Why could Electron Spin Resonance be observed in a heavy fermion Kondo lattice?

We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancelation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. The contribution to the ESR linewidth caused by the local magnetic field distribution is subject to motional narrowing supported by ferromagnetic correlations. The developed theoretical model successfully explains the ESR data of YbRh2Si2 in terms of their dependence on temperature and magnetic field.Comment: 5pages, 1 Figur

Electromagnetic Response of Layered Superconductors with Broken Lattice Inversion Symmetry

We investigate the macroscopic effects of charge density waves (CDW) and superconductivity in layered superconducting systems with broken lattice inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D) transition metal dichalcogenides (TMD). We work with the low temperature time dependent Ginzburg-Landau theory and study the coupling of lattice distortions and low energy CDW collective modes to the superconducting order parameter in the presence of electromagnetic fields. We show that superconductivity and piezoelectricity can coexist in these singular metals. Furthermore, our study indicates the nature of the quantum phase transition between a commensurate CDW phase and the stripe phase that has been observed as a function of applied pressure.Comment: 9 pages, 1 figure. Final version. Accepted in Phys.Rev.

Strongly correlated quantum dots in weak confinement potentials and magnetic fields

We explore a strongly correlated quantum dot in the presence of a weak confinement potential and a weak magnetic field. Our exact diagonalization studies show that the groundstate property of such a quantum dot is rather sensitive to the magnetic field and the strength of the confinement potential. We have determined rich phase diagrams of these quantum dots. Some experimental consequences of the obtained phase diagrams are discussed.Comment: 5 pages, 7 figures, new and updated figure

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

Exact eigenstate analysis of finite-frequency conductivity in graphene

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to the band centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away from the band centre. Further studies of current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. We calculate conductivity using Kubo Greenwood formula and show that, for low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparison with square lattice and find that graphene is more easily localized when subject to disorder.Comment: 11 pages,15 figure

Connecting Numerical Relativity and Data Analysis of Gravitational Wave Detectors

Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave signals from likely sources are crucial for the success of this endeavor. Modeling binary black hole sources of gravitational radiation requires solving the Eintein equations of General Relativity using powerful computer hardware and sophisticated numerical algorithms. This proceeding presents where we are in understanding ground-based gravitational waves resulting from the merger of black holes and the implications of these sources for the advent of gravitational-wave astronomy.Comment: Appeared in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag

A topological characterization of delocalization in a spin-orbit coupling system

We show that wavefunctions in a two-dimensional (2D) electron system with spin-orbit coupling can be characterized by a topological quantity--the Chern integer due to the existence of the intrinsic Kramers degeneracy. The localization-delocalization transition in such a system is studied in terms of such a Chern number description, which reproduces the known metal-insulator transition point. The present work suggests a unified picture for various known 2D delocalization phenomena based on the same topological characterization.Comment: RevTex, 12 pages; Two PostScript figure

Towards a New Proof of Anderson Localization

The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof of this Anderson localization phenomenon in one spatial dimension, extending the classical result to the case of a periodic background potential. The proof makes use of techniques previously developed to study the effects of noise on reheating in inflationary cosmology, employing methods of random matrix theory

Dynamical symmetry breaking in a 2D electron gas with a spectral node

We study a disordered 2D electron gas with a spectral node in a vicinity of the node. After identifying the fundamental dynamical symmetries of this system, the spontaneous breaking of the latter by a Grassmann field is studied within a nonlinear sigma model approach. This allows us to reduce the average two-particle Green's function to a diffusion propagator with a random diffusion coefficient. The latter has non-degenerate saddle points and is treated by the conventional self-consistent Born approximation. This leads to a renormalized chemical potential and a renormalized diffusion coefficient, where the DC conductivity increases linearly with the density of quasiparticles. Applied to the special case of Dirac fermions, our approach provides a comprehensive description of the minimal conductivity at the Dirac node as well as for the V-shape conductivity inside the bands.Comment: 13 pages, 4 figures, extended versio