The B-phase of superfluid ${}^3$He is a 3D time-reversal-invariant topological superfluid with an isotropic energy gap, $\Delta$, separating the ground state and bulk continuum states. We report calculations of surface spectrum and spin and mass current densities originating from the Andreev surface states for confined ${}^3$He-B. The surface states are Majorana Fermions with their spins polarized transverse to their direction of propagation along the surface, ${\mathbf{p}}_{\parallel }$. The negative-energy states give rise to a ground-state helical spin current confined on the surface. The spectral functions reveal the subtle role of the spin-polarized surface states in relation to the ground-state spin current. By contrast, these states do not contribute to the $T=0$ mass current. Superfluid flow through a channel of confined ${}^3$He-B is characterized by the flow field, ${\mathbf{p}}_s=\frac{\hslash }{2}\nabla \phi$. The flow field breaks $\mathrm{SO}{\left(2\right)}_{{\mathrm{L}}_{\mathrm{z}}+{\mathrm{S}}_{\mathrm{z}}}$ rotational symmetry and time reversal ($T$). However, the Bogoliubov-Nambu Hamiltonian remains invariant under the combined symmetry, $U_{\mathrm{z}}\left(\pi \right)\times T$, where $U_{\mathrm{z}}\left(\pi \right)$ is a $\pi$ rotation about the surface normal. As a result the B phase in the presence of a superflow remains a topological phase with a gapless spectrum of Majorana modes on the surface. Thermal excitation of the Doppler-shifted Majorana branches leads to a power-law suppression of the superfluid mass current for $0<T\lesssim 0.5T_c$, providing a direct signature of the Majorana branches of surface excitations in the fully gapped 3D topological superfluid, ${}^3$He-B. Results are reported for the superfluid fraction (mass current) and helical spin current for confined ${}^3$He-B, including the temperature dependencies, as well as dependencies on confinement, pressure and interactions between quasiparticles.

Recently, in certain flat band lattice systems at commensurate fillings, fractional quantum Hall states have been found, which have anyonic excitations. We study such systems away from commensuration, i.e., the ground state of an anyon gas in such a system. The presence of the underlying lattice allows access to an entirely new regime where the anyon kinetic energy can be larger than their interaction energy. Within the flux-attachment approach, using a mean field and then adding fluctuations, we find several possible superfluid states. Two have intrinsic topological order: fractionalized quasiparticles with a fusion structure of ${\left({\mathbb{Z}}_2\right)}^4$ and ${\left({\mathbb{Z}}_8\right)}^2$, respectively, and a third has no fractionalized excitations similar to a BCS-type state. This represents a mechanism for superconductivity driven purely by strong repulsion and complex hopping of electrons.

We introduce a universal scheme for invoking a full line shape and phase reversal of Fano resonances in plasmonic metamaterials. The effect is based on opening a new excitation channel through minor structural displacements which enable continuous tunability. At the example of a metamaterial designed for terahertz frequencies, consisting of two coupled split-ring resonators, it is demonstrated by simulation and experiment that displacements by only a fraction of the wavelength are sufficient to invoke a full line shape reversal, in combination with the change from inducing a phase delay to a phase advance for a transmitted wave. Our approach provides unprecedented control of Fano asymmetry and phase, potentially enabling the implementation of dynamically tuneable Fano metamaterials and Fano-plasmonic devices such as dynamic filters or phase shifters.

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho \left(\omega \right)\sim {\left|\omega \right|}^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.

The interplay of disorder and interactions is a subject of perennial interest. In this work, we have investigated the effect of disorder due to chemical substitution on the dynamics and transport properties of correlated Fermi liquids. A low-frequency analysis in the concentrated and dilute limits shows that the dynamical local potentials arising through disorder averaging generate a linear (in frequency) term in the scattering rate. Such non-Fermi-liquid behavior (nFL) is investigated in detail for Kondo hole substitution in heavy fermions within dynamical mean field theory. We find closed-form expressions for the dependence of the static and linear terms in the scattering rate on substitutional disorder and model parameters. We argue that the low-temperature resistivity will acquire a linear in temperature term, and show that the Drude peak structure in the optical conductivity will disappear beyond a certain disorder $p_c$, that marks the crossover from lattice coherent to single-impurity behavior. A full numerical solution of the dynamical mean field theory equations reveals that the nFL term will show up significantly only in certain regimes, although it is present for any nonzero disorder concentration in principle. We highlight the dramatic changes that occur in the quasiparticle scattering rate in the proximity of $p_c$. Remarkably, we find that the nFL behavior due to dynamical effects of impurity scattering has features that are distinct from those arising through Griffiths singularities or distribution of Kondo scales. Relevance of our findings to experiments on alloyed correlated systems is pointed out.

Recently, it has become possible to tune optical lattices continuously between square and triangular geometries. We compute thermodynamics and spin correlations in the corresponding Hubbard model using a determinant quantum Monte Carlo technique and show that the frustration effects induced by the variable hopping terms can be clearly separated from concomitant bandwidth changes by a proper rescaling of the interaction. An enhancement of the double occupancy by geometric frustration signals the destruction of nontrivial antiferromagnetic correlations at weak coupling and entropy $s\lesssim \ln \left(2\right)$ (and restores Pomeranchuk cooling at strong frustration), paving the way to the long-sought experimental detection of antiferromagnetism in ultracold fermions on optical lattices.

We explore theoretically the density of states (LDOS) probed by a scanning tunneling microscope (STM) tip of two-dimensional systems hosting an adatom and a subsurface impurity, both capacitively coupled to atomic force microscope (AFM) tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: The Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin degeneracy of the LDOS is lifted exclusively in the graphene system, in particular, for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. Our work proposes the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin filter.

We use time-resolved two-color Kerr microscopy to study low-temperature electron spin diffusion in bulk GaAs with high spatial and temporal resolution. This method enables direct real-space imaging of the advancing spread of an optically excited electron spin packet by spin diffusion. We observe a high initial expansion rate of the spin packet, which is strongly reduced with increasing time. Comparison with continuous-wave Kerr spectroscopy demonstrates that this decrease is caused by the influence of the transient cooling of hot photocarriers on the electron spin diffusion coefficient.

We calculate the intrinsic lifetime of a Dirac plasmon in a doped graphene sheet by analyzing the role of electron-electron interactions beyond the random phase approximation. The damping mechanism at work is intrinsic since it operates also in disorder-free samples and in the absence of lattice vibrations. We demonstrate that graphene's sublattice-pseudospin degree of freedom suppresses intrinsic plasmon losses with respect to those that occur in ordinary two-dimensional electron liquids. As a byproduct, we are able to present a microscopic calculation of the homogeneous dynamical conductivity at energies below the single-particle absorption threshold.

We investigate spin transport in diffusive graphene nanoribbons with both clean and rough zigzag edges, and long-range potential fluctuations. The long-range fields along the ribbon edges cause the local doping to come close to the charge neutrality point forming $p$-$n$ junctions with localized magnetic moments, similar to the predicted magnetic edge of clean zigzag graphene nanoribbons. The resulting random edge magnetization polarizes charge currents and causes sample-to-sample fluctuations of the spin currents obeying universal predictions. We show furthermore that, although the average spin conductance vanishes, an applied transverse in-plane electric field can generate a finite spin conductance. A similar effect can also be achieved by aligning the edge magnetic moments through an external magnetic field.

The coupling of orbital and spin degrees of freedom is the source of many interesting phenomena. Here, we study the electron dynamics in a quantum billiard driven by a periodic electric field—a mesoscopic rectangular quantum dot—with spin-orbit coupling. We find that the spatial and temporal profiles of the observables demonstrate the transition to chaotic dynamics with qualitative modifications of the power spectra and patterns of probability and spin density. The time dependence of the wave functions and spin density indicates spin-charge separation seen in the decay of the spin-charge density correlators. Experimental verification of this spin chaos effect can lead to a better understanding of the interplay between spin and spatial degrees of freedom in mesoscopic systems.

We theoretically discuss the properties of intersubband polaritons supported by a multiple-quantum-well structure embedded in the planar microcavity with dielectric and plasmonic mirrors. A semiclassical approach based on the transfer matrix formalism supplemented by the sheet model and the “microscopic” implementation of the effective medium approximation is employed. The presence of the intrasubband transition is taken into account. The obtained results show that in the case of realistic systems exhibiting superstrong coupling regime, radiative coupling between cavity modes can lead to the violation of a commonly used single-mode cavity approximation. It manifests itself as a formation of hybrid polariton modes having a non-negligible admixture of higher photonic modes and/or surface plasmonic modes. The comparison with results predicted by a microscopic quantum approach recently developed is also presented. Performing the above mentioned comparison we pay special attention to the role of intra- and interwell Coulomb couplings.

We study the transport of charge carriers through finite graphene structures. The use of numerical exact kernel polynomial and Green function techniques allows us to treat actual sized samples beyond the Dirac-cone approximation. Particularly we investigate disordered nanoribbons, normal-conductor/graphene interfaces, and normal-conductor/graphene/normal-conductor junctions with a focus on the behavior of the local density of states, single-particle spectral function, optical conductivity, and conductance. We demonstrate that the contacts and bulk disorder will have a major impact on the electronic properties of graphene-based devices.

The macroscopic dielectric permittivity of dielectric crystals is related to the microscopic atomic polarizability of constituent atoms by the known Clausius-Mossotti relation obtained in the middle of the 19th century. We derive a similar relation for recently discovered two-dimensional crystals (mono- and bilayer graphene, boron nitride, etc) and show that, in contrast to three-dimensional materials, much stronger electron-electron interaction in two dimensions leads to a spontaneous electric polarization of the ground state of two-dimensional crystals. The predicted ferroelectric transition may have interesting applications in electrodynamics and optics.

We apply the recently developed extremely correlated Fermi liquid (ECFL) theory to the Anderson impurity model, in the extreme correlation limit $U\to \infty$. We develop an expansion in a parameter $\lambda$, related to $n_d$, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to $O\left({\lambda }^2\right)$. These yield the impurity spectral function and also the self-energy $\Sigma \left(\omega \right)$ in terms of the two self-energies of the ECFL formalism. The imaginary parts of the latter have roughly symmetric low-energy behavior ($\propto {\omega }^2$), as predicted by Fermi liquid theory. However, the inferred impurity self-energy ${\Sigma }^{\prime \prime }\left(\omega \right)$ develops asymmetric corrections near $n_d\to 1$, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation, the Friedel sum rule is satisfied but we overestimate the quasiparticle weight $z$ relative to the known exact results, resulting in an overbroadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight $z$, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.

In calculations of transport quantities, such as the electrical conductivity, thermal conductivity, Seebeck, Peltier, Nernst, Ettingshausen, Righi-Leduc, or Hall coefficients, sums over the Brillouin zone of wave-vector derivatives of the dispersion relation commonly appear. When the self-energy depends only on frequency, as in single-site dynamical mean-field theory, it is advantageous to perform these sums once and for all. We show here that in the case of a hypercubic lattice in d dimensions, the sums needed for any of the transport coefficients can be expressed as integrals over powers of the energy weighted by the energy-dependent noninteracting density of states. It is also shown that our exact expressions for the transport functions can be obtained from differential equations that follow from sum rules. By substituting the Bethe lattice density of states, one can obtain the previously unknown transport function for the electrical or thermal Hall coefficients and for the Nernst coefficient of the Bethe lattice.

The orbital-lattice coupled excitation dynamics in orbitally degenerate correlated systems is examined. We present a theoretical framework where both local vibronic excitations and superexchange-type intersite interactions are treated on an equal footing. We generalize the spin-wave approximation so as to take local vibronic states into account. The present method is valid from weak to strong Jahn-Teller coupling magnitudes. Two characteristic excitation modes coexist, a low-energy dispersive mode and a high-energy multipeak mode; these are identified as a collective vibronic mode and Flanck-Condon excitations in a single Jahn-Teller center modified by the intersite interactions, respectively. The present formalism covers vibronic dynamics in several orbital-lattice coupled systems.

We have investigated the in-plane uniaxial pressure effect on the antiferromagnetic Mott insulator Ca${}_2$RuO${}_4$ from resistivity and magnetization measurements. We succeeded in inducing the ferromagnetic metallic phase at lower critical pressure than by hydrostatic pressure, indicating that the flattening distortion of the RuO${}_6$ octahedra is more easily released under in-plane uniaxial pressure. We also found a striking in-plane anisotropy in the pressure responses of various magnetic phases: although the magnetization increases monotonically with pressure diagonal to the orthorhombic principal axes, the magnetization exhibits peculiar dependence on pressure along the in-plane orthorhombic principal axes. This peculiar dependence can be explained by a qualitative difference between the uniaxial pressure effects along the orthorhombic $a$ and $b$ axes, as well as by the presence of twin domain structures.

We examine the structural and electronic properties of LaNiO${}_3$ and NdNiO${}_3$ epitaxial thin films grown on cubic (001) SrTiO${}_3$ from the viewpoint of bulk crystal symmetry and misfit strain. X-ray scattering and polarization-dependent x-ray absorption spectroscopy measurements are performed to determine the crystal symmetry and extract the local Ni $3d$ orbital response, respectively, to understand the strain-induced distortions of the bulk structure. A strain-induced orbital polarization is found in NdNiO${}_3$ films, but is absent in LaNiO${}_3$ films. The difference in electronic structure is attributed to the bulk thermodynamic phases through group theoretical methods, which reveals that thin film perovskites retain a “memory” of their preferred electronic and structural configurations.

We investigate how free probability allows us to approximate the density of states in tight-binding models of disordered electronic systems. Extending our previous studies of the Anderson model in one dimension with nearest-neighbor interactions [Chen et al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability continues to provide accurate approximations for systems with constant interactions on two- and three-dimensional lattices or with next-nearest-neighbor interactions, with the results being visually indistinguishable from the numerically exact solution. For systems with disordered interactions, we observe a small but visible degradation of the approximation. To explain this behavior of the free approximation, we develop and apply an asymptotic error analysis scheme to show that the approximation is accurate to the eighth moment in the density of states for systems with constant interactions, but is only accurate to sixth order for systems with disordered interactions. The error analysis also allows us to calculate asymptotic corrections to the density of states, allowing for systematically improvable approximations as well as insight into the sources of error without requiring a direct comparison to an exact solution.