Charge relaxation resistance in the cotunneling regime of multi-channel Coulomb blockade: Violation of Korringa-Shiba relation

Abstract

We study the low frequency admittance of a small metallic island coupled to a gate electrode and to a massive reservoir via a \emph{multi channel} tunnel junction. The ac current is caused by a slowly oscillating gate voltage. We focus on the regime of inelastic cotunneling in which the dissipation of energy (the real part of the admittance) is determined by two-electron tunneling with creation of electron-hole pairs on the island. We demonstrate that at finite temperatures but low frequencies the energy dissipation is ohmic whereas at zero temperature it is super-ohmic. We find that (i) the charge relaxation resistance (extracted from the real part of the admittance) is strongly temperature dependent, (ii) the imaginary and real parts of the admittance do not satisfy the Korringa-Shiba relation. At zero temperature the charge relaxation resistance vanishes in agreement with the recent zero temperature analysis [M. Filippone and C. Mora, Phys. Rev. B {\bf 86}, 125311 (2012) and P. Dutt, T. L. Schmidt, C. Mora, and K. Le Hur, Phys. Rev. B {\bf 87}, 155134 (2013)].

11 pages, 5 figures

References in corpus (9)

• Mesoscopic Charge Relaxation
• Quantum phase transitions in the Bose-Fermi Kondo model
• Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor
• Delayed currents and interaction effects in mesoscopic capacitors
• Fermi liquid approach to the quantum RC circuit: renormalization-group analysis of the Anderson and Coulomb blockade models
• Admittance and noise in an electrically driven nano-structure: Interplay between quantum coherence and statistics
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• Coulomb Blockade and Super Universality of the Theta-Angle
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Cited by in corpus (4)

• Cavity photons as a probe for charge relaxation resistance and photon emission in a quantum dot coupled to normal and superconducting continua
• Coulomb-blockade effect in nonlinear mesoscopic capacitors
• The Interacting Mesoscopic Capacitor Out of Equilibrium
• Phase-Coherent Dynamics of Quantum Devices With Local Interactions