Field induced dx2−y2+idxyd_{x^2-y^2}+id_{xy} state and marginal stability of high-Tc superconductors

It is shown that the {\em complex} $d_{xy}$ component is generated in d-wave superconductor in the magnetic field. As one enters superconducting state at finite field the normal to superconducting transition occurs into bulk $d_{x^2-y^2}+i d_{xy}$ state . The driving force for the transition is the linear coupling between magnetic field and non zero magnetization of the $d_{x^2-y^2}+i d_{xy}$ condensate. The external magnetic field violates parity and time reversal symmetries and the nodal quasiparticle states respond by generating the $id_{xy}$ component of the order parameter, with the magnitude estimated to be on the order of few Kelvin. Parity (P) and time reversal (T) symmetries are violated in this state.Comment: 4 pages, latex file with two eps figure file

Theory of NMR as a local probe for the electronic structure in the mixed state of the high-TcT_c cuprates

We argue that nuclear magnetic resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin-susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} a temperature dependence of $T_1$ which varies with frequency. We propose a nuclear quadrupole experiment to study the effects of a uniform supercurrent on the electronic structure and predict that $T_1$ varies with the direction of the supercurrent.Comment: RevTex, 5 pages, 3 figures embedded in the tex

Onset of Vortices in Thin Superconducting Strips and Wires

Spontaneous nucleation and the consequent penetration of vortices into thin superconducting films and wires, subjected to a magnetic field, can be considered as a nonlinear stage of primary instability of the current-carrying superconducting state. The development of the instability leads to the formation of a chain of vortices in strips and helicoidal vortex lines in wires. The boundary of instability was obtained analytically. The nonlinear stage was investigated by simulations of the time-dependent generalized Ginzburg-Landau equation.Comment: REVTeX 3.0, 12 pages, 5Postscript figures (uuencoded). Accepted for Phys. Rev.

Absence of the zero bias peak in vortex tunneling spectra of high temperature superconductors?

The c-axis tunneling matrix of high-Tc superconductors is shown to depend strongly on the in-plane momentum of electrons and vanish along the four nodal lines of the d(x^2-y^2)-wave energy gap. This anisotropic tunneling matrix suppresses completely the contribution of the most extended quasiparticles in the vortex core to the c-axis tunneling current and leads to a spectrum similar to that of a nodeless superconductor. Our results give a natural explanation of the absence of the zero bias peak as well as other features observed in the vortex tunneling spectra of high-Tc cuprates.Comment: 4 pages 3 figures, minor corrections, to appear in Phys Rev

Vortex in a d-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field H_{c1}\ltsim H\ll H_{c2} from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.Comment: 20 RevTEX pages, 6 EPS figures; considerably expanded versio

Interplay of disorder and magnetic field in the superconducting vortex state

We calculate the density of states of an inhomogeneous superconductor in a magnetic field where the positions of vortices are distributed completely at random. We consider both the cases of s-wave and d-wave pairing. For both pairing symmetries either the presence of disorder or increasing the density of vortices enhances the low energy density of states. In the s-wave case the gap is filled and the density of states is a power law at low energies. In the d-wave case the density of states is finite at zero energy and it rises linearly at very low energies in the Dirac isotropic case (\alpha_D=t/\Delta_0=1, where t is the hopping integral and \Delta_0 is the amplitude of the order parameter). For slightly higher energies the density of states crosses over to a quadratic behavior. As the Dirac anisotropy increases (as \Delta_0 decreases with respect to the hopping term) the linear region decreases in width. Neglecting this small region the density of states interpolates between quadratic and back to linear as \alpha_D increases. The low energy states are strongly peaked near the vortex cores.Comment: 12 REVTeX pages, 15 figure

Tracking Alzheimer's disease

Population-based brain mapping provides great insight into the trajectory of aging and dementia, as well as brain changes that normally occur over the human life span. We describe three novel brain mapping techniques, cortical thickness mapping, tensor-based morphometry (TBM), and hippocampal surface modeling, which offer enormous power for measuring disease progression in drug trials, and shed light on the neuroscience of brain degeneration in Alzheimer's disease (AD) and mild cognitive impairment (MCI). We report the first time-lapse maps of cortical atrophy spreading dynamically in the living brain, based on averaging data from populations of subjects with Alzheimer's disease and normal subjects imaged longitudinally with MRI. These dynamic sequences show a rapidly advancing wave of cortical atrophy sweeping from limbic and temporal cortices into higher-order association and ultimately primary sensorimotor areas, in a pattern that correlates with cognitive decline. A complementary technique, TBM, reveals the 3D profile of atrophic rates, at each point in the brain. A third technique, hippocampal surface modeling, plots the profile of shape alterations across the hippocampal surface. The three techniques provide moderate to highly automated analyses of images, have been validated on hundreds of scans, and are sensitive to clinically relevant changes in individual patients and groups undergoing different drug treatments. We compare time-lapse maps of AD, MCI, and other dementias, correlate these changes with cognition, and relate them to similar time-lapse maps of childhood development, schizophrenia, and HIV-associated brain degeneration. Strengths and weaknesses of these different imaging measures for basic neuroscience and drug trials are discussed