlled by thermal activation over a free-energy barrier, or in some circumstances, at low temperatures, by quantum tunneling through a barrier. We present an overview of several phenomena involving vortices that have direct implications for the electrical resistance of superconductors, including the Berezinskii-Kosterlitz-Thouless transition for vortex-proliferation in thin films, and the effects of vortex pinning in bulk type II superconductors on the non-linear resistivity of these materials in an applied magnetic field. We discuss how quantum fluctuations can cause phase slips and review the non-trivial role of dissipation on such fluctuations. We present a basic picture of the superconductor-to-insulator quantum phase transitions in films, wires, and Josephson junctions. We point out related problems in superfluid helium films and systems of ultra-cold trapped atoms. While our emphasis is on theoretical concepts, we also briefly describe experimental results, and we underline some of the open questions.

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally-obtained echo signals allows us to quantify the contributions of various processes such as coherent Larmor precession and spin diffusion to the nuclear spin evolution.

Motivated by the recent experiments by the Westervelt group using a mobile tip to probe the electronic state of quantum dots formed on a segmented nanowire, we study the shifts in Coulomb blockade peak positions as a function of the spatial variation of the tip potential, which can be termed "Coulomb blockade microscopy". We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high density electronic liquid state from a Wigner crystal state by microscopy with a weak tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other, and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one particle potential and kinetic energies. Finally, we propose that a weak tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.

We consider a layered system of fermionic molecules with permanent dipole moments aligned by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce inter-layer pairing. Due to competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every-other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light scattering experiments to detect dimerization.

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semiclassical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally obtained echo signals allows us to quantify the contributions to the nuclear spin evolution of various processes such as coherent Larmor precession and spin diffusion.

Intermediate band photovoltaics hold the promise of being highly efficient and cost effective photovoltaic cells. Intermediate states in the band gap, however, are known to facilitate nonradiative recombination. Much effort has been dedicated to producing metallic intermediate bands in hopes of producing lifetime recovery - an increase in carrier lifetime as doping levels increase. We show that lifetime recovery induced by the insulator-to-metal transition will not occur, because the metallic extended states will be localised by phonons during the recombination process. Only trivial forms of lifetime recovery, e.g., from an overall shift in intermediate levels, are possible. Future work in intermediate band photovoltaics must focus on optimizing subgap optical absorption and minimizing recombination, but not via lifetime recovery.

Observation of non-Abelian statistics for the (e/4) quasiparticles in the (\nu =\frac{5}{2}) fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localized quasiparticles, and, hence, an additional low temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, VG, provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the VG−T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors (\nu = 2p + 2/3) with hints of additional states appearing at (\nu = 2p + 3/5), where p = -2,-1, 0, and 1. This sequence of states breaks particle-hole symmetry and instead obeys a (\nu \rightarrow \nu + 2) symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors (\nu =−1/2) and (−1/4). Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as (\nu ) approaches (−1/2), suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.