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Conventional s-wave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero[1]. Several recent studies have focused on structures where such conventional s-wave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition [2, 3]. Here we present measurements and theoretical calculations of several HgTe quantum wells coupled to either aluminum or niobium superconductors and subject to a magnetic field in the plane of the quantum well. By studying the oscillatory response of Josephson interference to the magnitude of the in-plane magnetic field, we find that the induced pairing within the quantum well is spatially varying. Cooper pairs acquire a tunable momentum that grows with magnetic field strength, directly reflecting the response of the spin dependent Fermi surfaces to the in-plane magnetic field. In addition, in the regime of high electron density, nodes in the induced superconductivity evolve with the electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes, and Zhang [4]. This agreement allows us to quantitatively extract the value of g/v ˜ F , where g˜ is the effective g-factor and vF is the Fermi velocity. However, at low density our measurements do not agree with our model in detail. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter, as well as a general framework within which to investigate electronic spin texture at the Fermi surface of materials., Physics

The electron number parity of the ground state of a semiconductor nanowire proximity coupled to a bulk superconductor can alternate between the quantized values ±1 if parameters such as the wire length L, the chemical potential μ, or the magnetic field B are varied inside the topological superconductor phase. The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps δN in the charge of the nanowire, whose values decrease exponentially with the wire length. We study theoretically the dependence of δN on system parameters, and compare the locations in the μ−B plane of parity jumps when the nanowire is or is not proximity coupled to a bulk superconductor. We show that, despite the fact that the wave functions of the Majorana modes are localized near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly distributed charge measurements, one can rule out alternative explanations for earlier results. We shed light on a parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density., Physics

We investigate capacitively-coupled exchange-only two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin S and its projection Sz are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has a dramatic effect on the performance of two-qubit gates. By varying the level splittings of individual qubits, Ja and Jb, and the interqubit coupling time, t, we can find an infinite number of triples (Ja,Jb,t) for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact cnot gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits., Physics

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood. Here we show that spin–orbit coupling can quench dynamic nuclear polarization in a GaAs quantum dot, because spin conservation is violated in the electron–nuclear system, despite weak spin–orbit coupling in GaAs. Using Landau–Zener sweeps to measure static and dynamic properties of the electron spin–flip probability, we observe that the size of the spin–orbit and hyperfine interactions depends on the magnitude and direction of applied magnetic field. We find that dynamic nuclear polarization is quenched when the spin–orbit contribution exceeds the hyperfine, in agreement with a theoretical model. Our results shed light on the surprisingly strong effect of spin–orbit coupling in central-spin systems.

A theoretical proposal for realizing and detecting spin supercurrent in an isotropic antiferromagnetic insulator is reported. Superfluid spin transport is achieved by inserting the antiferromagnet between two metallic reservoirs and establishing a spin accumulation in one reservoir such that a spin bias is applied across the magnet. We consider a class of bipartite antiferromagnets with Néel ground states, and temperatures well below the ordering temperature, where spin transport is mediated essentially by the condensate. Landau-Lifshitz and magnetocircuit theories are used to directly relate spin current in different parts of the heterostructure to the spin-mixing conductances characterizing the antiferromagnet∣∣metal interfaces and the antiferromagnet bulk damping parameters, quantities all obtainable from experiments. We study the efficiency of spin angular-momentum transfer at an antiferromagnet∣∣metal interface by developing a microscopic scattering theory for the interface and extracting the spin-mixing conductance for a simple model. Within the model, a quantitative comparison between the spin-mixing conductances obtained for the antiferromagnet∣∣metal and ferromagnet∣∣metal interfaces is made., Physics

Inspired by the creation of a fast exchange-only qubit [Medford et al., Phys. Rev. Lett. 111, 050501 (2013)], we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same as or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about 1% of their level splittings, and we calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of interqubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate the existence of an optimal range of coupling strength maintaining stability during the operational time., Physics

We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the electron-hole liquid subject to zero and finite perpendicular magnetic fields using an effective medium approximation and a complementary mapping on resistor networks. In the presence of smooth disorder and in the limit of a weak electron-hole recombination rate, we find for small but finite overlap of the electron and hole bands an abrupt upturn in resistivity when lowering the temperature but no divergence at zero temperature. We discuss how this behavior is relevant for several experimental realizations and introduce a simple physical explanation for this effect., Physics

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., Engineering and Applied Sciences, Physics

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., Engineering and Applied Sciences, Physics

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., Engineering and Applied Sciences, Physics

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., Chemistry and Chemical Biology, Physics

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., Physics

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., Mathematics, Physics

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., Physics

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., Chemistry and Chemical Biology, Mathematics, Physics

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., Mathematics, Physics

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., Physics, Other Research Unit

Spin polarization may be generated far from the boundaries of a sample by nonlinear effects of an electric current, in the presence of "extrinsic" spin-orbit interactions, even when such generation is forbidden in the linear regime. We present a Corbino model where spin accumulation results from a combination of current gradients, nonlinearity, and cubic anisotropy. Further, we show that even with isotropic conductivity, nonlinear effects in a low-symmetry sidearm geometry can generate spin polarization far away from boundaries. Finally, we find that drift from the boundaries dominates spin polarization patterns observed in recent experiments on GaAs by Sih et al. [Phys. Rev. Lett. 97, 096605 (2006)]., Physics

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., Physics

We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach., Physics

We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew-scattering and side-jump contributions to the spin-Hall conductivity. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with experiments by Kato et al., Physics

Motivated by recent scanning tuneling microscopy STM experiments on Bi2Sr2CaCu2O8 J. E. Hoffman et al., Science 295, 466 2002 ; C. Howald et al., cond-mat/0201546 unpublished ; J. E. Hoffman et al., Science 297, 1149 2002 : K. McElroy et al. unpublished ; C. Howald et al., cond-mat/0208442 unpub- lished , we study the effects of weak translational symmetry breaking on the quasiparticle spectrum of a d-wave superconductor. We develop a general formalism to discuss periodic charge order, as well as quasipar- ticle scattering off localized defects. We argue that the STM experiments in Bi2 Sr2 CaCu2 O8 cannot be explained using a simple charge density wave order parameter, but are consistent with the presence of a periodic modulation in the electron hopping or pairing amplitude. We review the effects of randomness and pinning of the charge order and compare it to the impurity scattering of quasiparticles. We also discuss implications of weak translational symmetry breaking for angle resolved photoemission spectroscopy experi- ments., Physics

We study the magnetoplasmon collective-mode excitations of integer quantum Hall systems in a paraboli- cally confined quantum well nanostructure in the presence of a tilted magnetic field by using the time- dependent Hartree-Fock approximation. For even integer filling, we find that the dispersion of a spin density mode has a magnetoroton minimum at finite wave vectors, at a few times 106 cm 1 for parallel fields of order 1–10 T, only in the direction perpendicular to the in-plane magnetic field, while the mode energy increases monotonously with wave vector parallel to the in-plane magnetic field. When the in-plane magnetic field is strong enough well above 10 T ,we speculate that this roton minimum may reach zero energy, suggesting a possible second-order phase transition to a state with broken translational and spin symmetries. We discuss the possibility for observing such parallel field-induced quantum phase transitions. We also derive an expression for the dielectric function within the time-dependent Hartree-Fock approximation and include screening effects in our magnetoplasmon calculation. We discuss several exotic symmetry-broken phases that may be stable in finite parallel fields, and propose that the transport anisotropy, observed recently in parallel field experiments, may be due to the formation of a skyrmion stripe phase predicted in our theory. Our predicted anisotropic finite wave-vector suppression, perhaps even a mode softening leading to the quantum phase transition to the anisotropic phase, in the collective spin excitation mode of the wide well system in the direction transverse to the applied parallel magnetic field should be directly experimentally observable via the inelastic light-scattering spectroscopy., Physics