A Coherent RC Circuit

We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, M. B\"{u}ttiker, H. Thomas and A. Pr\^{e}tre first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the capacitor and a constant charge relaxation resistance value equal to half of the resistance quantum h/2e^2, when a single mode is transmitted between the capacitance and a reservoir. By applying a microwave excitation to a gate located on top of a coherent submicronic quantum dot that is coupled to a reservoir, we validate this theoretical prediction on the ac conductance of the quantum RC circuit. Our study demonstrates that the ac conductance is directly related to the dwell time of electrons in the capacitor. Thereby, we observed a counterintuitive behavior of a quantum origin: as the transmission of the single conducting mode decreases, the resistance of the quantum RC circuit remains constant while the capacitance oscillates.Comment: 30 page

rf-studies of vortex dynamics in isotropic type-II superconductors

We have measured the surface impedance of thick superconductors in the mixed state over a broad 2 kHz - 20 MHz frequency range. The depinning cross-over is observed; but it is much broader than expected from classical theories of pinning. A striking result is the existence of size effects which invalidate the common interpretation of the low-frequency surface inductance in terms of a single penetration depth. Instead, a two-mode description of vortex dynamics, assuming free vortex flow in the bulk and surface pinning, accounts quantitatively for the spectrum of the complex apparent penetration depth.Comment: 20 pages, 6 figures, 28 reference

Depinning transition in type-II superconductors

The surface impedance Z(f) of conventional isotropic materials has been carefully measured for frequencies f ranging from 1 kHz to 3 MHz, allowing a detailed investigation of the depinning transition. Our results exhibit the irrelevance of classical ideas to the dynamics of vortex pinning. We propose a new picture, where the linear ac response is entirely governed by disordered boundary conditions of a rough surface, whereas in the bulk vortices respond freely. The universal law for Z(f) thus predicted is in remarkable agreement with experiment, and tentatively applies to microwave data in YBaCuO films.Comment: 4 pages, 4 figures, 14 reference

Dirac fermion reflector by ballistic graphene sawtooth-shaped npn junctions

We have realized a Dirac fermion reflector in graphene by controlling the ballistic carrier trajectory in a sawtooth-shaped npn junction. When the carrier density in the inner p-region is much larger than that in the outer n-regions, the first straight np interface works as a collimator and the collimated ballistic carriers can be totally reflected at the second zigzag pn interface. We observed clear resistance enhancement around the np+n regime, which is in good agreement with the numerical simulation. The tunable reflectance of ballistic carriers could be an elementary and important step for realizing ultrahigh-mobility graphene field effect transistors utilizing Dirac fermion optics in the near future

Longitudinal and transverse noise in a moving Vortex Lattice

We have studied the longitudinal and the transverse velocity fluctuations of a moving vortex lattice (VL) driven by a transport current. They exhibit both the same broad spectrum and the same order of magnitude. These two components are insensitive to the velocity and to a small bulk perturbation. This means that no bulk averaging over the disorder and no VL crystallization are observed. This is consistently explained referring to a previously proposed noisy flow of surface current whose elementary fluctuator is measured isotropic.Comment: accepted for publication in Phys Rev

A high sensitivity ultra-low temperature RF conductance and noise measurement setup

We report on the realization of a high sensitivity RF noise measurement scheme to study small current fluctuations of mesoscopic systems at milliKelvin temperatures. The setup relies on the combination of an interferometric ampli- fication scheme and a quarter-wave impedance transformer, allowing the mea- surement of noise power spectral densities with GHz bandwith up to five orders of magnitude below the amplifier noise floor. We simultaneously measure the high frequency conductance of the sample by derivating a portion of the signal to a microwave homodyne detection. We describe the principle of the setup, as well as its implementation and calibration. Finally, we show that our setup allows to fully characterize a subnanosecond on-demand single electron source. More generally, its sensitivity and bandwith make it suitable for applications manipulating single charges at GHz frequencies.Comment: The following article has been submitted to Review of Scientific Instrument

Shot noise in carbon nanotube based Fabry-Perot interferometers

We report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interferences, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively. It allows to confirm the existence of two nearly degenerate orbitals. At resonance, the transmission of the nanotube approaches unity, and the nanotube becomes noiseless, as observed in quantum point contacts. In this weak backscattering regime, the dependence of the noise on the backscattering current is found weaker than expected, pointing either to electron-electron interactions or to weak decoherence

Violation of Kirchhoff's Laws for a Coherent RC Circuit

What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single mode conductor, the charge relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices

The relaxation time of a chiral quantum R-L circuit

We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the c cuit