In this paper, we calculate the entanglement Rényi entropy of two coupled gapless systems in general spatial dimension $d$. The gapless systems can be either conformal field theories or Fermi liquids. We assume the two systems are coupled uniformly in an $h$-dimensional submanifold of the space, with $0\le h\le d$. We will focus on the scaling of the Rényi entropy with the size of the system, and its scaling with the intersystem coupling constant $g$. Three approaches will be used for our calculation: (1) exact calculation with ground-state wave functional, (2) perturbative calculation with functional path integral, and (3) scaling argument.

We study the frequency dependence of the electron self-energy and the optical conductivity in a recently developed field theory of the spin-density-wave quantum phase transition in two-dimensional metals. We focus on the interplay between the Fermi surface “hot spots” and the remainder of the “cold” Fermi surface. Scattering of electrons off the fluctuations of the spin-density-wave order parameter, $\phi$, is strongest at the hot spots; we compute the conductivity due to this scattering in a rainbow approximation. We point out the importance of composite operators, built of products of the primary electron or $\phi$ fields: These have important effects also away from the hot spots. The simplest composite operator, ${\phi }^2$, leads to deviations from Landau Fermi-liquid behavior on the entire Fermi surface. We also find an intermediate frequency window in which the cold electrons lose their quasiparticle form due to effectively one-dimensional scattering processes. The latter processes are part of umklapp scattering, which leads to singular contributions to the optical conductivity at the lowest frequencies at zero temperature.

Finite-temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is the construction of the corresponding functionals for noninteracting particles in an arbitrary external potential. That problem is posed here in the context of the equilibrium statistical mechanics of an inhomogeneous system. The density functionals are defined and shown to be equal to the extremal state for a functional of the reduced one-particle statistical operators. Convexity of the latter functionals implies a class of general inequalities. First, it is shown that the familiar von Weizsäcker lower bound for zero temperature functionals applies at finite temperature as well. An upper bound is obtained in terms of a single-particle statistical operator corresponding to the Thomas-Fermi approximation. Next, the behavior of the density functionals under coordinate scaling is obtained. The inequalities are exploited to obtain a class of upper and lower bounds at constant temperature, and a complementary class at constant density. The utility of such constraints and their relationship to corresponding results at zero temperature are discussed.

Quantum phases provide us with important information for understanding the fundamental properties of a system. However, the observation of quantum phases, such as Berry's phase and the sign of the matrix element of the Hamiltonian between two nonequivalent localized orbitals in a tight-binding formalism, has been challenged by the presence of other factors, e.g. , dynamic phases and spin or valley degeneracy, and the absence of methodology. Here, we report a way to directly access these quantum phases, through polarization-dependent angle-resolved photoemission spectroscopy (ARPES), using graphene as a prototypical two-dimensional material. We show that the momentum- and polarization-dependent spectral intensity provides direct measurements of (i) the phase of the band wavefunction and (ii) the sign of matrix elements for nonequivalent orbitals. Upon rotating light polarization by $\pi /2$, we found that graphene with a Berry's phase of $n\pi$ ($n=1$ for single- and $n=2$ for double-layer graphene for Bloch wavefunction in the commonly used form) exhibits the rotation of ARPES intensity by $\pi /n$, and that ARPES signals reveal the signs of the matrix elements in both single- and double-layer graphene. The method provides a technique to directly extract fundamental quantum electronic information on a variety of materials.

Scanning Hall probe microscopy has been used to study vortex structures in very-high-quality single crystals of the unconventional superconductor Sr${}_2$RuO${}_4$ $(T_c\cong 1.5$ K). In none of our samples do we find credible evidence for the existence of the spontaneous fields or chiral domains predicted for the expected time-reversal symmetry-breaking order parameter. Even in our highest-quality samples we observe very strong vortex pinning and anomalous broadening of vortex profiles. The best samples also exhibit a clear field-driven triangular to square vortex lattice transition at low fields, as predicted by extended London theory calculations. In stark contrast, slightly less well-ordered samples exhibit pronounced vortex chaining/banding that we tentatively attribute to an extrinsic source of disorder.

Pb and Ga are immiscible in bulk form. Here, we show that atomically smooth $P{b}_{1-x}G{a}_x$ ($x\approx$ 0.06) alloy films can be stabilized on a Si(111)-$7\times 7$ substrate by quantum confinement. Similar to the case of pure Pb, the alloy films follow a bilayer-by-bilayer growth mode but the resulting quantum growth morphology is remarkably different. Their superconducting transition temperatures indicate hole doping, supporting the notion that Ga atoms are substitutionally incorporated. The critical current densities are very high and exhibit a unique nonmonotonic temperature dependence. This critical current anomaly is a direct consequence of the exceptional film morphology and is attributed to a superconducting transition inside two-monolayer thick vortex pinning centers.

We utilize time- and space-resolved Brillouin light scattering spectroscopy to study the parametric excitation of spin-wave eigenmodes in microscopic Permalloy dots. We show that the fundamental center eigenmode has the smallest excitation threshold. With the increase of the pumping power above this threshold, higher-order dipole-dominated eigenmodes with both even and odd spatial symmetry also become excited. At microwave power levels far above the threshold, the multimode excitation regime is suppressed due to the parametric excitation of short-wavelength exchange-dominated spin-wave modes. Our results provide important insight into the physics of parametric processes in microscopic magnetic systems.

Free-standing exfoliated monolayer graphene is an ultrathin flexible membrane, which exhibits out-of-plane deformation or corrugation. In this paper, a technique is described to measure the band structure of such free-standing graphene by angle-resolved photoemission. Our results show that photoelectron coherence is limited by the crystal corrugation. However, by combining surface morphology measurements of the graphene roughness with angle-resolved photoemission, energy-dependent quasiparticle lifetime and band-structure measurements can be extracted. Our measurements rely on our development of an analytical formulation for relating the crystal corrugation to the photoemission linewidth. Our angle-resolved photoemission spectroscopy measurements show that, despite significant deviation from planarity of the crystal, the electronic structure of exfoliated suspended graphene is nearly that of ideal, undoped graphene; we measure the Dirac point to be within 25 meV of $E_F$. Further, we show that suspended graphene behaves as a marginal Fermi liquid, with a quasiparticle lifetime that scales as ${(E-E_F)}^{-1}$; comparison with other graphene and graphite data is discussed.

We compute the dynamics of localized excitations produced by a quantum quench in the spin-1/2 XXZ chain. Using numerics combining the density-matrix renormalization group and exact time evolution, as well as analytical arguments, we show that fractionalization due to interactions in the prequench state gives rise to “ultrarelativistic” density waves that travel at the maximum band velocity. The system is initially prepared in the ground state of the chain within the gapless $XY$ phase, which admits a Luttinger liquid (LL) description at low energies and long wavelengths. The Hamiltonian is then suddenly quenched to a band insulator, after which the chain evolves unitarily. Through the gapped dispersion of the insulator spectrum, the postquench dynamics serve as a “velocity microscope,” revealing initial-state particle correlations via space-time density propagation. We show that the ultrarelativistic wave production is tied to the particular way in which fractionalization evades Pauli blocking in the zero-temperature initial LL state.

Based on first-principles calculations, we predict a half-metallic surface state in layered bulk insulator NaCoO${}_2$, with tunable surface hole concentration. The half-metallic surface has a single Fermi surface with a helical spin texture, similar to the surface state of topological insulators, but with the key difference of time-reversal symmetry breaking in the present case. We propose the realization of topological superconductivity and Majorana fermions when the half-metallic surface states are in proximity contact with a conventional superconductor.

We study the zero-temperature phase diagram of Ising spin systems in two dimensions in the presence of competing interactions: long-range antiferromagnetic and nearest-neighbor ferromagnetic of strength $J$. We first introduce the notion of a “corner energy,” which shows, when the antiferromagnetic interaction decays faster than the fourth power of the distance, that a striped state is favored with respect to a checkerboard state when $J$ is close to $J_c$, the transition to the ferromagnetic state, i.e., when the length scales of the uniformly magnetized domains become large. Next, we perform detailed analytic computations on the energies of the striped and checkerboard states in the cases of antiferromagnetic interactions with exponential decay and with power-law decay $r^{-p}$, $p>2$, which depend on the Manhattan distance instead of the Euclidean distance. We prove that the striped phase is always favored compared to the checkerboard phase when the scale of the ground-state structure is very large. This happens for $J\lesssim J_c$ if $p>3$, and for $J$ sufficiently large if $2<p⩽3$. Many of our considerations involving rigorous bounds carry over to dimensions greater than two and to more general short-range ferromagnetic interactions.

We present temperature dependent resistivity and ac-calorimetry measurements of CeVSb${}_3$ under pressure up to 8 GPa in a Bridgman anvil cell modified to use a liquid medium and in a diamond anvil cell using argon as a pressure medium. An initial increase of the ferromagnetic transition temperature $T_C$ with pressures up to 4.5 GPa is observed, followed by decrease of $T_C$ on further increase of pressure and finally its disappearance, in agreement with the Doniach model. We infer a ferromagnetic quantum phase transition around 7 GPa under hydrostatic pressure conditions from the extrapolation to 0 K of $T_C$ and the maximum of the A coefficient from low temperature fits of the resistivity $\rho \left(T\right)={\rho }_0+A{T}^n$. No superconductivity under pressure was observed down to 0.35 K for this compound. In addition, differences in the $T_C$(P) behavior when a slight uniaxial component is present are noticed and are correlated to the choice of pressure medium.

We analyze the information contained in energy-filtered diffraction patterns measured on core-level edges. By inversion of the sum rules for electron energy loss near edge structures we calculate the reciprocal space distribution of the contribution to the total signal originating from spin moment, orbital moment, spin-orbital interaction, and individual components of magnetic and spin-orbital anisotropy tensors. We demonstrate, in particular, that the diffraction patterns contain information about all three vector components of the spin and orbital magnetic moments.

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose for insulators a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.

We present self-energy calculations for Hg chalcogenides (Hg$X$, $X=\text{S}$, Se, and Te) with inverted band structures using an explicit spin-dependent formulation of the $GW$ approximation. Spin-orbit coupling is fully taken into account in calculating the single-particle Green function $G$ and the screened interaction $W$. We have found, apart from an upward shift of the occupied conductionlike ${\Gamma }_6$ state by about $0.7$ eV, an enhancement of spin-orbit splitting by about 0.1 eV, in good agreement with experiment. This renormalization originates mainly from spin-orbit induced changes in $G$ rather than $W$, which is affected only little by spin-orbit coupling.

We derive an effective low-energy theory for metallic (armchair and nonarmchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight-binding model. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic nonarmchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube.

The unique capabilities of capacitance measurements in bilayer graphene enable probing of layer-specific properties that are normally out of reach in transport measurements. Furthermore, capacitance measurements in the top-gate and penetration field geometries are sensitive to different physical quantities: The penetration field capacitance probes the two layers equally, whereas the top-gate capacitance preferentially samples the near layer, resulting in the “near-layer capacitance enhancement” effect observed in recent top-gate capacitance measurements. We present a detailed theoretical description of this effect and show that capacitance can be used to determine the equilibrium layer polarization, a potentially useful tool in the study of broken symmetry states in graphene, stemming from the interplay between interlayer screening, disorder, and the inverse-square-root van Hove singularity particular to the bilayer graphene band structure. We show how capacitance experiments can be used to probe the ground-state layer polarization, a potentially useful tool in the study of broken symmetry states in graphene.

Multiferroic properties have been investigated for single crystals of the triangular-lattice antiferromagnet NiBr${}_2$ with long-wavelength ($\sim 7$ nm) cycloidal spin structure whose spin-spiral plane is parallel to (001). X-ray diffraction revealed a magnetoelastic lattice modulation with half the periodicity of the magnetic modulation below the cycloidal ordering temperature ($T_{\mathrm{IC}}\sim 23$ K), indicating the elliptically distorted nature of the transverse helix. Field-reversible spontaneous polarization ($P$) appears in the [1$\overline{1}$0] direction perpendicular to the spin rotation axis ($\parallel$[001]) below $T_{\mathrm{IC}}$. $P$ shows nontrivial dependence on the magnitude and direction of the poling magnetic field ($H$), suggesting the possible $H$ selection of the propagation vector of the helix from the sixfold-degenerate directions, even for the in-plane cycloidal spin structure, through magnetic domain control in the higher-temperature spin-collinear antiferromagnetic phase.

Electron spin relaxation rate (eSR) is investigated on several organic semiconductors of different morphologies and molecular structures, using avoided level crossing muon spectroscopy as a local spin probe. We find that two functionalized acenes (polycrystalline tri(isopropyl)silyl-pentacene and amorphous 5,6,11,12-tetraphenyltetracene) exhibit eSRs with an Arrhenius-like temperature dependence, each with two characteristic energy scales similar to those expected from vibrations. Polycrystalline tris(8-hydroxyquinolate)gallium shows a similar behavior. The observed eSR for these molecules is no greater than 0.85 MHz at 300 K. The variety of crystal structures and transport regimes that these molecules possess, as well as the local nature of the probe, strongly suggest an intramolecular phenomenon general to many organic semiconductors, in contrast to the commonly assumed spin relaxation models based on intermolecular charge-carrier transport.

The physical properties and the band structure of the layered pnictide SrMnBi${}_2$ were investigated. This compound has a crystal structure similar to that of the superconducting Fe pnictides, and is a bad metal with large residual resistivity. Magnetic order sets in at very high temperatures, around 290 K, as shown by magnetization, resistivity, and specific heat data. Band structure calculations using density functional theory (DFT) are consistent with the thermodynamic and transport measurements, suggesting a checkerboard antiferromagnetic (cAFM) ground state and a localized picture for the magnetism. Moreover, DFT results indicate that the Mn 3$d$ electrons are strongly correlated, and that, unlike in the known superconductors, the Sr-Bi${}_{\left(1\right)}$ layer is metallic. One more notable feature of the DFT calculation is the multiple Dirac-cone-like dispersion close to the Fermi level.