Role of coherence in resistance quantization

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.Comment: 9 pages, 5 figure

Statistical theory of relaxation of high energy electrons in quantum Hall edge states

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm

Mesoscopic Charge Relaxation

We consider charge relaxation in the mesoscopic equivalent of an RC circuit. For a single-channel, spin-polarized contact, self-consistent scattering theory predicts a universal charge relaxation resistance equal to half a resistance quantum independent of the transmission properties of the contact. This prediction is in good agreement with recent experimental results. We use a tunneling Hamiltonian formalism and show in Hartree-Fock approximation, that at zero temperature the charge relaxation resistance is universal even in the presence of Coulomb blockade effects. We explore departures from universality as a function of temperature and magnetic field.Comment: 4 pages, 3 figure

Quantum capacitance: a microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.Comment: 7 fig

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio