We investigate in detail the behavior of the bipartite fluctuations of particle number $\widehat{N}$ and spin ${\widehat{S}}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and full counting statistics have been used in mesoscopic transport and cold-atomic gases. For systems that can be mapped to a problem of noninteracting fermions, we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection, we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization-group and quantum Monte Carlo calculations, and in principle accessible in condensed-matter and cold-atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

One of the defining properties of the conventional three-dimensional (“${\mathbb{Z}}_2$” or “spin-orbit”) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analog of such a magnetoelectric effect in the thermal (or gravitational) and magnetic dipole responses in all symmetry classes that admit topologically nontrivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry, which lack $\text{SU}\left(2\right)$ spin rotation symmetry (e.g., due to spin-orbit interactions), such as the B phase of ${}^3$He, the thermal response is the only probe that can detect the nontrivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover, we find, for a significant part of the “tenfold” list of topological insulators found in previous work in the absence of interactions, that in general dimensions, the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.

We assess the impact of structural relaxation of defects upon charging on trap-assisted tunneling in high-$\kappa$ dielectric materials. ${{\mathrm{ZrO}}_2\text{/}{\mathrm{Al}}_2{\mathrm{O}}_3\text{/}\mathrm{ZrO}}_2$ thin films are taken as an exemplary system. In our completely different approach, a first-principles defect model is derived from Hedins GW approximation calculations, which is then coupled to kinetic Monte Carlo charge transport simulations. Comparison between simulation and experiment demonstrates that it is often imperative to take structural relaxation processes into account when modeling nanoscale transport across defect states.

Plasmonic nanolasers and spasers continue to attract a great deal of interest from the physics and nanophotonics community, with the experimental observation of lasing as a focus of research. We report the observation of continuous wave lasing in metallic cavities of deep subwavelength sizes under electrical injection, operating at room temperature. The volume of the nanolaser is as small as 0.42λ${}^3$, where λ $=$ 1.55 μm is the lasing wavelength. This demonstration will help answer the question of how small a nanolaser can be made, and will likely stimulate a wide range of fundamental studies in basic laser physics and quantum optics on truly subwavelength scales. In addition, such nanolasers may lead to many potential applications, such as on-chip integrated photonic systems for communication, computing, and detection.

We report on structural, magnetic, and superconducting properties of the spin-valve multilayer system CoO${}_x$/Fe1/Cu/Fe2/In. For most of the thicknesses of the second iron layer $d_{\mathrm{Fe}2}$ up to 2 nm, we have observed a full spin-valve effect for the superconducting current, i.e., a complete transition from the normal to the superconducting state by changing the mutual orientation of the magnetizations of the Fe1 and Fe2 layers. For $d_{\mathrm{Fe}2}<1$ nm, the superconducting transition temperature $T_c^{\mathrm{P}}$ for the parallel orientation of magnetizations of the Fe1 and Fe2 layers is smaller than that for the antiparallel orientation $T_c^{\mathrm{AP}}$, which corresponds to the direct spin-valve effect. For $d_{\mathrm{Fe}2}⩾1$ nm, we have found the inverse spin-valve effect with $\Delta T_c=T_c^{\mathrm{AP}}-T_c^{\mathrm{P}}<0$. Further, in samples with a fixed thickness of the In layer, we have observed an oscillating dependence of its superconducting transition temperature $T_c$ on $d_{\mathrm{Fe}2}$. The analysis of the $T_c\left(d_{\mathrm{Fe}2}\right)$ dependence using the theory of the superconducting-ferromagnetic proximity effect has enabled determination of all microscopic parameters of the studied system. With these parameters, a satisfactory description of the sign-changing oscillating behavior of the spin-valve effect $\Delta T_c\left(d_{\mathrm{Fe}2}\right)$ has been obtained using a recent theory by Fominov et al. [Ya. V. Fominov et al., Pis'ma Zh. Eksp. Teor. Fiz. 91, 329 (2010) [JETP Lett. 91, 308 (2010)]].

In this paper we propose a multishell generic cloaking system. A transparency condition independent of the object's optical and geometrical properties is proposed in the quasistatic regime of operation. The suppression of dipolar scattering is demonstrated in both cylindrically and spherically symmetric systems. A realistic tunable low-loss shell design is proposed based on a composite metal-dielectric shell. The effects due to dissipation and dispersion on the overall scattering cross section are thoroughly evaluated. It is shown that a strong reduction of scattering by a factor of up to ${10}^3$ can be achieved across the entire optical spectrum. Full wave numerical simulations for complex shaped particles are performed validating the analytical theory. The proposed design does not require optical magnetism and is generic in the sense that it is independent of the object's material and geometrical properties.

Magnetophotoluminescence and excitation spectroscopy are used to probe the excited-state spectrum of negatively charged trions in an InGaAs quantum dot. A single dot optical charging device allows us to selectively prepare a specific few ($1e$, $2e$) electron states and stabilize hot trions against decay via electron tunneling from excited orbital states. The spin structure of the excited state results in the formation of metastable trions with strong optical activity that are directly observed in luminescence. Excitation spectroscopy is employed to map the excited singlet and triplet states of the two-electron wave function, and fine-structure splittings are measured for the lowest-lying and excited orbital states. Magneto-optical measurements allow us to compare the $g$ factors and diamagnetic response of different trion states.

The electrical transport properties for compositionally and structurally well-defined epitaxial α-(Ti${}_x$Fe${}_{1-x}$)${}_2$O${}_3$(0001) films have been investigated for $x$ ≤ 0.09. All films were grown by oxygen plasma-assisted molecular beam epitaxy using two different growth rates: 0.05–0.06 Å/s and 0.22–0.24 Å/s. Despite no detectable difference in cation valence and structural properties, films grown at the lower rate were highly resistive whereas those grown at the higher rate were semiconducting (ρ $=$ ∼1 Ω · cm at 25 °C). Hall effect measurements reveal carrier concentrations between 10${}^{19}$ and 10${}^{20}$ cm${}^{-3}$ at room temperature and mobilities in the range of 0.1 to 0.6 cm${}^2$/V · s for films grown at the higher rate. The conduction mechanism transitions from small-polaron hopping at higher temperatures to variable-range hopping at a transition temperature between 180 and 140 K. The absence of conductivity in the slow-grown films is attributed to donor electron compensation by cation vacancies, which may form to a greater extent at the lower rate because of higher oxygen fugacity at the growth front.

We introduce a method that combines the power of both the lattice Green' function Monte Carlo (LGFMC) with the auxiliary field quantum Monte Carlo (AFQMC) techniques, and allows us to compute exact ground-state properties of the Hubbard model for $U\lesssim 4t$ on finite clusters. Thanks to LGFMC, one obtains unbiased zero temperature results, not affected by the so-called Trotter approximation of the imaginary time propagator $e^{-H\tau }$. At the same time, the AFQMC formalism yields a remarkably fast convergence in $\tau$ before the fermion sign problem becomes prohibitive. As an application we report ground-state energies of the Hubbard model at $U/t=4$ with up to 100 sites.

We construct exactly soluble lattice models for fractionalized, time-reversal-invariant electronic insulators in two and three dimensions. The low-energy physics of these models is exactly equivalent to a noninteracting topological insulator built out of fractionally charged fermionic quasiparticles. We show that some of our models have protected edge modes [in two dimensions (2D)] and surface modes (in 3D), and are thus fractionalized analogs of topological insulators. We also find that some of the 2D models do not have protected edge modes; that is, the edge modes can be gapped out by appropriate time-reversal-invariant, charge-conserving perturbations. (A similar state of affairs may also exist in 3D.) We show that all of our models are topologically ordered, exhibiting fractional statistics as well as ground-state degeneracy on a torus. In the 3D case, we find that the models exhibit a fractional magnetoelectric effect.

The electronic spectra of rotationally faulted graphene bilayers are calculated using a continuum formulation for small fault angles that identifies two distinct electronic states of the coupled system. The low-energy spectra of one state features a Fermi velocity reduction, which ultimately leads to pairwise annihilation and regeneration of its low-energy Dirac nodes. The physics in the complementary state is controlled by pseudospin selection rules that prevent a Fermi velocity renormalization and produce second generation symmetry-protected Dirac singularities in the spectrum. These results are compared with previous theoretical analyses and with experimental data.

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the $d$-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B 75, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the $N$-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power-law transverse density-density correlations. While we have already presented results on this latter phase elsewhere [M. S. Block et al., Phys. Rev. Lett. 106, 046402 (2011)], we will expand upon those results in this work. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite $Z_2$ symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related to a nontrivial 3-cocycle of the $Z_2$ group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if $Z_2$ symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite $Z_2$ symmetry-protected topological order.

In ordinary dielectrics, the dynamical matrix at the zone center in general is a nonanalytic function of degree zero in the wave vector $\mathbf{q}$. Its expression (for a crystal of arbitrary symmetry) is well known and is routinely implemented in first-principles calculations. The nonanalytic behavior occurs in polar crystals and owes to the coupling of the macroscopic electric field $\mathbf{E}$ to the lattice. In magnetoelectric crystals both electric and magnetic fields, $\mathbf{E}$ and $\mathbf{H}$, are coupled to the lattice, formally on equal footing. We provide the general expression for the zone-center dynamical matrix in a magnetoelectric, where the $\mathbf{E}$ and $\mathbf{H}$ couplings are accounted for in a symmetric way. As in the ordinary case, the dynamical matrix is a nonanalytic function of degree zero in $\mathbf{q}$, and is exact in the harmonic approximation. For the sake of completeness, we address other issues, and in particular, we solve a problem, which might arise in first-principles implementations, where—differently than here—the basic fields are $\mathbf{E}$ and $\mathbf{B}$ (not $\mathbf{H}$).

The anisotropic irreversibility field $B_{Irr}$ of two YBa${}_2$Cu${}_3$O${}_{7-\mathrm{x}}$ thin films doped with additional rare earth (RE) $=$ (Gd, Y) and Zr and containing strong correlated pins (splayed BaZrO${}_3$ nanorods and RE${}_2$O${}_3$ nanoprecipitates) has been measured over a very broad range up to 45 T at temperatures 56 K < T < T${}_{\mathrm{c}}$. We found that the experimental angular dependence of $B_{Irr}$ (θ) does not follow the mass anisotropy scaling $B_{Irr}\left(\theta \right)=B_{Irr}\left(0\right){\left({\cos }^2\theta +{\gamma }^{-2}{\sin }^2\theta \right)}^{-1/2}$, where $\gamma ={(m_c/m_{ab})}^{1/2}=5-6$ for the RE-doped YBa${}_2$Cu${}_3$O${}_{7-\mathrm{x}}$ (REBCO) crystals, $m_{ab}$ and $m_c$ are the effective masses along the $ab$ plane and the $c$-axis, respectively, and θ is the angle between B and the $c$-axis. For B parallel to the $ab$ planes and to the c-axis correlated pinning strongly enhances $B_{Irr}$, while at intermediate angles, $B_{Irr}$(θ) follows the scaling behavior $B_{Irr}\left(\theta \right)\propto {\left({\cos }^2\theta +{\gamma }_{RP}^{-2}{\sin }^2\theta \right)}^{-1/2}$ with the effective anisotropy factor ${\gamma }_{RP}\approx 3$ significantly smaller than the mass anisotropy would suggest. In spite of the strong effects of $c$-axis BaZrO${}_3$ nanorods, we found even greater enhancements of $B_{Irr}$ for fields along the $ab$ planes than for fields parallel to the $c$-axis, as well as different temperature dependences of the correlated pinning contributions to $B_{Irr}$ for $B$//$ab$ and $B$//$c$. Our results show that the dense and strong pins, which can now be incorporated into REBCO thin films in a controlled way, exert major and diverse effects on the measured vortex pinning anisotropy and the irreversibility field over wide ranges of $B$ and $T$. In particular, we show that the relative contribution of correlated pinning to $B_{Irr}$ for $B$//$c$ increases as the temperature increases due to the suppression of thermal fluctuations of vortices by splayed distribution of BaZrO${}_3$ nanorods.

The three-dimensional Fermi-surface structure of hole-doped metallic layered nickelate Eu${}_{2-x}$Sr${}_x$NiO${}_4$ ($x=1.1$), an important counterpart to the isostructural superconducting cuprate La${}_{2-x}$Sr${}_x$CuO${}_4$, is investigated by energy-dependent soft-x-ray angle-resolved photoemission spectroscopy. In addition to a large cylindrical hole Fermi surface analogous to the cuprates, we observe a $\Gamma$-centered $3z^2-r^2$-derived small electron pocket. This finding demonstrates that in the layered nickelate the $3z^2-r^2$ band resides close to the $x^2-y^2$ one in energy. The resultant multiband feature with varying orbital character as revealed may strongly work against the emergence of the high-temperature superconductivity.

We report on a comprehensive study of spin-$\frac{1}{2}$ Kondo effect in a strongly coupled quantum dot realized in a high-quality InAs nanowire. The nanowire quantum dot is relatively symmetrically coupled to its two leads, so the Kondo effect reaches the unitary limit. The measured Kondo conductance demonstrates scaling with temperature, Zeeman magnetic field, and out-of-equilibrium bias. The suppression of the Kondo conductance with magnetic field is much stronger than would be expected based on a $g$-factor extracted from Zeeman splitting of the Kondo peak. This may be related to strong spin-orbit coupling in InAs.

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF) approximation. The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multilayer systems and the unstable wave vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave vector is found to be approximately twice the Fermi wave vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multilayer configurations, we find a large enhancement of density-wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using an RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.

We present a detailed study of the symmetry and structure of the pairing gap in Fe-based superconductors (FeSCs). We treat FeSCs as quasi-2D, decompose the pairing interaction in the $XY$ plane in $s$-wave and $d$-wave channels into contributions from scattering between different Fermi surfaces, and analyze how each scattering evolves with doping and input parameters. We verify that each interaction is well approximated by the lowest angular harmonics. We use this simplification to analyze the interplay between the interaction with and without spin-fluctuation components, the origin of the attraction in the $s^{\pm }$ and $d_{x^2-y^2}$ channels, the competition between them, the angular dependence of the $s^{\pm }$ gaps along the electron Fermi surface, the conditions under which the $s^{\pm }$ gap develops nodes, and the origin of superconductivity in heavily electron- or hole-doped systems, when only Fermi surfaces of one type are present. We also discuss the relation between RPA and RG approaches for FeSCs.

We report the characterization of Bi${}_2$Te${}_2$Se crystals obtained by the modified Bridgman and Bridgman-Stockbarger crystal-growth techniques. X-ray-diffraction study confirms an ordered Se-Te distribution in the inner and outer chalcogen layers, respectively, with a small amount of mixing. The crystals displaying high resistivity ($>1\Omega \mathrm{cm}$) and low carrier concentration ($\sim 5\times {10}^{16}$/cm${}^3$) at 4 K were found in the central region of the long Bridgman-Stockbarger crystal, which we attribute to very small differences in defect density along the length of the crystal rod. Analysis of the temperature-dependent resistivities and Hall coefficients reveals the possible underlying origins of the donors and acceptors in this phase.