PHC Sakura Obergurgl 05062010 Phys Rev B 81

(PHC Sakura) Obergurgl 05/06/2010 (Phys. Rev. B 81, 153305 (2010)) Dynamic response of a mesoscopic capacitor in the presence of strong electron interactions Yuji Hamamoto*, Thibaut Jonckheere, Takeo Kato*, Thierry Martin *University of Tokyo, Kashiwa Phys. Rev. B 2010 Quantum RC circuit

Perspectives: quantum optics with electrons Hambury Brown and Twiss experiment with single electrons Hong –Ou-Mandel experiment with single electrons

Electrochemical capacitance Charge relaxation resistance Experimental verification, LPA ENS (Science 06)

OUTLINE This work: beyond the single electron model and its mean field generalizations How can one include Coulomb Blockade exactly How to account for the existence of electronic correlations in the reservoir ? (STRONG ELECTRONIC CORRELATIONS) • Strong coupling between dot and reservoir • Monte Carlo calculations • Weak coupling: instantons and scaling equations

MODEL Our setup: a semi-infinite Luttiger Liquid with a Barrier reservoir AC modulated gate Quantum point contact: backscattering Quantum dot

Full Hamiltonian: bosonization backscattering Gate voltage Charging energy

Linear response calculation: Kubo type formula (Matsubara formalism: imaginary time)

Perturbation theory No drastic modification of the relaxation resistance for the case of WEAK backscattering Monte Carlo data SCALE !

Dilute instanton gas description Scaling equations: Tunneling amplitude Tunneling strength Grows strong coupling between dot and reservoir Tunneling reduced RG flow towards weak coupling with specified charge.

Justifies Define low frequency resistance instead as: extrapolate

Coherent transport (Thermal time=1/T) Decoherence before charge relaxation is achieved Quantum dot acts like a « reservoir » Furusaki Matveev PRL 02

CONCLUSION: Phys. Rev. B 81, 153305 (2010) Relaxation resistance (renormalized by interactions) well defined, as long as interaction are sufficiently weak KT phase transition dot acts like an incoherent reservoir low frequency resitence exceeds RC time diverges, and the relaxation resistance cannot be defined anymore. Interactions in a 1 D mesoscopic capacitor drastically modify its finite frequency behavior compared to single electron model