The heat flow between a quantum system and its reservoir is analyzed when initially both are in a separable thermal state and asymptotically approach a correlated equilibrium. General findings are illustrated for specific systems and various classes of non-Markovian reservoirs relevant for solid state realizations. System-bath correlations are shown to be substantial at low temperatures even in the weak coupling regime. As a consequence, predictions of work and heat for actual experiments obtained within conventional perturbative approaches may often be questionable. Correlations induce characteristic imprints in heat capacities which opens a proposal to measure them in solid state devices.

We report the results of a comprehensive study of charge-density wave (CDW) correlations in untwinned ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ single crystals with $0.4\le x\le 0.99$ using Cu $L_3$ edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for $0.45\le x\le 0.93$ (hole-doping levels $0.086\lesssim p\lesssim 0.163$), but not for samples with $x\le 0.44$ ($p\lesssim 0.084$) that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with $x=0.99$ ($p\sim 0.19$). This suggests the presence of two proximate zero-temperature CDW critical points at $p_{c1}\sim 0.08$ and $p_{c2}\sim 0.18$. Remarkably, $p_{c2}$ is close to the doping level that is optimal for superconductivity. The CDW reflections are observed at incommensurate in-plane wave vectors (${\delta }_a$, 0) and (0, ${\delta }_b$) with ${\delta }_a\lesssim {\delta }_b$. Both ${\delta }_a$ and ${\delta }_b$ decrease linearly with increasing doping, in agreement with recent reports on Bi-based high-$T_c$ superconductors, but in sharp contrast to the behavior of the ${\mathrm{La}}_{2-x}$(Ba,Sr)${}_x{\mathrm{CuO}}_4$ family. The CDW intensity and correlation length exhibit maxima at $p\sim 0.12$, coincident with a plateau in the superconducting transition temperature $T_c$. The onset temperature of the CDW reflections depends nonmonotonically on $p$, with a maximum of $\sim 160$ K for $p\sim 0.12$. The RXS reflections exhibit a uniaxial intensity anisotropy. Whereas in strongly underdoped samples the reflections at (${\delta }_a$, 0) are much weaker than those at (0, ${\delta }_b$), the anisotropy is minimal for $p\sim 0.12$, and reversed close to optimal doping. We further observe a depression of CDW correlations upon cooling below $T_c$, and (for samples with $p\ge 0.09$) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with $p\sim 0.08$, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against superconductivity [Blanco-Canosa et al., Phys. Rev. Lett. 110, 187001 (2013)]. We discuss the relationship of these results to prior observations of “stripe” order in ${\mathrm{La}}_{2-x}$(Ba,Sr)${}_x{\mathrm{CuO}}_4$, the “pseudogap” phenomenon, superconducting fluctuations, and quantum oscillations, as well as their implications for the mechanism of high-temperature superconductivity.

To explore the doping dependence of the recently discovered charge-density-wave (CDW) order in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$, we present a bulk-sensitive high-energy x-ray study for several oxygen concentrations, including strongly underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.44}$. Combined with previous data around the so-called 1/8 doping, we show that bulk CDW order exists at least for hole concentrations ($p$) in the ${\mathrm{CuO}}_2$ planes of $0.078\lesssim p\lesssim 0.132$. This implies that CDW order exists in close vicinity to the quantum critical point for spin-density-wave (SDW) order. In contrast to the pseudogap temperature $T^{*}$, the onset temperature of CDW order decreases with underdoping to $T_{\mathrm{CDW}}\sim 90$ K in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.44}$. Together with a weakened order parameter this suggests a competition between CDW and SDW orders. In addition, the CDW order in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.44}$ shows the same type of competition with superconductivity as a function of temperature and magnetic field as samples closer to $p=1/8$. At low $p$ the CDW incommensurability continues the previously reported linear increasing trend with underdoping. In the entire doping range the in-plane correlation length of the CDW order in $b$ axis direction depends only very weakly on the hole concentration, and appears independent of the type and correlation length of the oxygen-chain order. The onset temperature of the CDW order is remarkably close to a temperature $T^{†}$ that marks the maximum of $1/\left(T_{1}T\right)$ in planar ${}^{63}\mathrm{Cu}$ NQR/NMR experiments, potentially indicating a response of the spin dynamics to the formation of the CDW. Our discussion of these findings includes a detailed comparison to the charge stripe order in ${\mathrm{La}}_{2-\mathit{x}}{\mathrm{Ba}}_{\mathit{x}}{\mathrm{CuO}}_4$.

We describe a regime for low-field magnetoresistance in organic semiconductors, in which the spin-relaxing effects of localized nuclear spins and electronic spins interfere. The regime is studied by the controlled addition of localized electronic spins to a material that exhibits substantial room-temperature magnetoresistance ($\sim 20\%$). Although initially the magnetoresistance is suppressed by the doping, at intermediate doping there is a regime where the magnetoresistance is insensitive to the doping level. For much greater doping concentrations the magnetoresistance is fully suppressed. The behavior is described within a theoretical model describing the effect of carrier spin dynamics on the current.

We predict a class of topological crystalline insulators in the antiperovskite material family with the chemical formula $A_{3}BX$. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a “Dirac octet.” Our work suggests that antiperovskites are a promising venue for exploring the cooperative interplay between band topology, crystal symmetry, and electron correlation.

We theoretically investigate the vortex state of the cuprate high-temperature superconductors in the presence of magnetic fields. Assuming the recently derived nonlinear $\sigma$-model for fluctuations in the pseudogap phase, we find that the vortex cores consist of two crossed regions of elliptic shape, in which a static charge order emerges. Charge density wave order manifests itself as satellites to the ordinary Bragg peaks directed along the axes of the reciprocal copper lattice. Quadrupole density wave (bond order) satellites, if seen, are predicted to be along the diagonals. The intensity of the satellites should grow linearly with the magnetic field, in agreement with the result of recent experiments.

Expressions for the thermal noise from a collection of exchange-biased magnetic nanoparticles are derived and used to analyze the magnetic noise from thin films of partially oxidized nanoparticles. Functionalized Co nanoparticles with diameters between 3 and 6 nm were oxygenated in solution and then deposited on oxidized silicon substrates, self-assembling into arrays of magnetic nanoparticles during solvent evaporation. Magnetization measurements exhibited the development of exchange bias with oxygenation as evidenced by an increasing exchange field and coercivity. Noise measurements of the exchange-biased nanoparticles using a micro-superconducting quantum interference device sensor are shown to be consistent with theoretical expectations and are used to extract the magnetic energy distributions of the Co/CoO nanoparticles.

We develop a practical first-principles methodology to determine nonradiative carrier capture coefficients at defects in semiconductors. We consider transitions that occur via multiphonon emission. Parameters in the theory, including electron-phonon coupling matrix elements, are computed consistently using state-of-the-art electronic structure techniques based on hybrid density functional theory. These provide a significantly improved description of bulk band structures, as well as defect geometries and wave functions. In order to properly describe carrier capture processes at charged centers, we put forward an approach to treat the effect of long-range Coulomb interactions on scattering states in the framework of supercell calculations. We also discuss the choice of initial conditions for a perturbative treatment of carrier capture. As a benchmark, we apply our theory to several hole-capturing centers in GaN and ZnO, materials of high technological importance in which the role of defects is being actively investigated. Calculated hole capture coefficients are in good agreement with experimental data. We discuss the insights gained into the physics of defects in wide-band-gap semiconductors, such as the strength of electron-phonon coupling and the role of different phonon modes.

We consider an open quantum system in contact with fermionic metallic reservoirs in a nonequilibrium setup. For the case of spin, orbital, or potential fluctuations, we present a systematic formulation of real-time renormalization group at finite temperature, where the complex Fourier variable of an effective Liouvillian is used as flow parameter. We derive a universal set of differential equations free of divergencies written as a systematic power series in terms of the frequency-independent two-point vertex only, and solve it in different truncation orders by using a universal set of boundary conditions. We apply the formalism to the description of the weak to strong coupling crossover of the isotropic spin-$\frac{1}{2}$ nonequilibrium Kondo model at zero magnetic field. From the temperature and voltage dependence of the conductance in different energy regimes, we determine various characteristic low-energy scales and compare their universal ratio to known results. For a fixed finite bias voltage larger than the Kondo temperature, we find that the temperature dependence of the differential conductance exhibits nonmonotonic behavior in the form of a peak structure. We show that the peak position and peak width scale linearly with the applied voltage over many orders of magnitude in units of the Kondo temperature. Finally, we compare our calculations with recent experiments.

We derive a finite-basis-set correction for quasiparticle (QP) energies in the $GW$ approximation and many-body correlation energies in the random phase approximation. Since the correction requires only knowledge of the ground-state density distribution, it is straightforward to implement in any plane-wave code and significantly improves convergence at negligible computational cost. The expression also indicates that QP energies might converge to the wrong value using the projector augmented wave (PAW) method since the overlap densities of occupied orbitals and high-energy, plane-wave-like orbitals are inaccurately described. The error is shown to be related to the incompleteness of the partial waves inside the atomic spheres. It can be avoided by adopting norm-conserving partial waves. $G_0{W}_0$ and $G{W}_0$ results based on such norm-conserving PAW potentials are presented for a large set of semiconductors and insulators. Accurate extrapolation procedures to the infinite-basis-set limit and infinite-$k$-point limit are discussed in detail.

We study thermal transport at low temperatures in the disordered Fermi liquid with short-range interactions. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron-electron interaction. In the present scheme this fundamental relation is closely connected with a fixed point in the multiparametric RG flow of the gravitational potentials.

We introduce a broad class of simple models for quantum Hall states based on the expansion of their parent Hamiltonians near the one-dimensional limit of “thin cylinders,” i.e., when one dimension $L_y$ of the Hall surface becomes comparable to the magnetic length ${\ell }_B$. Formally, the models can be viewed as topological generalizations of the 1D Hubbard model with center-of-mass-preserving hopping of multiparticle clusters. In some cases, we show that the models can be exactly solved using elementary techniques, and yield simple wave functions for the ground states as well as the entire neutral excitation spectrum. We study a large class of Abelian and non-Abelian states in this limit, including the Read-Rezayi ${\mathbb{Z}}_k$ series, as well as states deriving from nonunitary or irrational conformal field theories: the “Gaffnian,” “Haffnian,” Haldane-Rezayi, and the “permanent” state. We find that the thin-cylinder limit of unitary (rational) states is “classical”: their effective Hamiltonians reduce to only Hartree-type terms, the ground states are trivial insulators, and excitation gaps result from simple electrostatic repulsion. In contrast, for states deriving from nonunitary or irrational conformal field theories, the thin-cylinder limit is found to be intrinsically quantum; it contains hopping terms that play an important role in the structure of the ground states and in the energetics of the low-lying neutral excitations.

A quantum spin Hall insulator is a two-dimensional state of matter consisting of an insulating bulk and one-dimensional helical edge states. While these edge states are topologically protected against elastic backscattering in the presence of disorder, interaction-induced inelastic terms may yield a finite conductivity. By using a kinetic equation approach, we find the backscattering rate ${\tau }^{-1}$ and the semiclassical conductivity in the regimes of high $\left(\omega \gg {\tau }^{-1}\right)$ and low $\left(\omega \ll {\tau }^{-1}\right)$ frequency. By comparing the two limits, we find that the parametric dependence of conductivity is described by the Drude formula for the case of a disordered edge. On the other hand, in the clean case where the resistance originates from umklapp interactions, the conductivity takes a non-Drude form with a parametric suppression of scattering in the dc limit as compared to the ac case. This behavior is due to the peculiarity of umklapp scattering processes involving necessarily the state at the “Dirac point.” In order to take into account Luttinger liquid effects, we complement the kinetic equation analysis by treating interactions exactly in bosonization and calculating conductivity using the Kubo formula. In this way, we obtain the frequency and temperature dependence of conductivity over a wide range of parameters. We find the temperature and frequency dependence of the transport scattering time in a disordered system as $\tau \sim {[max(\omega ,T)]}^{-2K-2}$, for $K>2/3$ and $\tau \sim {[max(\omega ,T)]}^{-8K+2}$ for $K<2/3$.

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high-energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a $4\pi$-periodic Majorana-Josephson coupling realizes supersymmetry for a certain characteristic ratio of the conventional Josephson to the Majorana-Josephson coupling strength. The supersymmetry we find is a “hidden” minimally bosonized supersymmetry that provides a nontrivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of a Majorana-Josephson coupling of the characteristic strength.

Time-reversal-invariant topological superconductors have a full paring gap in the bulk and gapless Majorana states at the edge or on the surface. Here, we theoretically propose topological superconductivity in a doped quantum spin-Hall insulator. We study the pairing symmetry of a doped two-dimensional tin film within a two-orbital model, and find that a novel spin-triplet pairing is favored when the interorbital attractive interaction is stronger than the intraorbital interaction. We propose that a doped tin film is a good candidate for a $2d$ topological superconductor. Edge channels are studied in a tight-binding model numerically. Finally, we discuss the robustness of topological superconductivity in two-dimensional tin films by comparing to $3d$ superconductivity in bulk tin.

We present the results of an optical spectroscopic study of two-dimensional atomic crystals of the high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$. Our measurements reveal a pronounced suppression of the optical conductivity ${\sigma }_1\left(\omega \right)$ with thickness. Using an effective medium approximation, we interpret this in terms of an insulating surface layer. The surface layer explains the insulating behavior previously observed in exfoliated ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ and has implications for future studies and potential applications of these materials.

The occurrences of collective quantum states, such as superconductivity (SC) and charge- or spin-density waves (CDWs or SDWs), are among the most fascinating phenomena in solids. To date, much effort has been made to explore the interplay between different orders, yet little is known about the relationship of multiple orders of the same type. Here we report optical spectroscopy study on CDWs in the rare-earth tritelluride compounds $R{\mathrm{Te}}_3 \left(R=\text{rare-earth elements}\right)$. Besides the prior reported two CDW orders, the study reveals unexpectedly the presence of a third CDW order in the series, which evolves systematically with the size of $R$ element. With increased chemical pressure, the first and third CDW orders are both substantially suppressed and compete with the second one by depleting the low-energy spectral weight. A complete phase diagram for the multiple CDW orders in this series is established.

We measure weak quasiparticle tunneling across a constriction in the second Landau level. At $\nu =7/3$, 8/3, and 5/2, comparison of temperature and dc bias dependence to weak tunneling theory allows extracting parameters that describe the edges' quasiparticle excitations. At $\nu =8/3$, our results are well described by a particle-hole conjugate Laughlin state but not compatible with the proposed non-Abelian quasiparticle excitations. For $\nu =5/2$, our measurements are in good agreement with previous experiments and favor the Abelian (3,3,1) or (1,1,3) states. At these filling factors, we further investigate the influence of the backscattering strength on the extracted scaling parameters. For $\nu =7/3$, the backscattering strength strongly affects the scaling parameters, whereas quasiparticle tunneling at $\nu =8/3$ and 5/2 appears more robust. Our results provide important additional insight about the physics in the second Landau level and contribute to the understanding of the physics underlying the fractional quantum Hall states at $\nu =7/3$, 8/3, and 5/2.

Electronic structures of single crystalline black phosphorus were studied by state-of-the-art angle-resolved photoemission spectroscopy (ARPES). Through high resolution photon energy dependence measurements, the band dispersions along out-of-plane and in-plane directions are experimentally determined. The electrons were found to be more localized in the $ab$ plane than is predicted in calculations. Beside the $k_z$-dispersive bulk bands, a surface resonant state is also observed in the momentum space. Our results strongly suggest that more details need to be considered to fully understand the electronic properties of black phosphorus theoretically.

We here present how a self-consistent solution of the dynamical mean-field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks with an approximate spacing proportional to the bandwidth divided by the number of bath sites. The self-consistency cycle is performed on the real-frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on ligand field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling, and low-symmetry crystal fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.