We present heat capacity measurements on a series of superconducting Cu${}_x$TiSe${}_2$ single crystals with different Cu content down to 600 mK and up to 1 T performed by ac microcalorimetry. The samples cover a large portion of the phase diagram from an underdoped to a slightly overdoped region with an increasing superconducting critical temperature and the charge density wave (CDW) order gradually suppressed. The superconducting electronic heat capacity as a function of normalized temperature $T/T_c$ shows no difference regardless of the concentration of copper, i.e., regardless of how much the CDW order is developed in the samples. The data analysis reveals consistently a single $s$-wave gap with an intermediate coupling strength $2\Delta /k_B{T}_c\approx 3.7$ for all samples.

The electron density of the $\alpha$ form of boron has been obtained by multipole refinement against high-resolution, single-crystal x-ray diffraction data measured on a high-quality single crystal at a temperature of 100 K. Topological properties of this density have been used to show that all chemical bonds between B${}_{12}$ clusters in $\alpha$-B${}_{12}$ are formed due to one orbital on each boron atom that is oriented perpendicular to the surface of the cluster. It is shown that the same orbital order on B${}_{12}$ clusters persists in both $\alpha$-B${}_{12}$ and $\gamma$-B${}_{28}$ polymorphs and in several dodecaboranes, despite the fact that in every case the B${}_{12}$ clusters participate in entirely different kinds of exocluster bonds. It is likely that the same orbital order of B${}_{12}$ clusters can explain bonding in other boron polymorphs and boron-rich solids.

We address the problem of finding mixed-metal borohydrides with favorable thermodynamics and illustrate the approach using the example of ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$. Using density functional theory (DFT), along with the grand-canonical linear programming method (GCLP), we examine the experimentally and computationally proposed crystal structures and the finite-temperature thermodynamics of dehydrogenation for the quaternary hydride ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$. We find the following: (i) For ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$, DFT calculations of the experimental crystal structures reveal that the structure from the neutron diffraction experiments of Ravnsbæk et al. is more stable [by 24 kJ/(mol f.u.)] than that based on a previous x-ray study. (ii) Our DFT calculations show that when using the neutron-diffraction structure of ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$, the recently theoretically predicted $\mathrm{LiZn}{\left({\mathrm{BH}}_4\right)}_3$ compound is unstable with respect to the decomposition into ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5+{\mathrm{LiBH}}_4$. (iii) GCLP calculations show that even though ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$ is a combination of weakly [$\mathrm{Zn}{\left({\mathrm{BH}}_4\right)}_2$] and strongly (${\mathrm{LiBH}}_4$) bound borohydrides, its decomposition is not intermediate between the two individual borohydrides. Rather, we find that the decomposition of ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$ is divided into a weakly exothermic step [${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5\to 2\mathrm{Zn}+\frac{1}{5}{\mathrm{LiBH}}_4+\frac{2}{5}{\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}+\frac{36}{5}{\mathrm{H}}_2$] and three strong endothermic steps ($12{\mathrm{LiBH}}_4\to 10\mathrm{LiH}+{\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}+13{\mathrm{H}}_2$; $\mathrm{Zn}+\mathrm{LiH}\to \mathrm{LiZn}+\frac{1}{2}{\mathrm{H}}_2$; $2\mathrm{Zn}+{\mathrm{Li}}_2{\mathrm{B}}_{12}{\mathrm{H}}_{12}\to 2\mathrm{LiZn}+12\mathrm{B}+6{\mathrm{H}}_2$). DFT-calculated $\Delta H_{\text{ZPE}}^{T=0\text{K}}$ values for the first three ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$ decomposition steps are $-19$, $+$37, $+$74 kJ/(mol ${\mathrm{H}}_2$), respectively. The behavior of ${\mathrm{LiZn}}_2{\left({\mathrm{BH}}_4\right)}_5$ shows that mixed-metal borohydrides formed by mixing borohydrides of high and low thermodynamics stabilities do not necessarily have an intermediate decomposition tendency. Our results suggest the correct strategy to find intermediate decomposition in mixed-metal borohydrides is to search for stable mixed-metal products such as ternary metal borides.

The dynamic responses of a rhodium catalyst and a graphene sheet are investigated upon random excitation with 80 kV electrons. An extraordinary electron microscope stability and resolution allow studying temporary atom displacements from their equilibrium lattice sites into metastable sites across projected distances as short as 60 pm. In the rhodium catalyst, directed and reversible atom displacements emerge from excitations into metastable interstitial sites and surface states that can be explained by single atom trajectories. Calculated energy barriers of 0.13 eV and 1.05 eV allow capturing single atom trapping events at video rates that are stabilized by the Rh [110] surface corrugation. Molecular dynamics simulations reveal that randomly delivered electrons can also reversibly enhance the $s{p}^3$ and the $s{p}^1$ characters of the $s{p}^2$-bonded carbon atoms in graphene. The underlying collective atom motion can dynamically stabilize characteristic atom displacements that are unpredictable by single atom trajectories. We detect three specific displacements and use two of them to propose a path for the irreversible phase transformation of a graphene nanoribbon into carbene. Collectively stabilized atom displacements greatly exceed the thermal vibration amplitudes described by Debye-Waller factors and their measured dose rate dependence is attributed to tunable phonon contributions to the internal energy of the systems. Our experiments suggest operating electron microscopes with beam currents as small as zepto-amperes/nm${}^2$ in a weak-excitation approach to improve on sample integrity and allow for time-resolved studies of conformational object changes that probe for functional behavior of catalytic surfaces or molecules.

We revisit the problem of spin-mediated superconducting pairing at the antiferromagnetic quantum-critical point with the ordering momentum $(\pi ,\pi )=2{\mathbf{k}}_F$. The problem has been previously considered by one of the authors [P. Krotkov and A. V. Chubukov, Phys. Rev. Lett. 96, 107002 (2006); Phys. Rev. B 74, 014509 (2006)]. However, it was later pointed out [D. Bergeron et al., Phys. Rev. B 86, 155123 (2012)] that the analysis neglected umklapp processes for the spin polarization operator. We incorporate umklapp terms and reevaluate the normal state self-energy and the critical temperature of the pairing instability. We show that the self-energy has a Fermi-liquid form and obtain the renormalization of the quasiparticle residue $Z$, the Fermi velocity, and the curvature of the Fermi surface. We argue that the pairing is a BCS-type problem, but go one step beyond the BCS theory and calculate the critical temperature $T_c$ with the prefactor. We apply the results to electron-doped cuprates near optimal doping and obtain $T_c\ge 10\mathrm{K}$, which matches the experimental results quite well.

We establish a physically meaningful representation of a quantum energy density for use in quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct Hamiltonian when integrated over a volume containing a cluster of particles. This property is demonstrated for a helium-neon “gas,” showing that atomic energies obtained from the energy density correspond to eigenvalues of isolated systems. The formation energies of defects or interfaces are typically calculated as total-energy differences. Using a model of $\delta$-doped silicon (where dopant atoms form a thin plane) we show how interfacial energies can be calculated more efficiently with the energy density, since the region of interest is small. We also demonstrate how the energy density correctly transitions to the bulk limit away from the interface where the correct energy is obtainable from a separate total-energy calculation.

We study an SU(2) symmetric spin-3/2 model on the $z=3$ Bethe lattice using the infinite time evolving block decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, an antiferromagnetic, as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by $S=1/2$ edge spins. Details of the iTEBD algorithm used for the simulations are included.

We consider a topologically nontrivial flat-band structure in one spatial dimension in the presence of nearest- and next-nearest-neighbor Hubbard interaction. The noninteracting band structure is characterized by a symmetry-protected topologically quantized Berry phase. At certain fractional fillings, a gapped phase with a filling-dependent ground-state degeneracy and fractionally charged quasiparticles emerges. At filling $\frac{1}{3}$, the ground states carry a fractional Berry phase in the momentum basis. These features at first glance suggest a certain analogy to the fractional quantum Hall scenario in two dimensions. We solve the interacting model analytically in the physically relevant limit of a large band gap in the underlying band structure, the analog of a lowest Landau level projection. Our solution affords a simple physical understanding of the properties of the gapped interacting phase. We pinpoint crucial differences to the fractional quantum Hall case by studying the Berry phase and the entanglement entropy associated with the degenerate ground states. In particular, we conclude that the “fractional topological phase in one-dimensional flat bands” is not a one-dimensional analog of the two-dimensional fractional quantum Hall states, but rather a charge density wave with a nontrivial Berry phase. Finally, the symmetry-protected nature of the Berry phase of the interacting phase is demonstrated by explicitly constructing a gapped interpolation to a state with a trivial Berry phase.

Spin-orbit (SO) interactions give a spin-dependent correction ${\widehat{\mathit{r}}}_{\mathrm{so}}$ to the position operator, referred to as the anomalous position operator. We study the contributions of ${\widehat{\mathit{r}}}_{\mathrm{so}}$ to the spin Hall effect (SHE) in quasi-two-dimensional (2D) semiconductor quantum wells with strong band-structure SO interactions that cause spin precession. The skew scattering and side-jump scattering terms in the SHE vanish, but we identify two additional terms in the SHE, due to ${\widehat{\mathit{r}}}_{\mathrm{so}}$, which have not been considered in the literature so far. One term reflects the modification of spin precession due to the action of the external electric field (the field drives the current in the quantum well), which produces, via ${\widehat{\mathit{r}}}_{\mathrm{so}}$, an effective magnetic field perpendicular to the plane of the quantum well. The other term reflects a similar modification of spin precession due to the action of the electric field created by random impurities, and appears in a careful formulation of the Born approximation. We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order. In electron systems with weak momentum scattering, the contribution of the anomalous spin precession due to the external electric field equals 1/2 the usual side-jump SHE, while the additional impurity-dependent contribution depends on the form of the band-structure SO coupling. For band-structure SO coupling linear in wave vector, the two anomalous spin precession contributions cancel. For band-structure SO coupling cubic in wave vector, however, they do not cancel, and the anomalous spin precession contribution to the SHE can be detected in a high-mobility 2D electron gas with strong SO coupling. In 2D hole systems, both anomalous spin precession contributions vanish identically.

The interplay of dynamical nuclear polarization (DNP) and leakage current through a double quantum dot in the spin-blockade regime is analyzed. A finite DNP is built up due to a competition between hyperfine (HF) spin-flip transitions and another inelastic escape mechanism from the triplets, which block transport. We focus on the temperature dependence of the DNP for zero energy detuning (i.e., equal electrostatic energy of one electron in each dot and a singlet in the right dot). Our main result is the existence of a transition temperature, below which the DNP is bistable, so a hysteretic leakage current versus external magnetic field $B$ appears. This is studied in two cases: (i) close to the crossing of the three triplet energy levels near $B=0$, where spin-blockade is lifted due to the inhomogeneity of the effective magnetic field from the nuclei. (ii) At higher $B$-fields, where the two spin-polarized triplets simultaneously cross two different singlet energy levels. We develop simplified models leading to different transition temperatures $T_{c,\mathrm{TT}}$ and $T_{c,\mathrm{ST}}$ for the crossing of the triplet levels and the singlet-triplet level crossings, respectively. We find $T_{c,\mathrm{TT}}$ analytically to be given solely by the HF couplings, whereas $T_{c,\mathrm{ST}}$ depends on various parameters and $T_{c,\mathrm{ST}}>T_{c,\mathrm{TT}}$. The key idea behind the existence of the transition temperatures at zero energy detuning is the suppression of energy absorption compared to emission in the inelastic HF transitions. Finally, by comparing the rate equation results with Monte Carlo simulations, we discuss the importance of having both HF interaction and another escape mechanism from the triplets to induce a finite DNP.

Using first-principles calculations, we study tunneling properties and electronic structures of Si(001)/SiO${}_2$/Si(001) junctions in a wide energy range covering the local energy gap in the SiO${}_2$ regions. We show that the tunneling spectra $T\left(E\right)$ as functions of energy $E$ have overall similarity to the projected densities of states (PDOS) at the centers of the SiO${}_2$ regions, but $T\left(E\right)$ and PDOS have significant difference in their dependencies on the SiO${}_2$ thickness. From the energy dependencies of $T\left(E\right)$ and PDOS, distinctive energy ranges are recognized in the valence and conduction bands, reflecting the local electronic structures in the SiO${}_2$ region induced from the Si regions. From the difference in the SiO${}_2$-thickness dependencies of $T\left(E\right)$ and PDOS and from eigenchannel analysis, we find that the tunneling wave function inside the SiO${}_2$ region decreases with a decay rate which itself decreases as the tunneling distance increases, resulting in a smaller averaged decay rate per length for a thicker SiO${}_2$ region. These results provide a rich picture for the SiO${}_2$ barrier in the aspects of tunneling and local electronic structures, and a theoretical framework generally applicable to other tunneling barriers.

We present direct experimental evidence of quantum confinement effects in single isolated nanodiamonds by scanning tunneling spectroscopy. For grains smaller than 4.5 nm, the band gap was found to increase with decreasing nanodiamond size and a well-defined, evenly spaced, 12-peak structure was observed on the conduction band side of the conductance curves. We attribute these peaks to the Coulomb blockade effect, reflecting the 12-fold degeneracy of the first electron-energy level in the confined nanodiamond. The present results shed light on the size dependence of the electronic properties of single nanodiamonds and are of major importance for future nanodiamond-based applications.

We analyze the spin-dependent conductance spectrum of a double quantum dot with Rashba spin-orbit and electron-electron interactions based on the Keldysh nonequilibrium Green's function formalism. A clear physical picture emerges from the single-particle analysis of electron-transfer pathways in a quantum dot molecule. It provides an insight into the mechanism that underlies the evolution of bonding resonances. This study demonstrates both numerically and analytically that the mechanism of quantum interference is altered, as either component of the Rashba spin-orbit interaction is modulated. Most importantly, the bonding state can be controlled by tuning the Rashba parameter: a bound state in the continuum becomes unbound upon gate control and vice versa, mediated by the transverse Rashba spin-orbit component. A spin-polarized current is shown to be produced by the interplay of the spin-resolved interference effect with the magnetic flux. Sharp spin polarization that arises from the negative differential conductance, observed over a wide range of values of relevant parameters, is discussed.

We propose two complementary design principles for engineering three-dimensional (3D) Weyl semimetals and superconductors in a layer-by-layer setup which includes even- and odd-parity orbitals in alternating layers—dubbed an orbital selective superlattice. Such a structure breaks mirror symmetry along the superlattice growth axis which, with the help of either a basal plane spin-orbit coupling or spinless $p+ip$ superconductivity, stabilizes a 3D Dirac node. To explore this idea, we develop a 3D generalization of the Haldane model and a Bogoliubov–de Gennes Hamiltonian for the two cases, respectively, and show that tunable single or multiple Weyl nodes with linear dispersion in all spatial directions can be engineered desirably in a widespread parameter space. We also demonstrate that a single helical Weyl band can be created at the $\Gamma$ point at the Fermi level in the superconducting case via gapping out either of the orbital states by violating its particle-hole symmetry but not any other symmetries. Finally, implications of our results for the realization of an anomalous Hall effect and Majorana bound state are discussed.

We demonstrate experimentally the condensation of exciton polaritons through optical trapping. The nonresonant pump profile is shaped into a ring and projected to a high quality factor microcavity where it forms a two-dimensional repulsive optical potential originating from the interactions of polaritons with the excitonic reservoir. Increasing the population of particles in the trap eventually leads to the emergence of a confined polariton condensate that is spatially decoupled from the decoherence inducing reservoir, before any buildup of coherence on the excitation region. In a reference experiment, where the trapping mechanism is switched off by changing the excitation intensity profile, polariton condensation takes place for excitation densities more than two times higher and the resulting condensate is subject to much stronger dephasing and depletion processes.

We investigate the chiral properties of near fields around plasmonic nanostructures and their relation to the electromagnetic chirality $C$. By combining chiral metal nanoparticles with achiral dye molecules and measuring the circular polarization dependence of the enhanced photoluminescence, we find a correlation between the dissymmetry of the luminescence enhancement and the calculated values of $C$. These effects are strong ($\sim$${10}^{-1}$), despite the weak circular dichroism of the particles ($\sim$${10}^{-5}$). We further show that $C$ represents the chiral selectivity of the near-field coupling between an emitter and a nanoantenna.

We study the time evolution and steady state of the charge current in a single-impurity Anderson model, using matrix product states techniques. A nonequilibrium situation is imposed by applying a bias voltage across one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we extract current-voltage characteristics from universal low-bias up to high-bias regimes, where band effects start to play a dominant role. We discuss three quenches, which after strongly quench-dependent transients yield the same steady-state current. Among these quenches we identify those favorable for extracting steady-state observables. The period of short-time oscillations is shown to compare well to real-time renormalization group results for a simpler model of spinless fermions. We find indications that many-body effects play an important role at high-bias voltage and finite bandwidth of the metallic leads. The growth of entanglement entropy after a certain time scale $\propto {\Delta }^{-1}$ is the major limiting factor for calculating the time evolution. We show that the magnitude of the steady-state current positively correlates with entanglement entropy. The role of high-energy states for the steady-state current is explored by considering a damping term in the time evolution.

We study the the interplay between spontaneously broken valley symmetry and spatial disorder in multivalley semiconductors in the quantum Hall regime. In cases where valleys have anisotropic electron dispersion a previous long-wavelength analysis [D. A. Abanin, S. A. Parameswaran, S. A. Kivelson, and S. L. Sondhi, Phys. Rev. B 82, 035428 (2010)] identified two new phases exhibiting the QHE. The first is the quantum Hall Ising nematic (QHIN), a phase with long-range orientational order manifested in macroscopic transport anisotropies. The second is the quantum Hall random-field paramagnet (QHRFPM) that emerges when the Ising ordering is disrupted by quenched disorder, characterized by a domain structure with a distinctive response to a valley symmetry-breaking strain field. Here we provide a more detailed microscopic analysis of the QHIN, which allows us to (i) estimate its Ising ordering temperature, (ii) study its domain-wall excitations, which play a central role in determining its properties, and (iii) analyze its response to quenched disorder from impurity scattering, which gives an estimate for domain size in the descendant QHRFPM. Our results are directly applicable to AlAs heterostructures, although their qualitative aspects inform other ferromagnetic QH systems, such as Si(111) heterostructures and trilayer graphene with trigonal warping.

Reliable evaluation of the lattice thermal conductivity is of importance for optimizing the figure of merit of thermoelectric materials. Traditionally, when deriving the phonon mediated thermal conductivity ${\kappa }_{\text{ph}}=\kappa -{\kappa }_{\text{el}}$ from the measured total thermal conductivity $\kappa$ the constant Lorenz number $L_0$ of the Wiedemann-Franz law ${\kappa }_{\mathbf{el}}=T{L}_0\sigma$ is chosen. The present study demonstrates that this procedure is not reliable when the Seebeck coefficient $\left|S\right|$ becomes large which is exactly the case for a thermoelectric material of interest. Another approximation using $L_0-S^2$, which seems to work better for medium values of $S^2$ also fails when $S^2$ becomes large, as is the case when the system becomes semiconducting/insulating. For a reliable estimation of ${\kappa }_{\text{el}}$, it is proposed that a full first-principles calculation by combining density functional theory with Boltzmann's transport theory has to be made. For the present study such an approach was chosen for investigating the clathrate type-I compound Ba${}_8$Au${}_{6-x}$Ge${}_{40+x}$ for a series of dopings or compositions $x$. For a doping of $0.8$ electrons corresponding to $x=0.27$ the calculated temperature dependent Seebeck coefficient agrees well with recent experiments corroborating the validity of the density functional theory approach.

We have examined the La substitution and its pressure effect on the Kondo semiconductor CeRu${}_2$Al${}_{10}$, which shows an unusual antiferromagnetic (AFM) order at $T_0=27$ K with the AFM ordered moment ($m_{\mathrm{AF}}$) parallel to the orthorhombic $c$ axis, not expected from the large anisotropy of the magnetic susceptibility ($\chi$) of ${\chi }_a\gg {\chi }_c\gg {\chi }_b$ in the paramagnetic state. $m_{\mathrm{AF}}$ could not be aligned along the $a$ axis, but could only be in the $bc$ plane. By only 10% La substitution corresponding to a negative chemical pressure effect, the direction of $m_{\mathrm{AF}}$ in the AFM ordered phase is changed from the $c$ to the $b$ axis. However, by applying a small pressure of $P\sim 0.3$ GPa, this $m_{\mathrm{AF}}\parallel b$ is easily changed to $m_{\mathrm{AF}}\parallel c$. Thus, the magnetic anisotropy could be easily controlled by tuning the pressure slightly. This indicates that the $c$-$f$ hybridization dominates the magnetic anisotropy in the AFM ordered state and plays an essential role in the unusual AFM order in Ce$T_2$Al${}_{10}$ ($T=\text{Ru}$,Os).