Abstract:
The response of superconducting aluminum to electromagnetic radiation is investigated in a broad frequency (45 MHz to 40 GHz) and temperature range ($T>T_c/2$), by measuring the complex conductivity. While the imaginary part probes the superfluid density (Cooper-pairs), the real part monitors the opening of the superconducting energy gap and -- most important here -- the zero-frequency quasi-particle response. Varying the mean free path gives some insight into the dynamics, scattering and coherence effects of the quasi-particles in the superconducting state.

Abstract:
We present a method to measure the absolute surface resistance of conductive samples at a set of GHz frequencies with superconducting lead stripline resonators at temperatures 1- 6K. The stripline structure can easily be applied for bulk samples and allows direct calculation of the surface resistance without the requirement of additional calibration measurements or sample reference points. We further describe a correction method to reduce experimental background on high-Q resonance modes by exploiting TEM-properties of the external cabling. We then show applications of this method to the reference materials gold, tantalum, and tin, which include the anomalous skin effect and conventional superconductivity. Furthermore, we extract the complex optical conductivity for an all-lead stripline resonator to find a coherence peak and the superconducting gap of lead.

Abstract:
Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, $Z_S(\omega,T)$, of single crystal La$_{0.8}$Sr$_{0.2}$MnO$_3$, as a function of frequency (0.045-45 GHz) and temperature (250-325 K). Through the dependence of the microwave surface impedance on the magnetic permeability, $\hat\mu(\omega,T)$, we have studied the local magnetic behavior of this material, and have extracted the spontaneous magnetization, $M_0(T)$, in {\em zero applied field}. The broadband nature of these measurements and the fact that no external field is applied to the material provide a unique opportunity to analyze the critical behavior of the spontaneous magnetization at temperatures very close to the ferromagnetic phase transition. We find a Curie temperature $T_C=305.5\pm 0.5$ K and scaling exponent $\beta=0.45\pm 0.05$, in agreement with the prediction of mean-field theory. We also discuss other recent determinations of the magnetization critical exponent in this and similar materials and show why our results are more definitive.

Abstract:
Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, $Z_S(\omega,T,H)$, of single crystal La$_{0.8}$Sr$_{0.2}$MnO$_3$, as a function of frequency (0.045-45 GHz), temperature (250-325 K), and magnetic field (0-1.9 kOe). The microwave surface impedance depends not only on the resistivity of the material, but also on the magnetic permeability, $\hat\mu(\omega,T,H)$, which gives rise to ferromagnetic resonance (FMR) and ferromagnetic anti-resonance (FMAR). The broadband nature of this experiment allows us to follow the FMR to low frequency and to deduce the behavior of both the local internal fields and the local magnetization in the sample.

Abstract:
Heavy-fermion compounds are characterized by electronic correlation effects at low energies which can directly be accessed with optical spectroscopy. Here we present detailed measurements of the frequency- and temperature-dependent conductivity of the heavy-fermion compound UPd2Al3 using broadband microwave spectroscopy in the frequency range 45 MHz to 40 GHz at temperatures down to 1.7 K. We observe the full Drude response with a relaxation time up to 50 ps, proving that the mass enhancement of the heavy charge carriers goes hand in hand with an enhancement of the relaxation time. We show that the relaxation rate as a function of temperature scales with the dc resistivity. We do not find any signs of a frequency-dependent relaxation rate within the addressed frequency range.

Abstract:
We have measured the frequency-dependent, complex impedance of thin metal strips in a broad range of microwave frequencies (45~MHz to 20~GHz). The spectra are in good agreement with theoretical predictions of an RCL model. The resistance, inductance, and capacitance, which govern the microwave response, depend on the strip width and thickness as well as on the strip and substrate materials. While the strip resistance scales inversely with the cross section, the inductance depends on the width of the strip, but not on the thickness (in the limit of small thickness).

Abstract:
We present simulations and analytic calculations of the electromagnetic microwave fields of coplanar waveguide (CPW) resonators in the vicinity of highly conducting metallic samples. The CPW structures are designed with the aim of investigating electron spin resonance (ESR) in metallic heavy-fermion systems, in particular YbRh$_2$Si$_2$, close to the quantum critical point. Utilizing CPW resonators for ESR experiments allows for studies at mK temperatures and a wide range of freely selectable frequencies. It is therefore of great interest to evaluate the performance of resonant CPW structures with nearby metallic samples. Here we study the microwave fields at the sample surface as a function of sample distance from the waveguide structure and analyze the implications of the sample on the performance of the resonator. The simulation results reveal an optimum sample distance for which the microwave magnetic fields at the sample are maximized and thus best suited for ESR studies.

Abstract:
The optical conductivity of heavy fermions can reveal fundamental properties of the charge carrier dynamics in these strongly correlated electron systems. Here we extend the conventional techniques of infrared optics on heavy fermions by measuring the transmission and phase shift of THz radiation that passes through a thin film of UNi2Al3, a material with hexagonal crystal structure. We deduce the optical conductivity in a previously not accessible frequency range, and furthermore we resolve the anisotropy of the optical response (parallel and perpendicular to the hexagonal planes). At frequencies around 7cm^-1, we find a strongly temperature-dependent and anisotropic optical conductivity that - surprisingly - roughly follows the dc behavior.

Abstract:
Electronic transport in highly doped but still insulating silicon at low temperatures is dominated by hopping between localized states; it serves as a model system of a disordered solid for which the electronic interaction can be investigated. We have studied the frequency-dependent conductivity of phosphorus-doped silicon in the THz frequency range (30 GHz to 3 THz) at low temperatures $T\geq 1.8$ K. The crossover in the optical conductivity from a linear to a quadratic frequency dependence as predicted by Efros and Shklovskii is observed qualitatively; however, the simple model does not lead to a quantitative agreement. Covering a large range of donor concentration, our temperature- and frequency-dependent investigations reveal that electronic correlation effects between the localized states play an important and complex role at low temperatures. In particular we find a super-linear frequency dependence of the conductivity that highlights the influence of the density of states, i.e. the Coulomb gap, on the optical conductivity. When approaching the metal-to-insulator transition by increasing doping concentration, the dielectric constant and the localization length exhibit critical behavior.

Abstract:
We have studied the optical properties of the heavy-fermion compound UNi2Al3 at frequencies between 100 GHz and 1 THz (3 cm^-1 and 35 cm^-1), temperatures between 2 K and 300 K, and magnetic fields up to 7 T. From the measured transmission and phaseshift of radiation passing through a thin film of UNi2Al3, we have directly determined the frequency dependence of the real and imaginary parts of the optical conductivity (or permittivity, respectively). At low temperatures the anisotropy of the optical conductivity along the a- and c-axes is about 1.5. The frequency dependence of the real part of the optical conductivity shows a maximum at low temperatures, around 3 cm^-1 for the a-axis and around 4.5 cm^-1 for the c-axis. This feature is visible already at 30 K, much higher than the Neel temperature of 4.6 K, and it does not depend on external magnetic fields as high as 7 T. We conclude that this feature is independent of the antiferromagnetic order for UNi2Al3, and this might also be the case for UPd2Al3 and UPt3, where a similar maximum in the optical conductivity was observed previously.