Index theoretic characterization of d-wave superconductors in the vortex state

We employ index theoretic methods to study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. This allows us to compare singly quantized $hc/2e$ and doubly quantized $hc/e$ vortices, the first of which must always be accompanied by $Z_2$ branch cuts. For an inversion symmetric vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of doubly quantized vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of $\Delta_0/t$ in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin Hall conductivity, which generally differs in the cases of the $hc/2e$ and $hc/e$ vortex lattices.Comment: 4 pages, 2 figures, 1 table (accepted for publication in PRL; substantially rewritten for presentation clarity; references to quantum order and visons omitted on referee's demand

Mixed state of a lattice d-wave superconductor

We study the mixed state in an extreme type-II lattice d-wave superconductor in the regime of intermediate magnetic fields H_{c1} << H << H_{c2}. We analyze the low energy spectrum of the problem dominated by nodal Dirac-like quasiparticles with momenta near k_F=(\pm k_D,\pm k_D) and find that the spectrum exhibits characteristic oscillatory behavior with respect to the product of k_D and magnetic length l. The Simon-Lee scaling, predicted in this regime, is satisfied only on average, with the magnitude of the oscillatory part of the spectrum displaying the same 1/l dependence as its monotonous ``envelope'' part. The oscillatory behavior of the spectrum is due to the inter-nodal interference enhanced by the singular nature of the low energy eigenfunctions near vortices. We also study a separate problem of a single vortex piercing an isolated superconducting grain of size L by L. Here we find that the periodicity of the quasiparticle energy oscillations with respect to k_D L is doubled relative to the case where the field is zero and the vortex is absent, both such oscillatory behaviors being present at the leading order in 1/L. Finally, we review the overall features of the tunneling conductance experiments in YBCO and BSCCO, and suggest an interpretation of the peaks at 5-20 meV observed in the tunneling local density of states in these materials.Comment: 16 pages, 11 figure

Thermodynamics of the quantum su(1,1)su(1,1) Landau-Lifshitz model

We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model, following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the quantum integrability of the theory, which is based on construction of self-adjoint extensions, leading to a regularized quantum Hamiltonian for an arbitrary n-particle sector. Starting from general discontinuity properties of the functions used to construct the self-adjoint extensions, we derive the thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and singular kernel, the self-consistency implies that only negative chemical potential values are allowed, which leads to the conclusion that, unlike its su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities.Comment: 10 page

Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde

The intermediate evolution phase in case of truncated selection

Using methods of statistical physics, we present rigorous theoretical calculations of Eigen's quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of a reproducing quasispecies. Depending on the mutation rates, we observe three phases, a selective one, an intermediate one with some residual order and a completely randomized phase. Our results are applicable for the general case of fitness landscape.Comment: 8 page

Solution of the Roth-Marques-Durian Rotational Abrasion Model

We solve the rotational abrasion model of Roth, Marques and Durian (arXiv:1009.3492), a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as a coefficient. The complexity of the solution is primarily in keeping track of the cases in the piecewise function that results from certain amputation and interpolation processes, so we also extract from it a model of an evolving planar tree graph that tracks the evolution of the coarse features of the contour.Comment: 5 pages, 4 figure

Fourier transform spectroscopy of d-wave quasiparticles in the presence of atomic scale pairing disorder

The local density of states power spectrum of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO) has been interpreted in terms of quasiparticle interference peaks corresponding to an "octet'' of scattering wave vectors connecting k-points where the density of states is maximal. Until now, theoretical treatments have not been able to reproduce the experimentally observed weights and widths of these "octet'' peaks; in particular, the predominance of the dispersing "q$_1$'' peak parallel to the Cu-O bond directions has remained a mystery. In addition, such theories predict "background'' features which are not observed experimentally. Here, we show that most of the discrepancies can be resolved when a realistic model for the out-of-plane disorder in BSCCO is used. Weak extended potential scatterers, which are assumed to represent cation disorder, suppress large-momentum features and broaden the low-energy "q$_7$''-peaks, whereas scattering at order parameter variations, possibly caused by a dopant-modulated pair interaction around interstitial oxygens, strongly enhances the dispersing "q$_1$''-peaks.Comment: 7 pages, 3 figure

Plasmonic modulator optimized by patterning of active layer and tuning permittivity

We study an ultra-compact plasmonic modulator that can be applied in photonic integrated circuits. The modulator is a metal-insulator-metal waveguide with an additional ultra-thin layer of indium tin oxide (ITO). Bias is applied to the multilayer core by means of metal plates that serve as electrodes. External field changes carrier density in the ultra-thin ITO layer, which influences the permittivity. The metal-insulator-metal system possesses a plasmon resonance, and it is strongly affected by changes in the permittivity of the active layer. To improve performance of the structure we propose several optimizations. We examine influence of the ITO permittivity on the modulator's performance and point out appropriate values. We analyze eigenmodes of the waveguide structure and specify the range for its efficient operation. We show that substituting the continuous active layer by a one-dimension periodic stripes increases transmittance through the device and keeps the modulator's performance at the same level. The dependence on the pattern size and filling factor of the active material is analyzed and optimum parameters are found. Patterned ITO layers allow us to design a Bragg grating inside the waveguide. The grating can be turned on and off, thus modulating reflection from the structure. The considered structure with electrical control possesses a high performance and can efficiently work as a plasmonic component in nanophotonic architectures.Comment: Optics Communications (2012