We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error-correcting code defined by the ground states of this model (the Fibonacci code). We quantify the complexity of these circuits with gate counts using different universal gate sets and find these measurements become significantly easier to perform if $n$-qubit Toffoli gates with $n=3,4$, and 5 can be carried out directly. In addition to measurement circuits, we construct simplified quantum circuits requiring only a few qubits that can be used to verify that certain self-consistency conditions, including the pentagon equation, are satisfied by the Fibonacci code.

Vibrational properties of iron-chalcogenide superconductor K${}_{0.75}$Fe${}_{1.75}$Se${}_2$ with $T_c\sim$ 30 K have been measured by Raman and optical spectroscopies over the temperature range 3–300 K. The sample undergoes $I4/m\to I4$ structural phase transition accompanied by loss of inversion symmetry at $T_1$, below 250 K, observed as the appearance of new fully symmetric Raman mode at $\sim$165 cm${}^{-1}$. Small vibration mode anomalies are also observed at $T_2\sim$ 160 K. From first-principles vibrational analysis of antiferromagnetic K${}_{0.8}$Fe${}_{1.6}$Se${}_2$ utilizing pseudopotentials all observed Raman and infrared modes have been assigned and the displacement patterns of the new Raman mode identified as involving predominantly the Se atoms.

The spectral distribution of parametrically excited dipole-exchange magnons in an in-plane magnetized epitaxial film of yttrium-iron garnet was studied by means of frequency- and wavevector-resolved Brillouin light scattering spectroscopy. The experiment was performed in a parallel pumping geometry, where an exciting microwave magnetic field was parallel to the magnetizing field. It was found that for both dipolar and exchange spectral areas parallel pumping excites the lowest volume magnon modes propagating in the film plane perpendicularly to the magnetization direction. No excitation of the high-order volume modes has been registered. In order to interpret the experimental observations, we used a microscopic Heisenberg model that includes exchange as well as dipole-dipole interactions to calculate the magnon spectrum and construct the eigenstates. As proven in our calculations, the observed magnons are characterized by having the highest possible ellipticity of precession, which suggests the lowest threshold of parametric generation. Applying different pumping powers we observe modifications in the magnon spectrum that are described theoretically by a softening of the spin stiffness.

Gate instability/hysteresis in modulation-doped $p$-type AlGaAs/GaAs heterostructures impedes the development of nanoscale hole devices, which are of interest for topics from quantum computing to novel spin physics. We present an extended study conducted using custom-grown, matched modulation-doped $n$-type and $p$-type heterostructures, with and without insulated gates, aimed at understanding the origin of the hysteresis. We show the hysteresis is not due to the inherent “leakiness” of gates on $p$-type heterostructures, as commonly believed. Instead, hysteresis arises from a combination of GaAs surface-state trapping and charge migration in the doping layer. Our results provide insights into the physics of Si acceptors in AlGaAs/GaAs heterostructures, including widely debated acceptor complexes such as Si-X. We propose methods for mitigating the gate hysteresis, including poisoning the modulation-doping layer with deep-trapping centers (e.g., by codoping with transition metal species) and replacing the Schottky gates with degenerately doped semiconductor gates to screen the conducting channel from GaAs surface states.

We have used the mechanical motion of a carbon nanotube (CNT) as a probe of the average charge on a quantum dot. Variations of the resonance frequency and the quality factor are determined by the change in average charge on the quantum dot during a mechanical oscillation. The average charge, in turn, is influenced by the gate voltage, the bias voltage, and the tunnel rates of the barriers to the leads. At bias voltages that exceed the broadening due to tunnel coupling, the resonance frequency and quality factor show a double dip as a function of gate voltage. We find that increasing the current flowing through the CNT at the Coulomb peak does not increase the damping, but in fact decreases damping. Using a model with energy-dependent tunnel rates, we obtain quantitative agreement between the experimental observations and the model. We theoretically compare different contributions to the single-electron induced nonlinearity, and show that only one term is significant for both the Duffing parameter and the mode coupling parameter. We also present additional measurements which support the model we develop: Tuning the tunnel barriers of the quantum dot to the leads gives a 200-fold decrease of the quality factor. Single-electron tunneling through an excited state of the CNT quantum dot also changes the average charge on the quantum dot, bringing about a decrease in the resonance frequency. In the Fabry-Pérot regime, the absence of charge quantization results in a spring behavior without resonance frequency dips, which could be used, for example, to probe the transition from quantized to continuous charge with a nanomechanical resonator.

In this paper, we discuss two-dimensional holographic metals from a condensed matter physics perspective. We examine the spin structure of the Green's function of the holographic metal, demonstrating that the excitations of the holographic metal are “chiral,” lacking the inversion symmetry of a conventional Fermi surface, with only one spin orientation for each point on the Fermi surface aligned parallel to the momentum. While the presence of a Kramer's degeneracy across the Fermi surface permits the formation of a singlet superconductor, it also implies that ferromagnetic spin fluctuations are absent from the holographic metal, leading to a complete absence of Pauli paramagnetism. In addition, we show how the Green's function of the holographic metal can be regarded as a reflection coefficient in anti–de Sitter space, relating the ingoing and outgoing waves created by a particle moving on the external surface.

We perform a symmetry analysis of a 2D electron system in HgTe/HgCdTe quantum wells in the situation when the chemical potential is outside of the gap, so the bulk of the quantum well is conducting. In order to investigate quantum transport properties of the system, we explore symmetries of the low-energy Hamiltonian, which is expressed in terms of two flavors of Dirac fermions, and physically important symmetry-breaking mechanisms. This allows us to predict emerging patterns of symmetry breaking that control the weak localization and antilocalization showing up in transverse-field magnetoresistance.

The linear magnetoelectric response of Cr${}_2$O${}_3$ at zero temperature is calculated from first principles by tracking the change in magnetization under a macroscopic electric field. Both the spin and the orbital contributions to the induced magnetization are computed, and in each case the response is decomposed into lattice and electronic parts. We find that the transverse response is dominated by the spin-lattice and spin-electronic contributions, whose calculated values are consistent with static and optical magnetoelectric measurements. In the case of the longitudinal response, orbital contributions dominate over spin contributions, but the net calculated longitudinal response remains much smaller than the experimentally measured one at low temperatures. We also discuss the absolute sign of the magnetoelectric coupling in the two time-reversed magnetic domains of Cr${}_2$O${}_3$.

We report a superconducting artificial atom with a coherence time of $T_2^{*}=92$ $\mu$s and energy relaxation time $T_1=70$ $\mu$s. The system consists of a single Josephson junction transmon qubit on a sapphire substrate embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds promise as a robust and easily produced artificial quantum system whose intrinsic coherence properties are sufficient to allow tests of quantum error correction.

The Mott insulating state formed from bosons is ubiquitous in solid ${}^4$He, cold-atom systems, Josephson junction networks, and perhaps underdoped high-$T_{\mathrm{c}}$ superconductors. We predict that close to the quantum phase transition to the superconducting state, the Mott insulator is not at all as featureless as is commonly believed. In three dimensions, there is a phase transition to a low-temperature state where, under influence of an external current, a superconducting state consisting of a regular array of “wires” that each carry a quantized flux of supercurrent is realized. This prediction of the “type-II Mott insulator” follows from a field-theoretical weak-strong duality, showing that this “current lattice” is the dual of the famous Abrikosov lattice of magnetic fluxes in normal superconductors. We argue that this can be exploited to investigate experimentally whether preformed Cooper pairs exist in high-$T_{\mathrm{c}}$ superconductors.

We study the interplay of structural and polar distortions in hexagonal YMnO${}_3$ and short-period PbTiO${}_3$/SrTiO${}_3$ (PTO/STO) superlattices by means of first-principles calculations at constrained electric displacement field $D$. We find that in YMnO${}_3$ the tilts of the oxygen polyhedra produce a robustly polar ground state, which persists at any choice of the electrical boundary conditions. Conversely, in PTO/STO the antiferrodistortive instabilities alone do not break inversion symmetry, and open-circuit boundary conditions restore a nonpolar state. We suggest that this qualitative difference naturally provides a route to rationalizing the concept of “improper ferroelectricity” from the point of view of first-principles theory. We discuss the implications of our arguments for the design of novel multiferroic materials with enhanced functionalities and for the symmetry analysis of the phase transitions.

The edge of spin-unpolarized or spin-polarized $\nu =2/3$ fractional quantum Hall states is predicted by the effective theory to support a backward-moving neutral mode in addition to a forward-moving charge mode. We study this issue from a microscopic perspective where these states are identified with an effective filling factor of 2 of composite fermions, but with an effective magnetic field that is antiparallel to the external field. A simple counting from the composite fermion description suggests that there might be two backward-moving edge modes, but explicit calculations show that one of these is projected out of the low-energy sector, while the remaining mode provides a good microscopic account of the actual counterpropagating edge mode. The forward-moving modes are identified as “Schur modes,” obtained by multiplying the ground-state wave function by the symmetric Schur polynomials. The edge of the 2/3 spin unpolarized state provides a particularly striking realization of “spin-charge separation” in one-dimensional Tomonaga-Luttinger liquids, with the spin and charge modes moving in opposite directions.

We study the coherent properties of transmission through Kondo impurities by considering an open Aharonov-Bohm ring with an embedded quantum dot. We develop a many-body scattering theory which enables us to calculate the conductance through the dot $G_d$, the transmission phase shift ${\varphi }_t$, and the normalized visibility $\eta$ in terms of the single-particle $\mathcal{T}$ matrix. For the single-channel Kondo effect, we find at temperatures much below the Kondo temperature $T_K$ that ${\varphi }_t=\pi /2$ without any corrections up to order ${(T/T_K)}^2$. The visibility has the form $\eta =1-{(\pi T/T_K)}^2$. For the non-Fermi-liquid fixed point of the two-channel Kondo, we find that ${\varphi }_t=\pi /2$ despite the fact that a scattering phase shift is not defined. The visibility is $\eta =1/2(1+4\lambda \sqrt{\pi T})$ with $\lambda \sim 1/\sqrt{T_K}$, thus, at zero temperature, exactly half of the conductance is carried by single-particle processes, and coherent transmission may actually increase with temperature. We explain that the spin summation masks the inherent scattering phases of the dot, which can be accessed only via a spin-resolved experiment. In addition, we calculate the effect of magnetic field and channel anisotropy, and generalize to the $k$-channel Kondo case.

Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similarly to the way spintronics uses electron spin. We show how a double-barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is included, the energy bands and energy gaps at the $K$ and $K^{\prime }$ points are different and they can be tuned by changing the potential.

We investigate theoretically the prospects for using a magnetic nanoelectromechanical single-electron tunneling (NEM-SET) device as an electronic spin filter. We find that strong magnetic exchange forces on the net spin of the mobile central dot of the NEM-SET structure lead to spin-dependent mechanical displacements (“spin polarons”), which give rise to vastly different tunneling probabilities for electrons of different spin. The resulting spin polarization of the current can be controlled by bias and gate voltages and be very close to 100$\%$ at voltages and temperatures below a characteristic correlation energy set by the sum of the polaronic and Coulomb blockade energies.

In this work, we demonstrate that significant changes in electron temperature and nuclear spin polarization can be created by applying an electric current in a two-dimensional electron system at Landau level filling factor $\nu =1/2$. The current induced effects on nuclear spins can be attributed to electron heating and the efficient coupling between the nuclear and electron spin systems at $\nu =1/2$. The electron temperature, elevated by the current, can be measured with a thermometer based on the measurement of the nuclear spin relaxation rate. The electron temperature is found to be proportional to the square root of the current density at $\nu =1/2$. Electron spin transitions at $\nu =2/3$ and $1/2$ are utilized for the measurement of the current induced changes in nuclear spin polarization. Consistent results are obtained from these two different methods of nuclear magnetometry. The finite thickness of the electron wave function is found to be important for evaluation of the nuclear spin polarization even in a narrow quantum well. The nuclear spin polarization follows a Curie law dependence on the electron temperature. This work also allows us to evaluate the electron $g$ factor in high magnetic fields as well as the polarization mass of composite fermions.

We present a detailed derivation of heat radiation, heat transfer, and (Casimir) interactions for $N$ arbitrary objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The results can be expressed as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that is not due to radiation pressure.

We present a theory of the quasi-two-dimensional electron gas (2DEG) systems that appear near the surface of SrTiO${}_3$ when a large external electric field attracts carriers to the surface. We find that nonlinear and nonlocal screening by the strongly polarizable SrTiO${}_3$ lattice plays an essential role in determining 2DEG properties. The electronic structure always includes weakly bound bulklike bands that extend over many SrTiO${}_3$ layers. At 2D carrier densities exceeding $\sim$${10}^{14}{\mathrm{cm}}^{-2}$, tightly bound bands emerge that are confined within a few layers of the surface.

We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e., with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs of integer quantum Hall states, topological insulators, and superconductors. We adapt the well-known Chern-Simons $K$-matrix description of quantum Hall states to classify such “integer” topological phases. Our main result is a general formalism that incorporates symmetries into the $K$-matrix description. Remarkably, this simple analysis yields the same list of topological phases as a recent group cohomology classification, and in addition provides field theories and explicit edge theories for all these phases. The bosonic topological phases, which only appear in the presence of interactions and which remain well defined in the presence of disorder, include (i) bosonic insulators with a Hall conductance quantized to even integers, (ii) a bosonic analog of quantum spin Hall insulators, and (iii) a bosonic analog of a chiral topological superconductor, whose $K$ matrix is the Cartan matrix of Lie group $E_8$. We also discuss interacting fermion systems where symmetries are realized in a projective fashion, where we find the present formalism can handle a wider range of symmetries than a recent group super-cohomology classification. Lastly, we construct microscopic models of these phases from coupled one-dimensional systems.

The ground-state phase diagram of a spin-$\frac{1}{2}$ XXZ chain with competing ferromagnetic nearest-neighbor ($J_1<0$) and antiferromagnetic second-neighbor ($J_2>0$) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $-4<J_1/J_2<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and Néel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and Néel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.