We study a model of a composite system constructed from a “pairing layer” of disconnected attractive-$U$ Hubbard sites that is coupled by single-particle tunneling, $t_{\perp }$, to a disordered metallic layer. For small interlayer tunneling the system is described by an effective long-range $XY$ phase model whose critical temperature, $T_c$, is essentially insensitive to the disorder and is exponentially suppressed by quantum fluctuations. $T_c$ reaches a maximum for intermediate values of $t_{\perp }$, which we calculate using a combination of mean-field, classical, and quantum Monte Carlo methods. The maximal $T_c$ scales as a fraction of the zero-temperature gap of the attractive sites when $U$ is smaller than the metallic bandwidth, and is bounded by the maximal $T_c$ of the two-dimensional attractive Hubbard model for large $U$. Our results indicate that a thin, rather than a thick, metallic coating is better suited for the enhancement of $T_c$ at the surface of a phase fluctuating superconductor.

We introduce a set of one-dimensional quantum lattice models which we refer to as the quantum torus chain. These models have discrete global symmetry and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd, these models exhibit either gapped symmetry-breaking phases with isolated critical points or gapped symmetry-breaking phases separated by gapless phases. We discuss the property of these phases and phase transitions for two special values of the parameter and point out many open problems.

We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for the qubit-resonator detuning of 5 GHz, is quantitatively explained by the generalized Rabi model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved $90\%$ contrast of the Rabi oscillations, which is mainly limited by the energy relaxation of the qubit.

We have investigated the magnetic structure in a polycrystalline sample of the $B20$-type MnGe by means of small-angle neutron scattering. On the projected diffraction plane normal to the incoming neutron beam, a Debye-ring-like pattern appears due to the random orientation of the spin helix $q$ vectors ($\parallel \langle 100\rangle$). When an external magnetic field is applied normal to the incoming neutron beam, an intense peak with wave vector ($q$) perpendicular to the applied magnetic field is observed as the hallmark of the formation of a skyrmion lattice with a multiple-$q$ helix in a wide temperature-magnetic-field region. This scattering intensity remains even after removing the magnetic field, which indicates that a skyrmion lattice is stabilized as the ground state. A different form of skyrmion lattice, either square or cubic, is proposed, which is also shown to be in good agreement with previous high-angle neutron diffraction results. Calculations based on such structures also describe the magnetic-field profile of the topological Hall resistivity.

We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, and for other two-dimensional disordered systems, based on the theory of “conformal restriction.” This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the “stochastic geometry” of fractal curves and other stochastic geometrical fractal objects in two-dimensional space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model for the transition. We show that the disorder-averaged PCCs are characterized by a classical probability distribution for certain geometric objects in the plane (which we call pictures), occurring with positive statistical weights, that satisfy the crucial so-called restriction property with respect to changes in the shape of the sample with absorbing boundaries; physically, these are boundaries connected to ideal leads. At the transition point, these geometrical objects (pictures) become fractals. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of “conformal restriction measures” to relate the disorder-averaged PCCs to correlation functions of (Virasoro) primary operators in a conformal field theory (of central charge $c=0$). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in two spatial dimensions, including for example the spin quantum Hall effect, the thermal metal phase in symmetry class D, and classical diffusion in two dimensions in a perpendicular magnetic field. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.

Ferroelectric domain walls (FDWs) are usually considered to be of Ising type, but there have been suggestions in recent years that Bloch-type FDWs are also possible in some cases, e.g., in the rhombohedral phase of BaTiO${}_3$. The mechanically compatible and electrically neutral FDWs in rhombohedral BaTiO${}_3$ are of 71${}^{\circ }$, 109${}^{\circ }$, and 180${}^{\circ }$ type. We have investigated these FDWs based both on first-principles calculations and on a Ginzburg-Landau-Devonshire (GLD) model [P. Marton, I. Rychetsky, and J. Hlinka, Phys. Rev. B 81, 144125 (2010)]. The results from both approaches confirm the Ising nature of the 71${}^{\circ }$ FDW and the Bloch nature of the 180${}^{\circ }$ FDW, and predict both Ising-type and Bloch-type FDWs are possible for the 109${}^{\circ }$ case. Considering the relatively small rhombohedral strain in BaTiO${}_3$, the competition between the energies of Bloch and Ising FDWs can be discussed in terms of a picture in which a Bloch wall is regarded as being composed of a pair of smaller-angle Ising ones. A reduction by 40$\%$ in the parameters describing the gradient term in the GLD model brings it into better agreement with the first-principles results for detailed properties such as the energies and widths of the FDWs.

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nanoscience to the dynamical mean-field theory (DMFT). Here, we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the one-dimensional Hubbard model and $2\times 2$ cluster DMFT of the two-dimensional Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including “difficult” regimes, such as in the pseudogap phase of the two-dimensional Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24-bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.

Structurally, the two mixed-valence manganese disks Mn${}_7$-11 and Mn${}_7$-16 differ only in the peripheral ligand but, as a result of a subtle interplay of intramolecular exchange interactions, differ strongly in their magnetic properties, e.g., Mn${}_7$-11 possesses a ground-state spin of $S=11$ and Mn${}_7$-16 of $S=16$. The exchange interactions in the disks were studied by inelastic neutron scattering. The analysis of the $Q$ dependence of the observed magnetic transition intensities reveals that ferromagnetic cluster spin-wave excitations were observed. In this framework, it was possible to successfully model the experimental data and provide a physical understanding of the magnetism in the two disks.

We report the transport properties of the proposed Heusler topological insulators YPtSb, LaPtBi, and LuPdSb. All compounds show ultrahigh hole mobility with value of 4124, 4275, and 1800 cm${}^2$ V${}^{-1}$ s${}^{-1}$ for YPtBi, LaPtBi, and LuPdSb, respectively, at 300 K. The temperature dependence of mobility shows strong and weak phonon scattering for LaPtBi and LuPdSb, respectively, while YPtSb shows strong impurity scattering. These ultrahigh values of the mobility are not only due to gaplessness but also to the presence of linear dispersion of the bands close to the Fermi energy, where charge carriers behave like relativistic particles. Furthermore, nonsaturating magnetoresistance (MR) is observed in the temperature range 2–300 K that shows linear behavior at high fields. A tentative relationship between the linear MR and mobility is discussed, which indicates that the mobility controls the linear part of MR.

The electrical resistivity $\rho$ of the iron-arsenide superconductor Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ was measured in applied pressures up to 2.6 GPa for four underdoped samples, with $x\simeq 0.16$, 0.18, 0.19, and 0.21. The antiferromagnetic ordering temperature $T_{\mathrm{N}}$, detected as a sharp anomaly in $\rho \left(T\right)$, decreases linearly with pressure. At pressures above $P\simeq 1.0$ GPa, a second sharp anomaly is detected at a lower temperature $T_0$, which rises with pressure. We attribute this second anomaly to the onset of a phase that causes a reconstruction of the Fermi surface. The new phase expands with increasing $x$ and it competes with superconductivity. We discuss the possibility that a second spin-density wave orders at $T_0$, with a $\mathbf{Q}$ vector distinct from that of the spin-density wave that sets in at $T_{\mathrm{N}}$.

Electron- and hole-transport properties of the $n$-type copolymer poly$\{$[$N$,$N^{\prime }$-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5${}^{\prime }$-(2,2${}^{\prime }$-dithiophene)$\}$ [P(NDI2OD-T2), PolyeraActivInk™ N2200] are investigated. Electron- and hole-only devices with Ohmic contacts are demonstrated, exhibiting trap-free space-charge-limited currents for both types of charge carriers. While hole and electron mobilities are frequently equal in organic semiconductors, room-temperature mobilities of 5 $\times$ 10${}^{-8}$ m${}^2$/V s for electrons and 3.4 $\times$ 10${}^{-10}$ m${}^2$/V s for holes are determined, both showing universal Arrhenius temperature scaling. The origin of the large difference between electron and hole mobility is explained by quantum-chemical calculations, which reveal that the internal reorganization energy for electrons is smaller than for holes, while the transfer integral is larger. As a result, electron transport is intrinsically superior to hole transport under the same injection and extraction conditions.

We discuss the formal relationship between the real-time Keldysh and imaginary-time theory for nonequilibrium in quantum dot systems. The latter can be reformulated using the recently proposed Matsubara-voltage approach. We establish general conditions for correct analytic continuation procedure on physical observables, and apply the technique to the calculation of static quantities in steady-state nonequilibrium for a quantum dot subject to a finite bias voltage and external magnetic field. Limitations of the Matsubara voltage approach are also pointed out.

We develop a technique to compute the high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the dynamical spin correlator decreases exponentially at high frequencies ${〈SS〉}_{\omega }\sim \exp (-{\tau }_{*}\omega )$ and compute the characteristic time ${\tau }^{*}$ of this dependence. In a typical random configuration, some fraction of spins form strongly coupled pairs, which behave as two-level systems. Their switching dynamics is driven by the high-frequency noise from the surrounding spins, resulting in low-frequency $1/f$ noise in the magnetic susceptibility and other physical quantities. We discuss application of these results to the problem of susceptibility and flux noise in superconducting circuits at mK temperatures.

The two-dimensional Hubbard model defined for topological band structures exhibiting a quantum spin Hall effect poses fundamental challenges in terms of phenomenological characterization and microscopic classification. In the limit of infinite coupling $U$ at half filling, the spin model Hamiltonians resulting from a strong-coupling expansion show various forms of magnetic ordering phenomena depending on the underlying spin-orbit coupling terms. We investigate the infinite-$U$ limit of the Kane-Mele-Hubbard model with $z$-axis intrinsic spin-orbit coupling as well as its generalization to a generically multidirectional spin-orbit term which has been claimed to account for the physical scenario in monolayer ${\text{Na}}_2{\text{IrO}}_3$. We find that the axial spin symmetry which is kept in the former but broken in the latter has a fundamental impact on the magnetic phase diagram as we vary the spin-orbit coupling strength. While the Kane-Mele spin model shows a continuous evolution from conventional honeycomb Néel to $XY$ antiferromagnetism which avoids the frustration imposed by the increased spin-orbit coupling, the multidirectional spin-orbit term induces a commensurate to incommensurate transition at intermediate coupling strength, and yields a complex spiral state with a 24 site unit cell in the limit of infinite spin-orbit coupling. From our findings, we conjecture that in the case of broken axial spin symmetry there is a large propensity for an additional phase at sufficiently large spin-orbit coupling and intermediate $U$.

We describe a lowest-order approximation (LOA) to the nonequilibrium Green's function in the presence of interactions, and generally address how one can build $\Phi$-derivable one-shot approximations that satisfy the continuity equation. These approximations produce conserved electronic currents in one shot, requiring only one self-energy evaluation and, when applicable, they are as accurate as but much faster than the corresponding self-consistent approximation. This challenges the currently adopted view that heavy self-consistent calculations are necessary to get a satisfactory prediction of transport in nanoscale structures. We illustrate this with the case of electron-phonon scattering expressed within the self-consistent Born approximation (SCBA). In the LOA, the SCBA is further approximated by accounting only for one-phonon processes. LOA and SCBA are compared in one-dimensional wire where electrons interact with one optical phonon mode at room temperature. The LOA is found to provide a considerable reduction in computational time. Its limitations and extensions to include two-phonon processes are discussed.

Defects in the topological insulator Bi${}_2$Te${}_2$Se are studied by scanning tunneling microscopy. Small numbers of Te${}_{\mathrm{Bi}}$ antisite defects are found and are postulated to be the origin of $n$-type carriers in this tetradymite composition near the $n$-to-$p$ crossover. Based on this defect chemistry, we design an alternative method for obtaining resistive Bi${}_{2+x}$Te${}_{2-x}$Se samples, by the introduction of compensating $p$-type carriers through Bi${}_{\mathrm{Te}}$ antisite defects induced by making the material slightly Bi rich. Our resistivity and Hall coefficient measurements of Bi${}_{2+x}$Te${}_{2-x}$Se crystals grown by the Bridgeman-Stockbarger method show that the carrier concentration at base temperature is significantly reduced from that of stoichiometric samples. Analysis of the measurements reveals the possible underlying chemical distribution along the boules during growth.

We have studied the magnetism of the Pr${}^{3+}$ ions in PrFeAsO${}_{1-x}$F${}_x$ ($x=0,0.15$) and its interaction with the Fe magnetic order (for $x=0$). Specific-heat data confirm the presence of a first excited crystal electric-field (CEF) level around 3.5 meV in the undoped compound PrFeAsO. This finding is in agreement with recent neutron-scattering experiments. The doped compound is found to have a much lower first CEF splitting of about 2.0 meV. The Pr ordering in PrFeAsO gives rise to large anomalies in the specific heat and the thermal-expansion coefficient. In addition, a field-induced transition is found at low temperatures that is most pronounced for the magnetostriction coefficient. This transition, which is absent in the doped compound, is attributed to a reversal of the Fe spin canting as the antiferromagnetic Pr order is destroyed by the external magnetic field.

Many correlated materials display a quantum-critical point between a paramagnetic and a spin-density wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here, we consider the case where pairs of hot spots coalesce, and the wave vector $(\pi ,\pi )$ of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility, and the self-energy at the hot spots are found using the two-particle self-consistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudonesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length $\xi$ scales like $1/T$, namely, $z=1$ instead of the naive $z=2$, the $(\pi ,\pi )$ static spin susceptibility $\chi$ like $1/\sqrt{T}$, and the imaginary part of the self-energy at the hot spots like $T^{3/2}$. The correction $T_1^{-1}\sim T^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as $-{\omega }^{3/2}\ln \omega$. This is less singular than earlier predictions of the form $-\omega \ln \omega$. The difference arises from the effects of umklapp terms that were not included in previous studies.

We present a new theoretical framework to analyze microwave amplifiers based on the dc SQUID. Our analysis applies input-output theory generalized for Josephson junction devices biased in the running state. Using this approach, we express the high-frequency dynamics of the SQUID as a scattering between the participating modes. This enables us to elucidate the inherently nonreciprocal nature of gain as a function of bias current and input frequency. This method can, in principle, accommodate an arbitrary number of Josephson harmonics generated in the running state of the junction. We report detailed calculations taking into account the first few harmonics that provide simple semiquantitative results showing a degradation of gain, directionality, and noise of the device as a function of increasing signal frequency. We also discuss the fundamental limits on device performance and applications of this formalism to real devices.

Examining phase stabilities and phase equilibria in strongly correlated materials asks for a next level in the many-body extensions to the local-density approximation (LDA) beyond mainly spectroscopic assessments. Here, we put the charge-self-consistent LDA+dynamical mean-field theory (DMFT) methodology based on projected local orbitals for the LDA+DMFT interface and a tailored pseudopotential framework into action in order to address such thermodynamics of realistic strongly correlated systems. Namely, a case study for the electronic phase diagram of the well-known prototype Mott-phenomena system V${}_2$O${}_3$ at higher temperatures is presented. We are able to describe the first-order metal-to-insulator transitions with negative pressure and temperature from the self-consistent computation of the correlated total energy in line with experimental findings.