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 University of Tokyo, Kashiwa

Obergurgl 05/06/2010 (Phys. Rev. B 81, 153305 (2010))

(PHC Sakura)

Phys. Rev. B 2010Quantum 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)

MODELOur setup: a semi-infinite Luttiger Liquid with a Barrier

reservoir

Quantum point contact: backscattering

Quantum dot

AC modulated gate

Full Hamiltonian: bosonization

Charging energy

backscattering

Gate voltage

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

No drastic modification of the relaxation resistance for the case of WEAK backscattering

SCALE !

Perturbation theory

Monte Carlo data

Scaling equations:

Tunneling strengthGrows

Tunneling reduced RG flow towards weak coupling with specified charge.

strong coupling between dot and reservoir

Tunneling amplitude

Dilute instanton gas description

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 PRL02

CONCLUSION:

Relaxation resistance (renormalized by interactions) well defined, as longas interaction are sufficiently weak

KT phase transitiondot acts like an incoherent reservoirlow frequency resitence exceedsRC time diverges, and the relaxation resistancecannot be defined anymore.

Interactions in a 1D mesoscopic capacitor drastically modify its finite frequency behavior compared to single electron model

Phys. Rev. B 81, 153305 (2010)