Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor
arXiv:0709.3956 · doi:10.1103/PhysRevB.77.085312
Abstract
We present an analysis of the effect of dephasing on the single channel charge relaxation resistance of a mesoscopic capacitor in the linear low frequency regime. The capacitor consists of a cavity which is via a quantum point contact connected to an electron reservoir and Coulomb coupled to a gate. The capacitor is in a perpendicular high magnetic field such that only one (spin polarized) edge state is (partially) transmitted through the contact. In the coherent limit the charge relaxation resistance for a single channel contact is independent of the transmission probability of the contact and given by half a resistance quantum. The loss of coherence in the conductor is modeled by attaching to it a fictitious probe, which draws no net current. In the incoherent limit one could expect a charge relaxation resistance that is inversely proportional to the transmission probability of the quantum point contact. However, such a two terminal result requires that scattering is between two electron reservoirs which provide full inelastic relaxation. We find that dephasing of a single edge state in the cavity is not sufficient to generate an interface resistance. As a consequence the charge relaxation resistance is given by the sum of one constant interface resistance and the (original) Landauer resistance. The same result is obtained in the high temperature regime due to energy averaging over many occupied states in the cavity. Only for a large number of open dephasing channels, describing spatially homogenous dephasing in the cavity, do we recover the two terminal resistance, which is inversely proportional to the transmission probability of the QPC. We compare different dephasing models and discuss the relation of our results to a recent experiment.
arXiv comment10 pages, 8 figures
References in corpus (16)
- An On-Demand Coherent Single Electron Source
- Violation of Kirchhoff's Laws for a Coherent RC Circuit
- Quantum mechanical time-delay matrix in chaotic scattering
- Mesoscopic Charge Relaxation
- Mesoscopic Capacitors: A Statistical Analysis
- Semiclassical theory of shot noise in mesoscopic conductors
- Effect of inelastic scattering on parametric pumping
- Charge-Relaxation and Dwell Time in the fluctuating Admittance of a Chaotic Cavity
- Voltage and dephasing probes: a full counting statistics discussion
- Full counting statistics for voltage and dephasing probes
- Mesoscopic Capacitance Oscillations
- Noise and Measurement Efficiency of a Partially Coherent Mesoscopic Detector
- Shot noise of photon-excited electron-hole pairs in open quantum dots
- Conductances in normal and normal-superconductor structures
- Quantum pump driven fermionic Mach-Zehnder interferometer
- Voltage probe model of spin decay in a chaotic quantum dot, with applications to spin-flip noise and entanglement production
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- A Coherent RC Circuit
- Electron quantum optics in quantum Hall edge channels
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- Single-electron source: Adiabatic versus non-adiabatic emission
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- Electronic Hong-Ou-Mandel interferometry in two-dimensional topological insulators
- Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
- Fermi liquid approach to the quantum RC circuit: renormalization-group analysis of the Anderson and Coulomb blockade models
- Dynamical separation of bulk and edge transport in HgTe-based 2D topological insulators
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- Detection of the relaxation rates of an interacting quantum dot by a capacitively coupled sensor dot
- Semiclassical approach to the ac-conductance of chaotic cavities
- Non-local interference and Hong-Ou-Mandel collisions of single Bogoliubov quasiparticles
- Subnanosecond single electron source in the time-domain
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- Admittance of the SU(2) and SU(4) Anderson quantum RC circuits
- Full density matrix dynamics for large quantum systems: Interactions, Decoherence and Inelastic effects
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- From Anderson Localization to Mesoscopic Physics
- Phase-Coherent Dynamics of Quantum Devices With Local Interactions
- Role of coherence in resistance quantization
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- Statistical properties of electrochemical capacitance in disordered mesoscopic capacitors
- Quantum capacitance: a microscopic derivation
- Current deformation and quantum inductance in mesoscopic capacitors
- AC-Conductance through an Interacting Quantum Dot
- Unified linear response theory of quantum electronic circuits
- Charge relaxation resistance in the cotunneling regime of multi-channel Coulomb blockade: Violation of Korringa-Shiba relation
- Electron-photon coupling in Mesoscopic Quantum Electrodynamics