Dynamical Coulomb blockade of tunnel junctions driven by alternating voltages

Abstract

The theory of the dynamical Coulomb blockade is extended to tunneling elements driven by a time-dependent voltage. It is shown that for standard set-ups where an external voltage is applied to a tunnel junction via an impedance, time-dependent driving entails an excitation of the modes of the electromagnetic environment by the applied voltage. Previous approaches for ac driven circuits need to be extended to account for the driven bath modes. A unitary transformation involving also the variables of the electromagnetic environment is introduced which allows us to split off the time dependence from the Hamiltonian in the absence of tunneling. This greatly simplifies perturbation-theoretical calculations based on treating the tunneling Hamiltonian as a perturbation. In particular, the average current flowing in the leads of the tunnel junction is studied. Explicit results are given for the case of an applied voltage with a constant dc part and a sinusoidal ac part. The connection with standard dynamical Coulomb blockade theory for constant applied voltage is established. It is shown that an alternating voltage source reveals significant additional effects caused by the electromagnetic environment. The hallmark of the dynamical Coulomb blockade in ac driven devices is a suppression of higher harmonics of the current by the electromagnetic environment. The theory presented basically applies to all tunneling devices driven by alternating voltages.

Skyrmions Driven by Intrinsic Magnons

“…Note that the term ∼ J † q · G K J q gives rise to random forces which naturally emerge from the coupling of the skyrmion with the reservoir of magnon fluctuations. In addition, the semiclassical terms analyzed so far are of order O[N A S], while quantum terms originating from the determinant appearing in (28) are of order O[(N A S) 0 ] and are neglected under the assumption N A S 1. The Langevin equation for the skyrmion, including quantum dissipation under an external oscillating field is presented in a forthcoming work.…”

Current noise in tunnel junctions

“…We further note that the response of the average tunneling current in the presence of an applied dc voltage U to a small alternating voltage of frequency ω can be written as where is the admittance of the junction. This quantity can be determined from the expression for the average tunneling current in the presence of dc and ac voltages . As shown in the Appendix, one has where is the Kramers‐Kronig transform of the current voltage characteristic .…”

“…It is now convenient to introduce the polar decomposition of the transmission factor into modulus and phase . The imaginary part of the transmission factor then reads In terms of and , the result takes the form …”

RF Field-Driven Electron Tunneling through Mesoscale Junctions

“…Since it is beyond the scope of this experimental studies paper, a reader interested is referred to the detailed texts by Ingold and Nazarov [18] [20] and Schon [22]. Similarly, for incorporating impedance and environment effects, detailed theoretical treatments are described elsewhere [18] and [23].…”

“…(a) The symbol of a tunnel junction; (b) The schematic of a simple tunnel junction circuit biased by a precision dc current source; (c) Our implementation of a mesoscale copper tunnel junction with an ultra-low noise precision dc source and a very sensitive ultra-low noise femto-ampere TIA. Journal of Modern Physics Schὃn [22] and H. Grabert [23], after necessary modifications. Although any of those approaches could be modified and devised as per our model, we devise a simple model based on the studies due to Ingold and Nazarov [18].…”