Thermal decay of the Coulomb blockade oscillations

Abstract

We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature $T$ and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum, $T\ll E_C$, and thermal, $T\gg E_C$, fluctuations are considered, where $E_C$ is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings in [A. Furusaki and K. A. Matveev, Phys. Rev. B {\bf 52}, 16676 (1995)]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as $\sqrt{T/E_C}\exp (-{\pi }^{2}T/E_C)$, where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the non-locality of the quantum effects. Our results agree with the recent experiment [S. Jezouin {\em et al}., Nature {\bf 536}, 58 (2016)] in the whole range of the parameter $T/E_C$.

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Cited by in corpus (9)

• Dephasing in Mach-Zehnder interferometer by an Ohmic contact
• Thermal drag effect in quantum Hall circuits
• Current correlations of Cooper-pair tunneling into a quantum Hall system
• Current cross-correlations in a quantum Hall collider at filling factor two
• Quantum ammeter
• Tunneling into a finite Luttinger liquid coupled to noisy capacitive leads
• Quantum criticality in coupled hybrid metal-semiconductor islands
• Charge-conserving equilibration of quantum Hall edge states
• Multi-mode Coulomb blockade oscillations