Low Temperature Transport in Tunnel Junction Arrays: Cascade Energy Relaxation

Abstract

Abstract. A theory of far-from-equilibrium transport in arrays of tunnel junctions is developed. We show that at low temperatures the energy relaxation ensuring tunneling current can become a cascade two-stage process. First, charge carriers lose their energy to a bosonic environment via non-phonon energy exchange. The role of such an environment can be taken by electromagnetic fluctuations or dipole excitations (electron-hole pairs). The environment, in its turn, relaxes the energy to the thermostat by means of phonon irradiation. We derive the current-voltage characteristics for the arrays and demonstrate that opening the energy gap in the spectrum of the environmental excitations completely suppresses the tunneling current. The consequences of the cascade relaxation in various physical systems are discussed.

Superinsulator–superconductor duality in two dimensions

“…Importantly, these excitations are the same particles that mediate the charge transfer. In the Cooper-pair insulators the dipoles are thus made up of the local excess (-2e) and local deficit (+2e) in the Cooper-pairs number and form the bosonic environment [11,12,160,163,164,165,166]. The important features of this dipole excitations environment is that the dipoles are generated in the process of tunnelling and that the dipole environment possesses an infinite number of degrees of freedom, and as such it efficiently takes away the energy from the tunnelling particles and plays the role of the thermostat itself.…”

“…In a two-dimensional array the dipole excitations form the two-dimensional Coulomb plasma, such a transition, and, respectively, the suppression of the relaxation rate takes place at the temperature of the charge BKT transition, T CBKT ≃Ē C , whereĒ C is the average charging energy of a single granule. Below this temperature charges and anti-charges get bound into the neutral CPD, the glassy state forms, the gap in the local density of states of the environmental excitation spectrum appears and the tunnelling current vanishes [11,12,164,165,166]. Although the detailed analytical calculations in two dimensions are not available at this point, the conjecture that the microscopic mechanisms of suppression of conductivity in one-and two dimensions is of the similar nature and are due to the appearance of the gap in the local density in the CPD excitation spectrum (i.e.…”

“…[12]. The tunnelling current in an array of superconducting granules can be written in the following form [169,164,166] I ∝ exp(−E/W) ,…”

Interplay of charge and heat transport in a nano-junction in the out-of-equilibrium cotunneling regime

“…General identities coupling the bosonic form-factors with and without tilde [see proof in Appendix B 2] are given by: Finally we define the form-factors n ω and N ω in Eqs. (18) n ω = 1 2…”

Universality and quantization of the power-to-heat ratio in nanogranular systems

“…In Ref. [29,41] one can also find the detailed rules how to build P (Ω) from the diagrams. One should take the products of the distribution functions shown in the diagram and integrate over all frequencies with prime except ω to get the corresponding contribution to P (ω).…”