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We calculate the dispersion relations for magnon waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when $kd \ll 1$, where $k$ is the wave number and $d$ the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive magnon waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The magnon waves can be longitudinal ($L$), transverse ($T$), or elliptically polarized. We find that a linearly polarized magnon wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled magnon waves., Comment: 8 pages, 5 figures

We calculate the dispersion relations of plasmonic waves propagating along a chain of semiconducting or metallic nanoparticles in the presence of both a static magnetic field ${\bf B}$ and a liquid crystalline host. The dispersion relations are obtained using the quasistatic approximation and a dipole-dipole approximation to treat the interaction between surface plasmons on different nanoparticles. For a plasmons propagating along a particle chain in a nematic liquid crystalline host with both ${\bf B}$ and the director parallel to the chain, we find a small, but finite, Faraday rotation angle. For ${\bf B}$ perpendicular to the chain, but director still parallel to the chain, the field couples the longitudinal and one of the two transverse plasmonic branches. This coupling is shown to split the two branches at the zero field crossing by an amount proportional to $|{\bf B}|$. In a cholesteric liquid crystal host and an applied magnetic field parallel to the chain, the dispersion relations for left- and right-moving waves are found to be different. For some frequencies, the plasmonic wave propagates only in one of the two directions., Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1502.04960

We calculate the dispersion relations for electromagnetic waves propagating at the interface between two dissimilar Drude metals in an external magnetic field B parallel to the interface. The propagating modes are bound to the inteface and travel perpendicular to B. In certain frequency ranges, the waves can propagate in one direction only. The frequency range for these one-way modes increases with increasing B. One group of modes occurs at moderate frequencies, between the lower and upper plasma frequencies of the two metals. The other occurs at much lower frequencies, between their lower and upper cyclotron frequencies. We discuss possible ways to realize such modes in real materials, including dissimilar superconductors., Comment: 10 pages, 3 figures

In the limit of low adatom concentration, we obtain exact analytic expressions for the local and total density of states (LDOS, TDOS) for a tight-binding model of adatoms on graphene. The model is not limited to nearest-neighbor hopping but can include hopping between carbon atoms at any separation. We also find an analytical expression for the spectral function $A({\bf k}, E)$ of an electron of Bloch vector ${\bf k}$ and energy E on the graphene lattice, to first order in the adatom concentration. We treat the electron-electron interaction by including a Hubbard term on the adatom, which we solve within a mean-field approximation. For finite Hubbard $U$, we find the spin-polarized LDOS, TDOS, and spectral function self-consistently. For any choice of parameters of the tight-binding model within mean field theory, we find a critical value of $U$ above which a moment develops on the adatom. For most choices of parameters, we find a substantial charge transfer from the adatom to the graphene host., Comment: 11 Pages, 6 figures, 1 table

Electronic nematic phases are broadly characterized by spontaneously broken rotational symmetry. Although they have been widely recognized in the context of high temperature cuprates, bilayer ruthenates, and iron-based superconductors, the focus so far has been exclusively on the uniform nematic phase. Recently, however, it was proposed that on a square lattice a nematic instability in the d-wave charge channel could lead to a spatially modulated nematic state, where the modulation vector q is determined by the relative location of the Fermi level to the van Hove singularity. Interestingly, this finite-q nematic phase has also been identified as an additional leading instability that is as strong as the superconducting instability near the onset of spin density wave order. Here we study the electrical conductivity tensor in the modulated nematic phase for a general modulation vector. Our results can be used to identify modulated nematic phases in correlated materials., Comment: 6 pages, 3 figures

We numerically study the superconductor-insulator phase transition in a model disordered 2D superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the (2+1)D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form -J\cos(\theta_i-\theta_j-A_{ij}), where A_{ij} has a mean of zero and a standard deviation \Delta A_{ij}. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values \Delta A_{ij} then corresponds to an applied field such that the average number of flux quanta per plaquette has various integer values N: larger N corresponds to larger \Delta A_{ij}. For any value of \Delta A_{ij}, there appears to be a critical coupling constant K_c(\Delta A_{ij})=\sqrt{[J/(2U)]_c}, where U is the charging energy, above which the system is a Mott insulator; there is also a corresponding critical conductivity \sigma^*(\Delta A_{ij}) at the transition. For \Delta A_{ij}=\infty, the order parameter of the transition is a renormalized coupling constant g. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of \Delta A_{ij} takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is z \sim 1.3. By contrast, z=1 for this model at \Delta A_{ij}=0. We suggest that the superconductor to insulator transition is actually of this I to BG class at all nonzero \Delta A_{ij}'s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion., Comment: 17 pages, 23 figures, accepted for publication in Phys. Rev. B

We calculate the thermodynamic properties of a collection of $N$ small Josephson junctions coupled to a single-mode resonant electromagnetic cavity, at finite temperature $T$, using several approaches. In the first approach, we include all the quantum-mechanical levels of the junction, but treat the junction-cavity interaction using a mean-field approximation developed previously for $T = 0$. In the other approaches, the junctions are treated including only the two lowest energy levels per junction, but with two different Hamiltonians. The first of these maps onto the Dicke model of quantum optics. The second is a modified Dicke model which contains an additional XY-like coupling between the junctions. The modified Dicke model can be treated using a mean-field theory, which in the limit of zero XY coupling gives the solution of the Dicke model in the thermodynamic limit using Glauber coherent states to represent the cavity. In all cases, for an $N$-independent junction-cavity coupling, there is a critical junction number $N$ above which there is a continuous transition from incoherence to coherence with decreasing $T$. If the coupling scales with $N$ so as to give a well-behaved thermodynamic limit, there is a critical minimum coupling strength for the onset of coherence. In all three models, the cavity photon occupation numbers have a non-Bose distribution when the system is coherent., Comment: 26 pages

We show how the partition function of a network of parallel superconducting wires weakly coupled together by the proximity effect, subjected a vector potential along the wires can be mapped onto N-distinguishable two dimensional quantum-mechanics problem with a perpendicular imaginary magnetic field. Then, we show, using a mean field approximation, that, for a given coupling, there is a critical temperature for onset of inter-wire phase coherence. The transition temperature $T_c$ is plotted on both cases for non-magnetic and a magnetic field perpendicular to the wires., Comment: 17 pages, 7 figures

We compute the spectral function $A({\bf k}, \omega)$ of a model two-dimensional high-temperature superconductor, at both zero and finite temperatures $T$. We assume that an areal fraction $c_{\beta}$ of the superconductor has a large gap $\Delta$ ($\beta$ regions), while the rest has a smaller $\Delta$ ($\alpha$ regions), both of which are randomly distributed in space. We find that $A({\bf k}, \omega)$ is most strongly affected by inhomogeneity near the point $\mathbf k = (\pi, 0)$ (and the symmetry-related points). For $c_\beta\simeq 0.5$, $A({\bf k}, \omega)$ exhibits two double peaks (at positive and negative energy) near this k-point if the difference between $\Delta_\alpha$ and $\Delta_\beta$ is sufficiently large in comparison to the hopping integral. The strength of the inhomogeneity required to produce a split spectral function peak suggests that inhomogeneity is unlikely to be the cause of a second branch in the dispersion relation. Thermal fluctuations also affect $A({\bf k}, \omega)$ most strongly near $\mathbf k = (\pi,0)$. Typically, peaks that are sharp at $T = 0$ become reduced in height, broadened, and shifted toward lower energies with increasing $T$; the spectral weight near $\mathbf k = (\pi, 0)$ becomes substantial at zero energy for $T$ greater than the phase-ordering temperature., Comment: Accepted for publication in Phys. Rev. B. Scheduled Issue: 01 Jan 2008. 26 Pages and 10 figures

A zigzag boundary between a $d_{x^2-y^2}$ and an $s$-wave superconductor is believed to behave like a long Josephson junction with alternating sections of $0$ and $\pi$ symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long $0$-$\pi$ junction. In this form, the equations describe a hybrid ladder of inductively coupled small $0$ and $\pi$ resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density $J_c(H_a)$ is maximum at non-zero applied magnetic field $H_a$, and depends strongly on the ratio of Josephson penetration depth $\lambda_J$ to facet length $L_f$. If $\lambda_J/L_f \gg 1$ and the number of facets is large, there is a broad range of $H_a$ where $J_c(H_a)$ is less than $2\%$ of the maximum critical current density of a long $0$ junction. All of these features are in qualitative agreement with recent experiments. In the limit $\lambda_J/L_f \to \infty$, our model reduces to a previously-obtained analytical superposition result for $J_c(H_a)$. In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor $Q_J(H_a)$, finding that $Q_J(H_a) \propto \sqrt{J_c(H_a)}$. We suggest that measuring the field-dependence of $Q_J(H_a)$ would provide further evidence that this RCSJ model applies to a long $0$-$\pi$ junction between a d-wave and an s-wave superconductor., Comment: 25 pages, 10 figures

We study a model for the pinning of vortices in a two-dimensional, inhomogeneous, Type-II superconductor in its mixed state. The model is based on a Ginzburg-Landau (GL) free energy functional whose coefficients are determined by the mean-field transition temperature T_{c0} and the zero-temperature penetration depth \lambda(0). We find that if (i) T_{c0} and \lambda(0) are functions of position, and (ii) \lambda^2(0) is proportional to T_{c0}^y, with y greater than 0, then the vortices tend to be pinned where T_{c0}, and hence the magnitude of the superconducting order parameter \Delta, are large. This behavior is in contrast to the usual picture of pinning in Type-II superconductors, where pinning occurs in the small-gap regions. We also compute the local density of states of a model BCS Hamiltonian with d-wave symmetry, in which the pairing field is obtained from Monte Carlo simulations of a GL free energy. Several features observed in scanning tunneling spectroscopy measurements on YBa_2Cu_3O_{6+x} and Bi_2Sr_2CaCu_2O_{8+x} are well reproduced by our model: far from the cores, the local density of states spectrum has a small gap and sharp coherence peaks, while near the cores it has a larger gap with low, broad peaks. Additionally, also in agreement with experiment, the spectrum near the core does not exhibit a zero-energy peak which is, however, observed in other theoretical studies., Comment: 25 pages, 11 figures. Accepted for publication in Phys. Rev. B

Recent experiments have shown that the superconducting energy gap in some cuprates is spatially inhomogeneous. Motivated by these experiments, and using exact diagonalization of a model d-wave Hamiltonian, combined with Monte Carlo simulations of a Ginzburg-Landau free energy functional, we have calculated the single-particle density of states LDOS$(\omega,r)$ of a model high-T$_c$ superconductor as a function of temperature. Our calculations include both quenched disorder in the pairing potential and thermal fluctuations in both phase and amplitude of the superconducting gap. Most of our calculations assume two types of superconducting regions: $\alpha$, with a small gap and large superfluid density, and $\beta$, with the opposite. If the $\beta$ regions are randomly embedded in an $\alpha$ host, the LDOS on the $\alpha$ sites still has a sharp coherence peak at $T = 0$, but the $\beta$ component does not, in agreement with experiment. An ordered arrangement of $\beta$ regions leads to oscillations in the LDOS as a function of energy. The model leads to a superconducting transition temperature $T_c$ well below the pseudogap temperature $T_{c0}$, and has a spatially varying gap at very low $T$, both consistent with experiments in underdoped Bi2212. Our calculated LDOS$(\omega,r)$ shows coherence peaks for $T < T_c$, which disappear for $T > T_c$, in agreement with previous work considering phase but not amplitude fluctuations in a homogeneous superconductor. Well above $T_c$, the gap in the LDOS disappears., Comment: 37 pages, 12 figures. Accepted by Phys. Rev. B. Scheduled Issue: 01 Nov 2006

The high-T_c cuprate superconductors are now believed to be intrinsically inhomogeneous. We develop a theory to describe how this inhomogeneity affects the intermodulation coefficient of such a material. We show that the continuum equations describing intermodulation in a superconducting layer with spatially varying properties are formally equivalent to those describing an inhomogeneous dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we calculate the effect of inhomogeneity on the intermodulation coefficient in a high-T_c material, using several assumptions about the topology of the layer, and some simple analytical approximations to treat the nonlinearity. For some topologies, we find that the intermodulation critical supercurrent density J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly leading to more desirable material properties. We discuss this result in light of recent spatial mappings of the superconducting energy gap in BSCCO-2212., Comment: 26 pages, 9 figures, accepted for publication in the Journal of Applied Physics

We have used Monte Carlo simulations, combined with finite-size scaling and two different real-space renormalization group approaches, to study a fully frustrated three-dimensional XY model on a simple cubic lattice. This model corresponds to a lattice of Josephson-coupled superconducting grains in an applied magnetic field ${\bf H} = (\Phi_0/a^2)(1/2,1/2,1/2)$. We find that the model has a continuous phase transition with critical temperature $T_c = 0.681 J/k_B$, where $J$ is the XY coupling constant, and critical exponents $\alpha/\nu = 0.87 \pm 0.01$, $v/\nu = 0.82 \pm 0.01$, and $\nu = 0.72 \pm 0.07$, where $\alpha$, $v$, and $\nu$ describe the critical behavior of the specific heat, helicity modulus, and correlation length. We briefly compare our results with other studies of this model, and with a mean-field approximation., Comment: 34 pages, 13 figures, 1 table, Phys. Rev. B in press

We show numerically that, in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can spontaneously break up into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied transverse field of 1/q flux quanta per plaquette the ground state is a regular pattern of one fluxon every q plaquettes. When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1/q units of vorticity. The fractional fluxons are basically walls between different domains of the ground state of the underlying 1/q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. It is shown that the fractional fluxons would produce a time-averaged voltage related in a characteristic way to the ac voltage frequency., Comment: 13 Figures. 10 pages

Using Monte Carlo techniques, we study a simple model which exhibits a competition between superconductivity and other types of order in two dimensions. The model is a site-diluted XY model, in which the XY spins are mobile, and also experience a repulsive interaction extending to one, two, or many shells of neighbors. Depending on the strength and range of the repulsion and spin concentration, the spins arrange themselves into a remarkable variety of patterns at low temperatures $T$, including phase separation, checkerboard order, and straight or labyrinthine patterns of stripes, which sometimes show hints of nematic or smectic order. This pattern formation profoundly affects the superfluid density, $\gamma$. Phase separation tends to enhance $\gamma$, checkerboard order suppresses it, and stripe formation increases the component of $\gamma$ parallel to the stripes and reduces the perpendicular one. We verify that $\gamma(T = 0)$ is proportional to the effective conductance of a random conductance network whose conductances equal the couplings of the XY system. Possible connections between the model and real materials, such as single high-T$_c$ cuprate layers, are briefly discussed., Comment: 30 pages, 10 figures. Accepted by Physical Review B, scheduled issue 01 Dec 2005

We calculate the effective resistivity of a macroscopically disordered two dimensional conductor consisting of two components in a perpendicular magnetic field. When two components have equal area fractions, we use a duality theorem to show that the magnetoresistance is non-saturating and at high fields varies exactly linearly with magnetic field. At other compositions, an effective medium calculation leads to a saturating magnetoresistance. We briefly discuss possible connections between these results and magnetoresistance measurements on heavily disordered chalconide semiconductors., Comment: 4 EPS figures, REVTEX style; Typos and Figures 1 and 2 corrected

We describe a method to calculate the electrical force acting on a sphere in a suspension of dielectric spheres in a host with a different dielectric constant, under the assumption that a spatially uniform electric field is applied. The method uses a spectral representation for the total electrostatic energy of the composite. The force is expressed as a certain gradient of this energy, which can be expressed in a closed analytic form rather than evaluated as a numerical derivative. The method is applicable even when both the spheres and the host have frequency-dependent dielectric functions and nonzero conductivities, provided the system is in the quasistatic regime. In principle, it includes all multipolar contributions to the force, and it can be used to calculate multi-body as well as pairwise forces. We also present several numerical examples, including host fluids with finite conductivities. The force between spheres approaches the dipole-dipole limit, as expected, at large separations, but departs drastically from that limit when the spheres are nearly in contact. The force may also change sign as a function of frequency when the host is a slightly conducting fluid., Comment: 29 pages, 8 figures, Accepted for Publication in Physical Review E

We present a model to describe an underdamped long Josephson junction coupled to a singlemode electromagnetic cavity, and carry out numerical calculations using this model in various regimes. The coupling may occur through either the electric or the magnetic eld of the cavity mode. When a current is injected into the junction, we nd that the time-averaged voltage exhibits self-induced resonant steps due to coupling between the current in the junction and the electric eld of the cavity mode. These steps are similar to those observed and calculated in small Josephson junctions. When a soliton is present in the junction (corresponding to a quantum of magnetic ux parallel to the junction plates), the SIRS's disappear if the electric eld in the cavity is spatially uniform. If the cavity mode has a spatially varying electric eld, there is a strong coupling between the soliton and the cavity mode. This coupling causes the soliton to become phase-locked to the cavity mode, and produces step-like anomalies on the soliton branch of the IV characteristics. If the coupling is strong enough, the frequency of the cavity mode is greatly red-shifted from its uncoupled value. We present simple geometrical arguments which account for this behavior., Comment: 29 pages 15 figures

We calculate the surface plasmon dispersion relations for a periodic chain of spherical metallic nanoparticles in an isotropic host, including all multipole modes in a generalized tight-binding approach. For sufficiently small particles ($kd \ll 1$, where $k$ is the wave vector and $d$ is the interparticle separation), the calculation is exact. The lowest bands differ only slightly from previous point-dipole calculations provided the particle radius $a \lesssim d/3$, but differ substantially at smaller separation. We also calculate the dispersion relations for many higher bands, and estimate the group velocity $v_g$ and the exponential decay length $\xi_D$ for energy propagation for the lowest two bands due to single-grain damping. For $a/d=0.33$, the result for $\xi_D$ is in qualitative agreement with experiments on gold nanoparticle chains, while for larger $a/d$, such as $a/d=0.45$, $v_g$ and $\xi_D$ are expected to be strongly $k$-dependent because of the multipole corrections. When $a/d \sim 1/2$, we predict novel percolation effects in the spectrum, and find surprising symmetry in the plasmon band structure. Finally, we reformulate the band structure equations for a Drude metal in the time domain, and suggest how to include localized driving electric fields in the equations of motion., Comment: 19 pages 3 figures To be published in Phy. Rev. B

We describe a simple model for the melting and optical properties of a DNA/gold nanoparticle aggregate. The aggregate is modeled as a cluster of gold nanoparticles on a periodic lattice connected by DNA bonds, and the extinction coefficient is computed using the discrete dipole approximation. The optical properties at fixed wavelength change dramatically at the melting transition, which is found to be higher and narrower in temperature for larger particles, and much sharper than that of an isolated DNA link. All these features are in agreement with available experiments., Comment: 4 pages, 3 figures. To be published in Physica B