We study superconducting states of doped inversion-symmetric Weyl semimetals. Specifically, we consider a lattice model realizing a Weyl semimetal with an inversion symmetry and study the superconducting instability in the presence of a short-ranged attractive interaction. With a phonon-mediated attractive interaction, we find two competing states: a fully gapped finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov pairing state and a nodal even-parity pairing state. We show that, in a BCS-type approximation, the finite-momentum pairing state is energetically favored over the usual even-parity paired state and is robust against weak disorder. Although energetically unfavorable, the even-parity pairing state provides an electronic analog of the ${}^3$He-$A$ phase in that the nodes of the even-parity state carry nontrivial winding numbers and therefore support a surface flat band. We briefly discuss other possible superconducting states that may be realized in Weyl semimetals.

We present a theoretical study of the quasiparticle and subgap conductance of generic $X/I_{\text{sf}}/S_M$ junctions with a spin-filter barrier $I_{\text{sf}}$, where $X$ is either a normal $N$ or a ferromagnetic metal $F$ and $S_M$ is a superconductor with a built-in exchange field. Our study is based on the tunneling Hamiltonian and the Green's-function technique. First, we focus on the quasiparticle transport, both above and below the superconducting critical temperature. We obtain a general expression for the tunneling conductance which is valid for arbitrary values of the exchange field and arbitrary magnetization directions in the electrodes and in the spin-filter barrier. In the second part, we consider the subgap conductance of a $N/I_{\text{sf}}/S$ junction, where $S$ is a conventional superconductor. In order to account for the spin-filter effect at interfaces, we heuristically derive boundary conditions for the quasiclassical Green's functions. With the help of these boundary conditions, we show that the proximity effect and the subgap conductance are suppressed by spin filtering in a $N/I_{\text{sf}}/S$ junction. Our work provides useful tools for the study of spin-polarized transport in hybrid structures both in the normal and in the superconducting state.

Exotic superconductivity has often been discovered in materials with a layered (two-dimensional) crystal structure. The low dimensionality can affect the electronic structure and can realize high transition temperatures ($T_{\mathrm{c}}$) and/or unconventional superconductivity mechanisms. We show superconductivity in a new bismuth-oxysulfide compound Bi${}_4$O${}_4$S${}_3$. Crystal structure analysis indicates that this superconductor has a layered structure composed of a stacking of spacer layers and BiS${}_2$ layers. Band calculation suggests that the Fermi level for Bi${}_4$O${}_4$S${}_3$ is just on the peak position of the partial density of states of the Bi 6$p$ orbital within the BiS${}_2$ layer. The BiS${}_2$ layer will be a basic structure which provides another universality class for a layered superconducting family, and this opens up a new field in the physics and chemistry of low-dimensional superconductors.

We theoretically study a multiband Hubbard model of pyrochlore oxides of the form $A_2$$B_2$O${}_7$, where $B$ is a heavy transition metal ion with strong spin-orbit coupling, in a thin-film geometry orientated along the [111] direction. Along this direction, the pyrochlore lattice consists of alternating kagome and triangular lattice planes of $B$ ions. We consider a single kagome layer, a bilayer, and the two different trilayers. As a function of the strength of the spin-orbit coupling, the direct and indirect $d$-orbital hopping, and the band filling, we identify a number of scenarios where a noninteracting time-reversal-invariant $Z_2$ topological phase is expected and we suggest some candidate materials. We study the interactions in the half-filled $d$ shell within Hartree-Fock theory and identify parameter regimes where a zero magnetic field Chern insulator with Chern number $\pm 1$ can be found. The most promising geometries for topological phases appear to be the bilayer which supports both a $Z_2$ topological insulator and a Chern insulator, and the triangular-kagome-triangular trilayer which supports a relatively robust Chern insulator phase.

We study the two-dimensional repulsive Hubbard model by functional renormalization group methods, using our recently proposed channel decomposition of the interaction vertex. The main technical advance of this work is that we calculate the full Matsubara frequency dependence of the self-energy and the interaction vertex in the whole frequency range without simplifying assumptions on its functional form, and that the effects of the self-energy are fully taken into account in the equations for the flow of the two-body vertex function. At Van Hove filling, we find that the Fermi-surface deformations remain small at fixed particle density and have a minor impact on the structure of the interaction vertex. The frequency dependence of the self-energy, however, turns out to be important, especially at a transition from ferromagnetism to $d$-wave superconductivity. We determine non-Fermi-liquid exponents at this transition point.

We study electron quantum transport through a strongly interacting Anderson quantum dot at finite bias voltage and magnetic field at zero temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic (generalized master) equation for the reduced density operator. To this end, we further develop the general, finite-temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville Fock space strongly simplifies the construction of operators and superoperators that transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule of quantum mechanics for the total system of quantum dot plus reservoirs. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator kernel becomes explicit. Using the constraints of the causal structure, we construct a parametrization of the exact effective time-evolution kernel for which we analytically find the eigenvectors and eigenvalues in terms of a minimal set of only 30 independent coefficients. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Contreras-Pulido et al., Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling $\Gamma$. Furthermore, in the wide-band limit, the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. The remaining diagrams can be identified simply by their topology and are manifestly independent of the energy cutoff term by term. By an exact reformulation of this series, we integrate out all infinite-temperature effects, obtaining an expansion targeting only the nontrivial, finite-temperature corrections, and the exactly conserved transport current follows directly from the time-evolution kernel. From this new series, the previously formulated RT-RG equations are obtained naturally. We perform a complete one-plus-two-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence of all renormalized quantities on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville space and symmetry restrictions, we obtain analytical RT-RG equations, which can be solved numerically in an efficient way, and we extensively study the model parameter space, excluding the Kondo regime where the one-plus-two-loop approach is obviously invalid. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak, even at a voltage $\sim$magnetic field $\sim$tunnel coupling $\Gamma$. Moreover, we find a tunnel-induced nonlinearity of the stability diagrams (Coulomb diamonds) at finite voltage, both in the single-electron tunneling and inelastic cotunneling regime.

We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of the quantum double or Levin-Wen model, we obtain a bound on the first-order perturbation of topological entanglement entropy in terms of its energy gap and subsystem size. The bound decreases superpolynomially with the size of the subsystem, provided the energy gap is nonzero. We also study the finite-temperature stability of stabilizer models, for which we prove a stronger statement than the strong subadditivity of entropy. Using this statement and assuming (i) finite correlation length and (ii) small conditional mutual information of certain configurations, first-order perturbation effect for arbitrary local perturbation can be bounded. We discuss the technical obstacles in generalizing these results.

We report electronic-structure and physical properties of metal-doped picene as well as selective synthesis of the phase that exhibits 18-K superconducting transition. First, Raman scattering is used to characterize the number of electrons transferred from the dopants to picene molecules, where a softening of Raman scattering peaks enables us to determine the number of transferred electrons. From this, we have identified that three electrons are transferred to each picene molecule in the superconducting doped picene solids. Second, we report pressure dependence of $T_c$ in 7- and 18-K phases of K${}_3$picene. The 7-K phase shows a negative pressure dependence, while the 18-K phase exhibits a positive pressure dependence which can not be understood with a simple phonon mechanism of BCS superconductivity. Third, we report a synthesis method for superconducting K${}_3$picene by a solution process with monomethylamine CH${}_3$NH${}_2$. This method enables us to prepare selectively the K${}_3$picene sample exhibiting 18-K superconducting transition. The method for preparing K${}_3$picene with $T_c$ $=$ 18 K found here may facilitate clarification of the mechanism of superconductivity.

We herein describe our investigation of the superconducting and magnetic properties of the rare-earth ternary germanide intermetallic compounds La${}_2$Pt${}_3$Ge${}_5$ and Pr${}_2$Pt${}_3$Ge${}_5$. Single crystals of La${}_2$Pt${}_3$Ge${}_5$ and Pr${}_2$Pt${}_3$Ge${}_5$ were synthesized using the high-temperature metal flux method. Both types of crystal formed in a U${}_2$Co${}_3$Si${}_5$-type orthorhombic structure (space group $Ibam$). La${}_2$Pt${}_3$Ge${}_5$ showed the onset of superconducting phase transition at $T_c$ $=$ 8.1 K, which, to the best of our knowledge, is the highest $T_c$ of all the $R$${}_2$$M$${}_3$$X$${}_5$ ($R$ $=$ rare-earth elements, $M$ $=$ transition metal, and $X$ $=$ $s\text{−}p$ metal) superconductors, and from the specific heat data, it was found to have multigap superconductivity. Pr${}_2$Pt${}_3$Ge${}_5$ showed both a superconducting phase transition at $T_c$ $=$ 7.8 K and two antiferromagnetic transitions at $T_{N1}$ $=$ 3.5 K and $T_{N2}$ $=$ 4.2 K, which indicates the coexistence of superconductivity and magnetism. However, the correlation between the superconductivity and the magnetism was too weak to be observed. In its normal state, Pr${}_2$Pt${}_3$Ge${}_5$ revealed strong magnetic anisotropy, probably due to the crystalline electric field effect.

We consider the trial wave functions for the fractional quantum Hall effect that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e., short-range correlations only) inside the quantum Hall droplet and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk two-dimensional chiral CFT which underlies the trial wave function. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation. This approach is then used to analyze the entanglement spectrum of the ground state obtained with a bipartition $A\cup B$ in real space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization-group arguments. We prove that generalized screening implies that the entanglement Hamiltonian $H_E=-\ln {\rho }_A$ is isospectral to an operator that is local along the cut between $A$ and $B$. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wave functions given by conformal blocks and tensor product states, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of $p_x\pm i{p}_y$ paired superfluids are treated in a similar fashion in the Appendixes.

We experimentally study intrinsic tunneling and high magnetic field (up to 65 T) transport characteristics of the single-layer cuprate Bi${}_{2+x}$Sr${}_{2-y}$CuO${}_{6+\delta }$, with a very low superconducting critical temperature $T_c\lesssim 4$ K. It is observed that the superconducting gap, the collective bosonic mode energy, the upper critical field, and the fluctuation temperature range are scaling down with $T_c$, while the corresponding pseudogap characteristics remain the same as in high-$T_c$ cuprates with 20 to 30 times higher $T_c$. The observed disparity of the superconducting and pseudogap scales clearly reveals their different origins.

We have measured spin-triplet supercurrent in Josephson junctions of the form S/${\text{F}}^{\prime }$/F/${\text{F}}^{\prime }$/S, where S is superconducting Nb, ${\text{F}}^{\prime }$ is a thin Ni layer with in-plane magnetization, and F is a Ni/[Co/Ni]${}_n$ multilayer with out-of-plane magnetization. The supercurrent in these junctions decays very slowly with F-layer thickness and is much larger than in similar junctions not containing the two ${\text{F}}^{\prime }$ layers. Those two features are the characteristic signatures of spin-triplet supercurrent, which is maximized by the orthogonality of the magnetizations in the F and ${\text{F}}^{\prime }$ layers. Magnetic measurements confirm the out-of-plane anisotropy of the Co/Ni multilayers. These samples have their critical current optimized in the as-prepared state, which will be useful for future applications.

Motivated by recent work on Hall viscosity, we derive from first principles the Kubo formulas for the stress-stress response function at zero wave vector that can be used to define the full complex frequency-dependent viscosity tensor, both with and without a uniform magnetic field. The formulas in the existing literature are frequently incomplete, incorrect, or lack a derivation; in particular, Hall viscosity is overlooked. Our approach begins from the response to a uniform external strain field, which is an active time-dependent coordinate transformation in $d$ space dimensions. These transformations form the group GL$(d,\mathbb{R})$ of invertible matrices, and the infinitesimal generators are called strain generators. These enable us to express the Kubo formula in different ways, related by Ward identities; some of these make contact with the adiabatic transport approach. The importance of retaining contact terms, analogous to the diamagnetic term in the familiar Kubo formula for conductivity, is emphasized. For Galilean-invariant systems, we derive a relation between the stress response tensor and the conductivity tensor that is valid at all frequencies and in both the presence and absence of a magnetic field. In the presence of a magnetic field and at low frequency, this yields a relation between the Hall viscosity, the $q^2$ part of the Hall conductivity, the inverse compressibility (suitably defined), and the diverging part of the shear viscosity (if any); this relation generalizes a result found recently by others. We show that the correct value of the Hall viscosity at zero frequency can be obtained (at least in the absence of low-frequency bulk and shear viscosity) by assuming that there is an orbital spin per particle that couples to a perturbing electromagnetic field as a magnetization per particle. We study several examples as checks on our formulation. We also present formulas for the stress response that directly generalize the Berry (adiabatic) curvature expressions for zero-frequency Hall conductivity or viscosity to the full tensors at all frequencies.

We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling properties of the real-space entanglement spectra on infinite cylinders. The real-space entanglement spectrum obeys a scaling form dictated by the edge conformal field theory, allowing us to accurately extract the two entanglement velocities of the Moore-Read state. In contrast, the orbital space spectrum is observed to scale according to a complex set of power laws that rule out a similar collapse.

When a frequency chirped excitation is applied to a classical high-$Q$ nonlinear oscillator, its motion becomes dynamically synchronized to the drive and large oscillation amplitude is observed, provided the drive strength exceeds the critical threshold for autoresonance. We demonstrate that when such an oscillator is strongly coupled to a quantized superconducting qubit, both the effective nonlinearity and the threshold become a nontrivial function of the qubit-oscillator detuning. Moreover, the autoresonant threshold is dependent on the quantum state of the qubit and may be used to realize a high-fidelity, latching readout whose speed is not limited by the oscillator $Q$.

Using $GW$ first-principles calculations for few-layer and bulk MoS${}_2$, we study the effects of quantum confinement on the electronic structure of this layered material. By solving the Bethe-Salpeter equation, we also evaluate the exciton energy in these systems. Our results are in excellent agreement with the available experimental data. Exciton binding energy is found to dramatically increase from 0.1 eV in the bulk to 1.1 eV in the monolayer. The fundamental band gap increases as well, so that the optical transition energies remain nearly constant. We also demonstrate that environments with different dielectric constants have a profound effect on the electronic structure of the monolayer. Our results can be used for engineering the electronic properties of MoS${}_2$ and other transition-metal dichalcogenides and may explain the experimentally observed variations in the mobility of monolayer MoS${}_2$.

We report magnetization, specific heat, and NMR investigations on YFe${}_2$Al${}_{10}$ over a wide range of temperature and magnetic field and zero field (NQR) measurements. Magnetic susceptibility, specific heat, and spin-lattice relaxation rate divided by $T(1/T_{1}T)$ follow a weak power law ($\sim$$T^{-0.4}$) temperature dependence, which is a signature of the critical fluctuations of Fe moments. The value of the Sommerfeld-Wilson ratio and the linear relation between $1/T_{1}T$ and $\chi$ suggest the existence of ferromagnetic correlations in this system. No magnetic ordering down to 50 mK in $C_p\left(T\right)/T$ and the unusual $T$ and $H$ scaling of the bulk and NMR data are associated with a magnetic instability which drives the system to quantum criticality. The magnetic properties of the system are tuned by field wherein ferromagnetic fluctuations are suppressed and a crossover from quantum critical to Fermi-liquid behavior is observed with increasing magnetic field.

We report spin- and angle-resolved photoemission studies of a topological semimetal from the infinitely adaptive series between elemental Bi and Bi${}_2$Se${}_3$. The compound, based on Bi${}_4$Se${}_3$, is a 1:1 natural superlattice of alternating Bi${}_2$ layers and Bi${}_2$Se${}_3$ layers; the inclusion of S allows the growth of large crystals, with the formula Bi${}_4$Se${}_{2.6}$S${}_{0.4}$. The crystals cleave along the interfaces between the Bi${}_2$ and Bi${}_2$Se${}_3$ layers, with the surfaces obtained having alternating Bi or Se termination. The resulting terraces, observed by photoemission electron microscopy, create avenues suitable for the study of one-dimensional topological physics. The electronic structure, determined by spin- and angle-resolved photoemission spectroscopy, shows the existence of a surface state that forms a large, hexagonally shaped Fermi surface around the $\Gamma$ point of the surface Brillouin zone, with the spin structure indicating that this material is a topological semimetal.

The $f$-sum rule for the magnetic permeability, derived previously for an assembly of isolated macrospins, is generalized for an arbitrary nonuniform three-dimensional magnetization texture, in which the magnetizations at different points are coupled by exchange and magnetostatic interactions. The sum value depends only on the magnetic texture at rest. It has no direct contribution from the exchange energy, but depends on the anisotropy, applied field, and demagnetizing energies. The derived formula is tested against numerical calculations for several complex and very different magnetization structures. This generalized sum rule should be useful for experiments, numerical simulations, and metrology.

Single-crystalline UGe${}_2$ was investigated by means of magnetic susceptibility, magnetization, electrical resistivity, magnetoresistivity, and specific-heat measurements, all carried out in wide temperature and magnetic-field ranges. An analysis of the obtained data points out the dual behavior of the 5$f$ electrons in this compound, i.e., possessing simultaneously local and itinerant characters in two substates. The magnetic and thermal characteristics of the compound were modeled using the effective crystal field (CF) in the intermediate coupling scheme and initial parameters obtained in the angular overlap model. Various configurations of the localized 5$f^n$ ($n$ $=$ 1, 2, and 3) electrons on the uranium ion have been probed. The best results were obtained for the 5$f^2$ (U${}^{4+})$ configuration. The CF parameters obtained in the paramagnetic region allowed us to reproduce satisfactorily the experimental findings in the whole temperature range including also the magnitude of the ordered magnetic moment of uranium at low temperature. The electrical resistivity data after subtraction of the phonon contribution reveal the presence of a Kondo-like interaction in UGe${}_2$ supporting the idea of partial localization of the 5$f$ electrons in UGe${}_2$. On the other hand, magnetoresistivity and an excess of specific heat originated from the hybridized (itinerant) part of 5$f$ states, apparent around the characteristic temperature $T^{*}$, give a distinct signature for the presence of the coupled charge-density wave and spin-density wave fluctuations over all the ferromagnetic region with a maximum at $T^{*}$, postulated earlier in the literature.