General solution for the complex frequency shift in microwave measurements of thin films

Perturbation of a microwave cavity by a small sample with variable dielectric, magnetic, or conducting properties is considered. The complex frequency shift is derived in terms of a volume integral, or equivalently, in terms of a surface integral. These are used to obtain a general formula for thin films in the microwave electric field maximum. The complex frequency shift depends on the depolarization factor of the film and on its thickness in a nontrivial way. The previously known expressions for the complex frequency shift are shown to be good approximations of the present solution in the low and high conductivity limits. Our formula is applied to calculate the signal shapes in superconducting films of various geometric parameters and conductivities. It is shown that a diversity of signal shapes can result, and experimental support of those shapes is provided. The role of the dielectric substrate on which the thin film is grown is simply reduced to an asymmetry effect

Microwave response of thin niobium films under perpendicular static magnetic fields

The microwave response of high quality niobium films in a perpendicular static magnetic field has been investigated. The complex frequency shift was measured up to the upper critical fields. The data have been analyzed by the effective conductivity model for the type-II superconductors in the mixed state. This model is found to yield consistent results for the coherence lengths in high-kappa superconducting samples, and can be used with HTSC even at temperatures much below T_c. It is shown that for samples with high values of depinning frequency, one should measure both components of the complex frequency shift in order to determine the flow resistivity. The thick Nb film (160 nm) has low resistivity at 10 K, comparable to the best single crystals, and low kappa value. In contrast, the thinnest (10 nm) film has kappa ~ 9.5 and exhibits a high depinning frequency (~20 GHz). The upper critical field determined from microwave measurements is related to the radius of nonoverlaping vortices, and appears to be larger than the one determined by the transition to the normal state.Comment: 8 pages, 7 figures; submitted to PRB; measured rho_n; changes due to the referees' comments (abstract, conclusions, extended introduction

A matrix product solution for a nonequilibrium steady state of an XX chain

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from nearest neighbor z-z, are zero.Comment: 11 page

Pseudogap in the Optical Spectra of UPd_2Al_3

The in-plane optical conductivity of UPd_2Al_3 was measured at temperatures $2 {\rm K}<T<300$ K in the spectral range from 1 cm^{-1} to 40 cm^{-1} (0.14 meV to 5 meV). As the temperature decreases below 25 K a well pronounced pseudogap of 0.2 meV develops in the optical response. In addition we observe a narrow conductivity peak at zero frequency which at 2 K is less than 1 cm^{-1} wide but which contains only a fraction of the delocalized carriers. The gap in the electronic excitations might be an inherent feature of the heavy fermioin ground state.Comment: 4 pages, 4 figures (submitted to Phys. Rev. Lett.

A Transport and Microwave Study of Superconducting and Magnetic RuSr2EuCu2O8

We have performed susceptibility, thermopower, dc resistance and microwave measurements on RuSr2EuCu2O8. This compound has recently been shown to display the coexistence of both superconducting and magnetic order. We find clear evidence of changes in the dc and microwave resistance near the magnetic ordering temperature (132 K). The intergranular effects were separated from the intragranular effects by performing microwave measurements on a sintered ceramic sample as well as on a powder sample dispersed in an epoxy resin. We show that the data can be interpreted in terms of the normal-state resistivity being dominated by the CuO2 layers with exchange coupling to the Ru moments in the RuO2 layers. Furthermore, most of the normal-state semiconductor-like upturn in the microwave resistance is found to arise from intergranular transport. The data in the superconducting state can be consistently interpreted in terms of intergranular weak-links and an intragranular spontaneous vortex phase due to the ferromagnetic component of the magnetization arising from the RuO2 planes.Comment: 20 pages including 6 figures in pdf format. To be published in Phys. Rev.