Subharmonic Shapiro Steps and Assisted Tunneling in Superconducting Point Contacts

Abstract

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n)hωr/2e, where n, m are integer numbers and ωr is the radiation frequency. The subharmonic steps (n = 1) are a consequence of multiple Andreev reflections (MAR) and provide a signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs.Introduction.-Our understanding of the electronic transport through superconducting nanostructures has experienced a notable development in last few years [1]. Partly, this has been due to the appearance on scene of the metallic atomic-size contacts, which can be produced by means of scanning tunneling microscope and breakjunction techniques [2][3][4][5]. These nanowires have turned out to be ideal systems to test the modern transport theories in mesoscopic superconductors. Thus, for instance Scheer and coworkers [3] found a quantitative agreement between the measurements of the current-voltage characteristics of different atomic contacts and the predictions of the theory for a single-channel superconducting contact [6,7]. These experiments not only helped to clarify the structure of the subgap current in superconducting contacts, but also showed that the set of the transmission coefficients in an atomic-size contact is amenable to measurement. This possibility has recently allowed a set of experiments that confirm the theoretical predictions for transport properties like supercurrent [4] and noise [5]. From these combined theoretical and experimental efforts a coherent picture of transport in superconducting point contacts has emerged with multiple Andreev reflections (MAR) [8] as a central concept. However, in spite of these recent successes, one of the most remarkable predictions of MAR theory remains to be confirmed, namely the ac Josephson effect. The theory says that in a constant voltage biased superconducting point contact, the time-dependent current is given by I(t) = n I n e inω0t . This means that the occurrence of MARs gives rise to the appearance of alternating currents that oscillate not only with the Josephson frequency ω 0 = 2eV /h, V being the voltage, as in the case of tunnel junctions, but also with all its harmonics. So far there is no experimental evidence of the existence of such components.In this paper, we present a theoretical analysis of the current in a superconducting point contact under a microwave radiation. We show that the interplay between the ac Josephson current components and a microwave signal leads to the appearance of Shapiro steps at voltages V = (m/n)hω r /2e, where n, m are integer numbers and ω r is the frequency of the radiation. This means that in

Phase diffusion and fractional Shapiro steps in superconducting quantum point contacts

“…We further extend the analysis to a more general environment including two resistances and a finite capacitance. For the case of highly transmissive junctions, like atomic size contacts, the presence of higher harmonics in the current-phase relation leads to fractional Shapiro steps 3 .…”

“…3 within a fully microscopic approach in which an ideal voltage bias on the contact was assumed. However, a more realistic description of this phenomenon requires to take into account environmental effects, the most important being certainly the effect of phase diffusion caused by thermal noise in the circuit in which the contact is embedded.…”

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

“…Interestingly, in the regime of extremely strong driving, λ > λ 3 1, (and for finite friction) regular dynam- Sketched in (b) is the particle dynamics in the effective potential V eff (ϕ), see Eq. (6), corresponding to phase space orbits in the right panels of (a).…”

“…When this domain is approached, the dc-current through the JJ grows substantially in parallel with larger current variations depending on the driving amplitude. (iv) For extremely strong driving λ > λ 3 1 and finite friction (Sec. III C), the dynamics turns into a regular motion again with a large time scale separation between the motion happening within one of the local wells in V eff (t, ϕ) and global dynamics exploring V eff over a wide range of ϕ.…”

“…Accordingly, there has been a long tradition of studying non-linear phenomena in driven superconducting circuits, starting as early as the 1960s with the discovery of Shapiro steps 1 . While Shapiro-steps have remained a tool in exploring new directions in Josephson physics, for instance in atomic point contacts [2][3][4][5][6] , other nonlinear phenomena, like synchronization, have been investigated in arrays of JJs: as a test-bed for generic theory models to capture synchronization phenomena 7,8 , but as importantly with the prospect of applications as sources of more intense coherent radiation 9 , cf. also new developments using intrinsic arrays [10][11][12] .…”