Effect of Impurity Scattering on the Nonlinear Microwave Response in High-Tc Superconductors

We theoretically investigate intermodulation distortion in high-Tc superconductors. We study the effect of nonmagnetic impurities on the real and imaginary parts of nonlinear conductivity. The nonlinear conductivity is proportional to the inverse of temperature owing to the dependence of the damping effect on energy, which arises from the phase shift deviating from the unitary limit. It is shown that the final-states interaction makes the real part predominant over the imaginary part. These effects have not been included in previous theories based on the two-fluid model, enabling a consistent explanation for the experiments with the rf and dc fields

Electronic theory for superconductivity in Sr2_2RuO4_4: triplet pairing due to spin-fluctuation exchange

Using a two-dimensional Hubbard Hamiltonian for the three electronic bands crossing the Fermi level in Sr$_2$RuO$_4$ we calculate the band structure and spin susceptibility $\chi({\bf q}, \omega)$ in quantitative agreement with nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) experiments. The susceptibility has two peaks at {\bf Q}$_i = (2\pi/3, 2\pi/3)$ due to the nesting Fermi surface properties and at {\bf q}$_i = (0.6\pi, 0)$ due to the tendency towards ferromagnetism. Applying spin-fluctuation exchange theory as in layered cuprates we determine from $\chi({\bf q}, \omega)$, electronic dispersions, and Fermi surface topology that superconductivity in Sr$_2$RuO$_4$ consists of triplet pairing. Combining the Fermi surface topology and the results for $\chi({\bf q}, \omega)$ we can exclude $s-$ and $d-$wave symmetry for the superconducting order parameter. Furthermore, within our analysis and approximations we find that $f$-wave symmetry is slightly favored over p-wave symmetry due to the nesting properties of the Fermi surface.Comment: 5 pages, 5 figures, misprints correcte

Topological Qubit Design and Leakage

We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Op- erations are performed on these by exchanging the anyons. One might argue that, in order to have as many simple single qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups which means they are valid for all anyon models. We also make some remarks on generalizations to other exchange groups.Comment: 13 pages, 3 figure

Microwave Absorption of Surface-State Electrons on Liquid 3^3He

We have investigated the intersubband transitions of surface state electrons (SSE) on liquid $^3$He induced by microwave radiation at temperatures from 1.1 K down to 0.01 K. Above 0.4 K, the transition linewidth is proportional to the density of $^3$He vapor atoms. This proportionality is explained well by Ando's theory, in which the linewidth is determined by the electron - vapor atom scattering. However, the linewidth is larger than the calculation by a factor of 2.1. This discrepancy strongly suggests that the theory underestimates the electron - vapor atom scattering rate. At lower temperatures, the absorption spectrum splits into several peaks. The multiple peak structure is partly attributed to the spatial inhomogeneity of the static holding electric field perpendicular to the electron sheet.Comment: 15 pages, 7 figures, submitted to J. Phys. Soc. Jp

Influence of gap structures to specific heat in oriented magnetic fields: Application to the orbital dependent superconductor, Sr2_2RuO4_4

We discuss influence of modulation of gap function and anisotropy of Fermi velocity to field angle dependences of upper critical field, $H_{c2}$, and specific heat, $C$, on the basis of the approximate analytic solution in the quasiclassical formalism. Using 4-fold modulation of the gap function and the Fermi velocity in the single-band model, we demonstrate field and temperature dependence of oscillatory amplitude of $H_{c2}$ and $C$. We apply the method to the effective two-band model to discuss the gap structure of Sr$_2$RuO$_4$, focusing on recent field angle-resolved experiments. It is shown that the gap structures with the intermediate magnitude of minima in $[100]$ direction for $\gamma$ band, and tiny minima of gaps in $[110]$ directions for $\alpha$ and $\beta$ bands give consistent behaviors with experiments. The interplay of the above two gaps also explains the anomalous temperature dependence of in-plane $H_{c2}$ anisotropy, where the opposite contribution from the passive $\alpha\beta$ band is pronounced near $T_c$.Comment: 7 pages, 11 figures in JPSJ forma

Low Frequency Nonlinear Magnetic Response of an Unconventional Superconductor

We consider an unconventional superconductor in a low frequency harmonic magnetic field. In the Meissner regime at low T a nonlinear magnetic response arises from quasiparticle excitations near minima in the energy gap. Various physical quantities then acquire higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependence of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small finite minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and the nonlinear torque. They both have separable temporal and angular dependences. In contrast, when there are quasinodes these quantities have more complicated and nonseparable field, temporal, and angular dependences. We illustrate this on the example of an s+id gap. We discuss how to perform measurements so as to maximize the nonlinear signal and how to investigate in detail the properties of the superconducting minima, thus determining the gap function symmetry.Comment: To appear in Phys Rev B. Ten figures, 13 text page

Renormalization of the elementary excitations in hole- and electron-doped cuprates due to spin fluctuations

Extending our previous studies we present results for the doping-, momentum-, frequency-, and temperature- dependence of the kink-like change of the quasiparticle velocity resulting from the coupling to spin fluctuations. In the nodal direction a kink is found in both the normal and superconducting state while in the antinodal direction a kink occurs only below $T_c$ due to the opening of the superconducting gap. A pronounced kink is obtained only for hole-doped, but not for electron-doped cuprates and is characteristically different from what is expected due to electron-phonon interaction. We further demonstrate that the kink structure is intimately connected to the resonance peak seen in inelastic neutron scattering. Our results suggest similar effects in other unconventional superconductors like ${Sr}_2{RuO}_4$.Comment: revised version, 12 pages, 19 figures. accepted for publication in PR