Quasiparticle scattering from vortices in d-wave superconductors I: Superflow contribution

In the vortex state of a d-wave superconductor, massless Dirac quasiparticles are scattered from magnetic vortices via a combination of two basic mechanisms: effective potential scattering due to the superflow swirling about the vortices and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex. In this paper, we study the superflow contribution by calculating the differential cross section for a quasiparticle scattering from the effective non-central potential of a single vortex. We solve the massless Dirac equation in polar coordinates and obtain the cross section via a partial wave analysis. We also present a more transparent Born-limit calculation and in this approximation we provide an analytic expression for the differential cross section. The Berry phase contribution to the quasiparticle scattering is considered in a separate paper.Comment: 22 pages, 6 figure

Quasiparticle scattering from vortices in d-wave superconductors. II. Berry phase contribution

In the mixed state of a d-wave superconductor, Bogoliubov quasiparticles are scattered from magnetic vortices via a combination of two effects: Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle upon circling a vortex, and effective potential scattering due to the superflow swirling about the vortices. In this paper, we consider the Berry phase contribution in the absence of superflow, which results in branch cuts between neighboring vortices across which the quasiparticle wave function changes sign. Here, the simplest problem that captures the physics is that of scattering from a single finite branch cut that stretches between two vortices. Elliptical coordinates are natural for this two-center problem, and we proceed by separating the massless Dirac equation in elliptical coordinates. The separated equations take the form of the Whittaker-Hill equations, which we solve to obtain radial and angular eigenfunctions. With these eigenfunctions in hand, we construct the scattering cross section via partial wave analysis. We discuss the scattering effect of Berry phase in the absence of superflow, having considered the superflow effect in the absence of Berry phase in a separate paper. We also provide qualitative comparison of transport cross sections for the Berry phase and the Superflow effects. The important issue of interference between the two effects is left to future work.Comment: 29 pages, 7 figures, New results and discussion adde

The Effect of the Housing Boom on Farm Land Values via Tax-Deferred Exchanges

This project examines Section 1031 of the Internal Revenue Code and agriculture land exchanges. Stakeholders in rural communities and agriculture are particularly interested in Section 1031 because the recent growth in transaction values of farmland may have, in part, been stimulated by Section 1031 land exchanges. Further, although many have speculated that such exchanges are widely used, little empirical research exists about the provision. We examine the theory of exchanges and develop a theoretical premium value for exchanges. We also present the first evidence of like-kind exchanges involving farmland using Federal tax data.Like-Kind Exchange, Capital Gains Tax, Agricultural Land, Land Economics/Use, Public Economics, Q15, H24,

Renormalization of thermal conductivity of disordered d-wave superconductors by impurity-induced local moments

The low-temperature thermal conductivity \kappa_0/T of d-wave superconductors is generally thought to attain a "universal" value independent of disorder at sufficiently low temperatures, providing an important measure of the magnitude of the gap slope near its nodes. We discuss situations in which this inference can break down because of competing order, and quasiparticle localization. Specifically, we study an inhomogeneous BCS mean field model with electronic correlations included via a Hartree approximation for the Hubbard interaction, and show that the suppression of \kappa_0/T by localization effects can be strongly enhanced by magnetic moment formation around potential scatterers.Comment: 2 pages, 1 figure, submitted to M2S-HTSC VIII, Dresden 200

The microwave induced resistance response of a high mobility 2DEG from the quasi-classical limit to the quantum Hall regime

Microwave induced resistance oscillations (MIROs) were studied experimentally over a very wide range of frequencies ranging from ~20 GHz up to ~4 THz, and from the quasi-classical regime to the quantum Hall effect regime. At low frequencies regular MIROs were observed, with a periodicity determined by the ratio of the microwave to cyclotron frequencies. For frequencies below 150 GHz the magnetic field dependence of MIROs waveform is well described by a simplified version of an existing theoretical model, where the damping is controlled by the width of the Landau levels. In the THz frequency range MIROs vanish and only pronounced resistance changes are observed at the cyclotron resonance. The evolution of MIROs with frequency are presented and discussed.Comment: 4 pages, presented at EP2DS, to be published in Physica

Microwave Photoconductivity in Two-Dimensional Electron Systems due to Photon-Assisted Interaction of Electrons with Leaky Interface Phonons

We calculate the contribution of the photon-assisted interaction of electrons with leaky interface phonons to the dissipative dc photoconductivity of a two-dimensional electron system in a magnetic field. The calculated photoconductivity as a function of the frequency of microwave radiation and the magnetic field exhibits pronounced oscillations. The obtained oscillation structure is different from that in the case of photon-assisted interaction with impurities. We demonstrate that at a sufficiently strong microwave radiation in the certain ranges of its frequency (or in certain ranges of the magnetic field) this mechanism can result in the absolute negative conductivity.Comment: 3 pages, 1 figur

Effect of external magnetic field on electron spin dephasing induced by hyperfine interaction in quantum dots

We investigate the influence of an external magnetic field on spin phase relaxation of single electrons in semiconductor quantum dots induced by the hyperfine interaction. The basic decay mechanism is attributed to the dispersion of local effective nuclear fields over the ensemble of quantum dots. The characteristics of electron spin dephasing is analyzed by taking an average over the nuclear spin distribution. We find that the dephasing rate can be estimated as a spin precession frequency caused primarily by the mean value of the local nuclear magnetic field. Furthermore, it is shown that the hyperfine interaction does not fully depolarize electron spin. The loss of initial spin polarization during the dephasing process depends strongly on the external magnetic field, leading to the possibility of effective suppression of this mechanism.Comment: 10 pages, 2 figure

Formation of d-wave superconducting order in a randomly doped lattice

We consider the interplay between superconducting coupling and dopant impurity scattering of charge carriers in planar square lattice systems and examine physical conditions (doping level, temperature, local symmetry of coupling and scattering potentials) necessary in this model system to obtain a d-wave superconducting order, like that observed in real doped cuprate HTSC materials. Using the Lifshitz model for the disorder introduced into system by dopants, we analyze also the non-uniform structure of such d-wave parameter, including both its magnitude and phase variation. The results indicate that d-wave superconductivity turns possible in a doped metal until it can be destroyed at too high doping levels.Comment: 22 pages, 2 figure