Influence of Stationary Charge Imbalance on Shapiro Step Features

Influence of stationary charge imbalance on Shapiro step features Author: Kulikov K.V. Co-authors: Nashaat M., Shukrinov Yu.M. Dubna, Russia 6 December 2019

Noneauilibrium effects Charge imbalance The injection of quasiparticles into the superconducting layer create electron- hole imbalance in it S N The shift of the chemical potential of a superconducting condensate from its equilibrium value appears The shift of the chemical potential can be expressed in terms of the invariant potential which is zero in the equilibrium state o Artemenko S. and Kobelkov A. Phys. Rev. Lett., 78, 3551 (1997). o D. A. Ryndyk, Phys. Rev. Lett., 80, 3376 (1998). o Shukrinov Yu. M. and Mahfouzi F., Physica C, 460, 1303 (2007). o Keller J. and Ryndyk D. A., Phys. Rev. B, 71 (2005) 054507. o Rother S., Koval Y., M uller P., Kleiner R., Ryndyk D. A., Keller J. and Helm C., Phys. Rev. B, 67 (2003) 024510. 2

System of coupled JJ D. A. Ryndyk, Phys. Rev. Lett. 80, (1998), 3376- 3379 S. N. Artemenko and A. G. Kobelkov, Phys. Rev. Lett. 78, (1997) 3551 Yu. M. Shukrinov, M. Nashaat, K. V. Kulikov, R. Dawood, H. El Samman and Th. M. El Sherbini, Europhisics Letters 115, 20003 (2016). D. A. Ryndyk, J. Keller and C. Helm, J. Phys.: Condens. Matter, 14, 815, (2002) o o o o In the nonequilibrium mode, the usual Josephson relation is violated and instead a generalized Josephson relation appears Using the expression for the charge density and the continuity equation, one can write equation for the charge imbalance potential o Yu. M. Shukrinov, F. Mahfouzi, and P. Seidel, Physica C: Superconductivity 449, 62 (2006). o Yu. M. Shukrinov, and F. Mahfouzi, J. Phys.: Conf. Ser. 43, 1 (2006). 3

Charge imbalance in the system of IJJ o D. A. Ryndyk, J. Keller and C. Helm, J. Phys.: Condens. Matter, 14, 815, (2002) We use normalized equation for current to calculate phase dynamics In parallel, at each time step we use normalized kinetic equations with nonperiodic boundary conditions to calculate nonequilibrium potentials Then we calculate voltage across the JJs by means of normalized Josephson relation with non periodic boundary condition K. V. Kulikov, M. Nashaat and Yu. M. Shukrinov, EPL, 127 (2019) 67004 4

CVC of IJJ at nonequilibrium condition The presence of nonequilibrium potential gives a non zero voltage at each current step. So, the finite slope appears on the IV- characteristics in the superconducting state. Charge imbalance potential has nonzero value in the S-layers when all JJs are in the R-state. Important fact here is that the presence of the charge imbalance in R-state gives a shift of the phase derivative of JJs. K. V. Kulikov, M. Nashaat and Yu. M. Shukrinov, EPL, 127 (2019) 67004 5

CVC of IJJ at nonequilibrium condition For the fixed value of current, the Josephson frequency of the first and last JJs are smaller than in the middle junctions. Nonequilibrium frequency of oscillations in the JJs. potential decreases the The minimums of Josephson frequency is in the JJs at the edges of the stack, since there is a connection to normal leads. The distribution of the Josephson frequency along the stack depends on coupling between the junctions and the value of nonequilibrium parameter. K. V. Kulikov, M. Nashaat and Yu. M. Shukrinov, EPL, 127 (2019) 67004 6

Shapiro step at nonequilibrium condition The Shapiro step demonstrate a finite slope of the step, which appears under the influence of charge imbalance potential. The nonequilibrium parameter and has a maximum in the first and last JJs, decreasing in the middle of the stack. o Yu. M. Shukrinov, M. Nashaat, K. V. Kulikov, R. Dawood, H. El Samman and Th. M. El Sherbini, Europhisics Letters 115, 20003 (2016). values of the slope depends on the Small spikes of voltage appear on the IVC below and above the Shapiro step. Those spikes appear due to the fact that JJs in the stack switched nonsimultaneously to the locked regime. Junctions in the middle of the stack switched to the locked regime at a smaller current. K. V. Kulikov, M. Nashaat and Yu. M. Shukrinov, EPL, 127 (2019) 67004 7

Shapiro step on internal branch It was shown that Shapiro step shifts down when the first or last JJ is in the resistive state in comparison with the position of Shapiro step where one of the middle JJs is in the resistive state. o S. Rother, Y. Koval, P. Muller, R. Kleiner, D. A. Ryndyk, J. Keller and C. Helm, PRB, 67, 024510 (2003) o D. A. Ryndyk, J. Keller and C. Helm, J. Phys.: Condens. Matter, 14, 815, (2002) Shapiro step shifts down when first JJ is in R- state. This effect is in a perfect agreement with the experimental results. Furthermore, Shapiro steps demonstrate a finite slope due to the difference of the nonequilibrium potentials on the opposite edges of the step. We note, that it is impossible to obtained the slope of Shapiro step in case of voltage bias JJs. K. V. Kulikov, M. Nashaat and Yu. M. Shukrinov, EPL, 127 (2019) 67004 8

Summary o We have investigated the effect of the stationary charge imbalance on the system of coupled JJs. The main result of this study is that nonzero charge imbalance in the R- state leads to a decrease of the Josephson frequencies in the JJs of the stack. o The difference in Josephson frequencies leads to the nonuniform switch of junctions to the Shapiro step regime and appearance of voltage spikes on the IV-characteristics of the stack. o We have shown that stationary charge imbalance brings to the slope of the Shapiro step. Such slope can also be seen on the internal branch step in the current bias setup. o The stationary charge imbalance shifts the Shapiro step from the canonical position Thank you for attention. 9