Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of ${\mathbb{Z}}_2$ gauge theory) is a $\text{U}\left(1\right)\times \text{U}\left(1\right)$ Chern-Simons theory in which gauge charges (i.e., $e$ and $m$ particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact $\text{U}\left(1\right)\times \text{U}\left(1\right)$ gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and $\text{U}\left(1\right)\times \text{U}\left(1\right)$ magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel–type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and $\mathrm{\Theta }\ne \pi$, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry ($\mathsf{Charles}$) of 3D Abelian topological phases. We show that line twist defects, which realize $\mathsf{Charles}$ transformations, exhibit non-Abelian fusion properties.

Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) and are performed using DCA simulations with an interaction-expansion continuous-time quantum Monte Carlo cluster solver. We calculated explicitly the temperature dependence of different uniform superconducting pairing susceptibilities and found a consistent picture emerging upon gradually increasing the cluster size: while at weak coupling the $d+id$ singlet pairing dominates close to the VHS filling, an enhanced tendency towards $p$-wave triplet pairing upon further increasing the interaction strength is observed. The relevance of these systematic results for existing proposals and ongoing pursuits of odd-parity topological superconductivity are also discussed.

Drude oscillators provide a harmonic description of charge fluctuations and are widely studied as a model system and for ab initio calculations. In the dipole approximation the Hamiltonian describing the interaction of Drudes is quadratic, so it can be diagonalized exactly, but the energy diverges at short range. Here we consider the quantum mechanics of Drude oscillators interacting through the full Coulombic Hamiltonian for which the interaction energy does not have this defect. This protypical model for interactions between matter includes electrostatics, induction, and dispersion. Potential energy curves for rare-gas dimers are very closely matched by Drude correlation energies plus a single exponential function. The exact and accurate results presented here help to delineate between the basic properties of the physical model and the effects that arise from the dipole approximation.

The high tunability of the density of states of graphene makes it an ideal probe of quantum transport in different regimes. In particular, the supercurrent that can flow through a nonsuperconducting (N) material connected to two superconducting (S) electrodes, crucially depends on the length of the N relative to the superconducting coherence length. Using graphene as the N material we have investigated the full range of the superconducting proximity effect, from short to long diffusive junctions. By combining several S/graphene/S samples with different contacts and lengths, and measuring their gate-dependent critical currents $\left(I_c\right)$ and normal state resistance $R_N$, we compare the product $e{R}_N{I}_c$ to the relevant energies, the Thouless energy in long junctions and the superconducting gap of the contacts in short junctions, over three orders of magnitude of Thouless energy. The experimental variations strikingly follow a universal law, close to the predictions of the proximity effect both in the long and short junction regime, as well as in the crossover region, thereby revealing the interplay of the different energy scales. Differences in the numerical coefficients reveal the crucial role played by the interfacial barrier between graphene and the superconducting electrodes, which reduces the supercurrent in both short and long junctions. Surprisingly, the reduction of supercurrent is independent of the gate voltage and of the nature of the electrodes. A reduced induced gap and Thouless energy are extracted, revealing the role played by the dwell time in the barrier in the short junction, and an effective increased diffusion time in the long junction. We compare our results to the theoretical predictions of Usadel equations and numerical simulations, which better reproduce experiments with imperfect NS interfaces.

We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight-binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ), and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consumption of the calculations. Our approach can be applied to quantum devices of an arbitrary geometry and any number of degrees of freedom or leads attached. We provide a couple of examples of possible applications of the theory, including current equilibration at the $p\text{−}n$ junction in graphene and scanning gate microscopy mapping of electron trajectories in the magnetic focusing experiment on a graphene ribbon. Additionally, we provide a simple toy example of electron transport through 1D wire with added onsite perturbation and obtain a simple formula for conductance showing that Green's function of the device can be obtained from the conductance versus impurity strength characteristics.

We generalize the spin Meissner effect for an exciton-polariton condensate confined in annular geometries to the case of nontrivial topology of the condensate wave function. In contrast to the conventional spin Meissner state, topological spin Meissner states can in principle be observed at arbitrary high magnetic fields not limited by the critical magnetic field value for the condensate in a simply connected geometry. One special example of the topological Meissner states are half-vortices. We show that in the absence of magnetic field, half-vortices in a ring exist in a form of a superposition of elementary half-vortex states, which resolves recent experimental results where such puzzling superposition was observed. Furthermore, we show that if a pure half-vortex state is to be observed, a nonzero magnetic field of a specific magnitude needs to be applied. Studying exciton polaritons in a ring in the presence of TE-TM splitting, we observe spin Meissner states that break the rotational symmetry of the system by developing inhomogeneous density distributions. We classify various states arising in the presence of nonzero TE-TM splitting based on what states they can be continued from by increasing the TE-TM splitting parameter from zero. With further increasing TE-TM splitting, states with broken symmetry may transform into stable half-dark solitons and therefore may serve as a useful tool to generate various nontrivial states of a spinor condensate.

We study the frequency dependencies in the renormalization of the fermion Green's function for the $\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region, we self-consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency-dependent Lindhard screening and retardation effects.

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in one-dimensional open chains, which generalizes the seminal work by Fendley [J. Stat. Mech. (2012) P11020]. The first essential property is that the ground states are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the ground states. These two properties are shown to be topologically robust, and applicable to a wider family of topologically ordered Hamiltonians than has been previously considered. As an application of these edge modes, we formulate a notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain ground state is topological, i.e., it originates from the topological manifold of the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalize Cooper pairing in superconductors. The stability of these condensates is investigated on both open and closed chains.

Topologically ordered quantum phases are robust in the sense that perturbations in the Hamiltonian of the system will not change the topological nature of the ground-state wave function. However, in order to exploit topological order for applications such as self-correcting quantum memories and information processing, these states need to be also robust both dynamically and at finite temperature in the presence of an environment. It is well known that systems like the toric code in two spatial dimensions are fragile in temperature. In this paper, we show a completely analytic treatment of the toric code away from equilibrium, after a quantum quench of the system Hamiltonian. We show that, despite being subject to unitary evolution (and at zero temperature), the long-time behavior of the topological entropy is thermal, therefore vanishing. If the quench preserves a local gauge structure, there is a residual long-lived topological entropy. This also is the thermal behavior in presence of such gauge constraints. The result is obtained by studying the time evolution of the topological 2-Rényi entropy in a fully analytical, exact way.

Time-dependent systems have recently been shown to support novel types of topological order that cannot be realized in static systems. In this paper we consider a range of time-dependent, interacting systems in one dimension that are protected by an Abelian symmetry group. We classify the distinct topological phases that can exist in this setting and find that they may be described by a bulk invariant associated with the unitary evolution of the closed system. In the open system, nontrivial phases correspond to the appearance of edge modes, which have signatures in the many-body quasienergy spectrum and which relate to the bulk invariant through a form of bulk-edge correspondence. We introduce simple models which realize nontrivial dynamical phases in a number of cases, and outline a loop construction that can be used to generate such phases more generally.

It is known that electron scattering by surface polar phonons (SPPs) of the substrate reduces their mobility in supported graphene. However, there is no experimental evidence for the contribution of the drag of electrons by SPPs to thermoelectric phenomena in graphene: graphene thermopower exhibits good agreement with Mott's law, which means that the diffusion contribution to the thermopower is dominant in a wide range of carrier densities and temperatures. Here we develop a complete theory of drag of electrons in graphene by SPPs. By solving the Boltzmann transport equation for electrons scattered by SPPs we derive SPP-drag contribution to the thermopower in graphene. Compared to diffusion thermopower, obtained values appear to be one order of magnitude lower for various substrates. This can be explained by the low occupation number of the SPPs and short mean free path of such phonons stemming from their small group velocity. We conclude that experiments on thermopower in graphene can be treated within the framework of Mott's law.

The distribution and dynamic behavior of Abrikosov vortices in type-$\mathrm{II}$ superconductors could modulate the nearby magnetic field, thus enriching new physics in the proximal two-dimensional electron gas. Here we investigate the effects of vortex dynamics on the quantum transport properties of graphene in proximity to the superconducting single-crystalline ${\mathrm{NbSe}}_2$ thin flakes. Pronounced asymmetric magnetoresistivity plateaus emerge near zero field below the critical temperature of ${\mathrm{NbSe}}_2$, accompanied by hysteresis loops. In sharp contrast, only weak localization behavior is observed for graphene placed on ${\mathrm{SiO}}_2\text{/}\mathrm{Si}$ substrate. Such magnetoresistivity plateaus and hysteresis can be attributed to the vortex pinning effect at the edge defects of the single-crystalline ${\mathrm{NbSe}}_2$ flakes. Our findings may shed light on the realization of emergent states in the two-dimensional electron gases by manipulation of vortex dynamics and distribution in the proximal superconductors.

We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled-layer construction.

Investigation of real two-dimensional systems with Dirac-like electronic behavior under the influence of magnetic field is challenging and leads to many interesting physical results. In this paper we study a 2D graphene model with a particular form of magnetic field as a superposition of a homogeneous field and an Aharonov-Bohm vortex. For this configuration, electronic wave functions and the energy spectrum are obtained and it is shown that the magnetic Aharonov-Bohm vortex plays the role of a charge impurity. As a demonstration of vacuum properties of the system, vacuum current, as well as an electric current, is calculated and their representation for particular limiting cases of a magnetic field is obtained.

We study the spin Hall magnetoresistance effect in ferrimagnet/normal metal bilayers, comparing the response in collinear and canted magnetic phases. In the collinear magnetic phase, in which the sublattice magnetic moments are all aligned along the same axis, we observe the conventional spin Hall magnetoresistance. In contrast, in the canted phase, the magnetoresistance changes sign. Using atomistic spin simulations and x-ray absorption experiments, we can understand these observations in terms of the magnetic field and temperature dependent orientation of magnetic moments on different magnetic sublattices. This enables a magnetotransport based investigation of noncollinear magnetic textures.

Electrical resistivity, magnetization, and specific heat measurements were performed on polycrystalline samples of the filled-skutterudite systems ${\mathrm{La}}_{1-x}{M}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}(M=\text{Ce}$ and $\mathrm{Th})$. Superconductivity in ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$ was quickly suppressed with Ce substitution and no evidence for superconductivity was found down to 1.1 K for $x>0.2$. Temperature-dependent specific heat data at low temperatures for ${\mathrm{La}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ show a change from power-law to exponential behavior, which may be an indication for multiband superconductivity in ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$. A similar crossover was observed in the ${\mathrm{Pr}}_{1-x}{\mathrm{Ce}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ system. However, the suppression rates of the superconducting transition temperatures $T_c$($x$) in the two systems are quite disparate, indicating a difference in the nature of superconductivity, which is conventional in ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$ and unconventional in ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$. In comparison, a nearly linear and smooth evolution of $T_c$ with increasing Th was observed in the ${\mathrm{La}}_{1-x}{\mathrm{Th}}_x{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ system, with no change of the superconducting energy gap in the temperature dependence of the specific heat, suggesting similar types of superconductivity in both the ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$ and ${\mathrm{ThPt}}_4{\mathrm{Ge}}_{12}$ compounds.

The energy dissipation of quasiclassical homogeneous turbulence in superfluid ${}^4\mathrm{He}$ (He II) is controlled by an effective kinematic viscosity ${\nu }^{\prime }$, which relates the energy decay rate $dE/dt$ to the density of quantized vortex lines $L$ as $dE/dt=-{\nu }^{\prime }{\left(\kappa L\right)}^2$. The precise value of ${\nu }^{\prime }$ is of fundamental importance in developing our understanding of the dissipation mechanism in He II, and it is also needed in many high-Reynolds-number turbulence experiments and model testing that use He II as the working fluid. However, a reliable determination of ${\nu }^{\prime }$ requires the measurements of both $E\left(t\right)$ and $L\left(t\right)$, which was never achieved. Here we discuss our study of the quasiclassical turbulence that emerges in the decay of thermal counterflow in He II above 1 K. We were able to measure $E\left(t\right)$ by using a recently developed flow-visualization technique and $L\left(t\right)$ via second-sound attenuation. We report the ${\nu }^{\prime }$ values in a wide temperature range determined from a comparison of the time evolution of $E\left(t\right)$ and $L\left(t\right)$.

We perform an experiment to test between two theories of the electrodynamics of superconductors: the standard London theory and an alternative proposed by J. E. Hirsch [Phys. Rev. B 69, 214515 (2004)]. The two alternatives give different predictions with respect to the screening of an electric field by a superconductor, and we try to detect this effect using atomic force microscopy on a niobium sample. We also perform the reverse experiment, where we demonstrate a superconductive tip mounted on a qPlus force sensor. Due to limited accuracy, we are able neither to prove nor to disprove Hirsch's hypothesis. Within our accuracy of 0.17 N/m, the superconductive transition does not alter the atomic-scale interaction between tip and sample.

The structural and electronic properties of a series of ${\mathrm{SrMnO}}_3$ thin films grown on different substrates leading to different biaxial strains are examined by means of aberration-corrected high-angle annular dark-field scanning transmission electron microscopy and electron energy-loss spectroscopy (EELS). Here, we report a comprehensive theoretical investigation on the impact of oxygen nonstoichiometry and strain on the O-$K$ and Mn-$L_{2,3}$ electron energy-loss near-edge structures of ${\mathrm{SrMnO}}_3$ with the aid of the all-electron density functional theory code wien2k. Our experimental and theoretical EELS data reveal pronounced peak-height changes and energy shifts as a function of strain, which are ascribed to differences in the oxygen vacancy density rather than to a direct effect of lattice distortions. In addition, we find that the formation of oxygen vacancies in ${\mathrm{SrMnO}}_3$ is likely to be enhanced by tensile strain. Compared to the unstrained material, the vacancy formation energy is reduced by 0.25 eV under 3.78% tensile strain.

Molybdenum (Mo) is a transition metal with a wide range of technical applications. There has long been strong interest in its high-pressure behavior, and it is often used as standard for high-pressure experiments. Combining powder x-ray diffraction and dynamic ramp compression, structural and equation of state data were collected for solid Mo to 1 TPa (10 Mbar). Diffraction results are consistent with Mo remaining in the body-centered-cubic structure into the TPa regime. Stress-density data show that Mo under ramp loading is less compressible than the room-temperature isotherm but more compressible than the single-shock Hugoniot.