Imaging the Meissner effect in hydride superconductors using quantum sensors.

By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena1. The megabar regime represents an interesting frontier, in which recent discoveries include high-temperature superconductors, as well as structural and valence phase transitions2-6. However, at such high pressures, many conventional measurement techniques fail. Here we demonstrate the ability to perform local magnetometry inside a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach uses a shallow layer of nitrogen-vacancy colour centres implanted directly within the anvil7-9; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the nitrogen-vacancy centre to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH9 (ref. 10). By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping both the diamagnetic response and flux trapping, we directly image the geometry of superconducting regions, showing marked inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed-loop optimization of superhydride materials synthesis.

Bilayer graphene. Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene.

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH 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 ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = -2, -1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

Detecting non-Abelian anyons by charging spectroscopy.

Observation of non-Abelian statistics for the e/4 quasiparticles in the ν = 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, V(G), 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 V(G)-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.

Model for dissipative conductance in fractional quantum Hall states.

We present a model of dissipative transport in the fractional quantum Hall regime. Our model takes account of tunneling through saddle points in the effective potential for excitations created by impurities. We predict the temperature range over which activated behavior is observed and explain why this range nearly always corresponds to around a factor two in temperature in both integer quantum Hall and fractional quantum Hall systems. We identify the ratio of the gap observed in the activated behavior and the temperature of the inflection point in the Arrhenius plot as an important diagnostic for determining the importance of tunneling in real samples.

Dynamic nuclear polarization in double quantum dots.

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.

Bulk-edge coupling in the non-Abelian nu=5/2 quantum hall interferometer.

Recent schemes for probing non-Abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by the edge and the intereference signal is fully restored. Furthermore, we find that the strength of the coupling can be tuned by the source-drain voltage.

Influence of interactions on flux and back-gate period of quantum Hall interferometers.

In quantum Hall systems with two narrow constrictions, tunneling between opposite edges can give rise to quantum interference and Aharonov-Bohm-like oscillations of the conductance. When there is an integer quantized Hall state within the constrictions, a region between them, with higher electron density, may form a compressible island. Electron tunneling through this island can lead to residual transport, modulated by Coulomb-blockade-type effects. We find that the coupling between the fully occupied lower Landau levels and the higher-partially occupied level gives rise to flux subperiods smaller than one flux quantum. We generalize this scenario to other geometries and to fractional quantum Hall systems, and compare our predictions to experiments.

Detection of current-induced spins by ferromagnetic contacts.

Detection of current-induced spin accumulation via ferromagnetic contacts is discussed. Onsager's relations forbid that in a two-probe configuration, spins excited by currents in time-reversal symmetric systems can be detected by switching the magnetization of a ferromangetic detector contact. Nevertheless, current-induced spins can be transferred as a torque to a contact magnetization and can affect the charge currents in many-terminal configurations. We demonstrate the general concepts by solving the microscopic transport equations for the diffuse Rashba system with magnetic contacts.

Superfluid-insulator transition in a moving system of interacting bosons.

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.

Spin-charge separation and localization in one dimension.

We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained by tunneling between two parallel wires in an GaAs/AlGaAs heterostructure while varying electron density. We observed two spin modes and one charge mode of the coupled wires and mapped the dispersion velocities of the modes down to a critical density, at which spontaneous localization was observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that was not observed. The measured spin velocity was smaller than theoretically predicted.

Spin current and polarization in impure two-dimensional electron systems with spin-orbit coupling.

We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting Delta and elastic scattering rate tau(-1). We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

SU(4) Fermi liquid state and spin filtering in a double quantum dot system.

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.

Strong enhancement of drag and dissipation at the weak- to strong-coupling phase transition in a bilayer system at a total Landau level filling nu = 1.

We consider a bilayer electronic system at a total Landau level filling factor nu = 1, and focus on the transition from the regime of weak interlayer coupling to that of the strongly coupled (1,1,1) phase (or "quantum Hall ferromagnet"). Making the assumption that in the transition region the system is made of puddles of the (1,1,1) phase embedded in a bulk of the weakly coupled state, we show that the transition is accompanied by a strong increase in longitudinal Coulomb drag that reaches a maximum of approximately h/2e(2). In that regime the longitudinal drag increases with decreasing temperature.

Spin-orbit effects in a GaAs quantum dot in a parallel magnetic field.

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. Counterintuitively we argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B( parallel), even if they are negligible for B( parallel) = 0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B( parallel). Our picture is consistent with the experimental observations of Folk et al.

Effects of spatial variation in membrane diffusibility and solubility on the lateral transport of membrane components.

There exist many examples of membrane components (e.g. receptors) accumulating in special domains of cell membranes. We analyze how certain variations in lateral diffusibility and solubility of the membrane would increase the efficiency of transport to these regions. A theorem is derived to show that the mean-time-of capture, tc, for particles diffusing to a trap from an annular region surrounding it, is intermediate to the tc values that correspond to the minimum and maximum diffusion coefficients that obtain in this region. An analytical solution for tc as a function of the gradient of diffusivity surrounding a trap is derived for circular geometry. Since local diffusion coefficients can be increased dramatically by reducing the concentration of intra-membrane particles and/or allowing them to form aggregates, such mechanisms could greatly enhance the diffusion-limited transport of particular membrane components to a trap (e.g. coated pit). If the trap is surrounded by an annular region in which the probe particles' partition function is increased, say, by the local segregation of certain phospholipids, tc is shown to vary inversely with the logarithm of the relative partition function. We provide some conjectural examples to illustrate the magnitude of the effects which heterogeneities in diffusibility and solubility may have in biological membranes.

Pentagonal and icosahedral order in rapidly cooled metals.

The discovery of an alloy of aluminum and manganese with sharp Bragg diffraction spots and an icosahedral point group symmetry was announced last year. The icosahedral symmetry appears to be an intrinsic property of the material and not an artifact of twinning. There are remarkable similarities between the observed diffraction patterns and aperiodic tesselations of space called Penrose tiles. The relation between the experiments and Penrose tiles, as well as phenomenological descriptions of the icosahedral aluminum-manganese alloy as a superposition of incommensurate density waves, are reviewed. Other types of exotic crystallography are also discussed.