Note on the Coulomb blockade of a weak tunnel junction with Nyquist noise: Conductance formula for a broad temperature range

Abstract

We revisit the Coulomb blockade of the tunnel junction with conductance much smaller than $e^2/\hslash$. We study the junction with capacitance $C$, embedded in an Ohmic electromagnetic environment modelled by a series resistance $R$ which produces the Nyquist noise. In the semiclassical limit the Nyquist noise charges the junction by a random charge with a Gaussian distribution. Assuming the Gaussian distribution, we derive analytically the temperature-dependent junction conductance $G(T)$ valid for temperatures $k_{B}T\gtrsim (R_K/2\pi R)E_c$ and resistances $R\gtrsim R_K$, where $R_K=h/e^2$ and $E_c=e^2/2C\text{is}$ the single-electron charging energy. Our analytical result shows the leading dependence $G(T)\propto e^{-E_c/4k_{B}T}$, so far believed to exist only if $(R_K/\pi R)E_c\ll k_{B}T\ll E_c$ and $R\gg R_K$. The validity of our result for $k_{B}T\gtrsim (R_K/2\pi R)E_c$ and $R\gtrsim R_K$ is confirmed by a good agreement with the numerical studies which do not assume the semiclassical limit, and by a reasonable agreement with experimental data for $R$ as low as $R_K$. Our result also reproduces various asymptotic formulae derived in the past. The factor of $1/4$ in the activation energy $E_c/4$ is due to the semiclassical Nyquist noise.

to be published in physica status solidi c (2017)

References in corpus (1)

• Effect of the electromagnetic environment on current fluctuations in driven tunnel junctions