Coulomb Blockade of a Noisy Metallic Box: A Realization of Bose-Fermi Kondo Models

We focus on a metallic quantum dot coupled to a reservoir of electrons through a single-mode point contact and capacitively connected to a back gate, by including that the gate voltage can exhibit noise; this will occur when connecting the gate lead to a transmission line with a finite impedance. The voltage fluctuations at the back gate can be described through a Caldeira-Leggett model of harmonic oscillators. For weak tunneling between the lead and the dot, exploiting the anisotropic Bose-Fermi spin model, we show that zero-point fluctuations of the environment can markedly alter the Matveev Kondo fixed point leading to an amplification of the charge quantization phenomenon.

Figure 1

Circuit diagram of the metallic dot coupled to a bulk lead and subject to a fluctuating back-gate voltage $V_g+\delta V_g(t)$. The circuit is supposed to exhibit an Ohmic resistance $R=Z(\omega =0)$. We incorporate the finite resistance in a Hamiltonian fashion, through a long dissipative transmission line with capacitance $C_t$ and inductance $L$: $R=(L/C_t{)}^{1/2}$.

Figure 2

Average dot’s charge $⟨Q⟩$ versus the rescaled voltage $N=V_g{C}_g/e$ for weak tunneling $(|t|\rho )\ll 1$ and in the case of a single-mode spin-polarized point contact. When $R$ will exceed $R_c[|t|\rho ]\approx 4|t|\rho R_K/\nu$, we predict the restoration of perfect Coulomb steps [14]. Inset: Evolution of the Coulomb blockade oscillations for $R=0$ and various dot-lead couplings.