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Journal of Applied Physics

Current-voltage characteristics of unbalanced superconducting Wheatstone bridges

Marc M. Cahay, G. Qian, Rohit C. Kothari

Published Aug 15, 1995• 1 citation
Publisher

Abstract

We compute the current-voltage characteristics of unbalanced superconducting Wheatstone bridges biased with constant and radio frequency current sources. An analytical expression for the critical supercurrent at which a nonzero voltage appears across the transverse junction of the bridge is derived. Analytical expressions of the first three Shapiro steps are also given and found to be in good agreement with numerical simulations.

DOI
10.1063/1.360117

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We compute the current-voltage characteristics of unbalanced superconducting Wheatstone bridges biased with constant and radio frequency current sources. An analytical expression for the critical supercurrent at which a nonzero voltage appears across the transverse junction of the bridge is derived. Analytical expressions of the first three Shapiro steps are also given and found to be in good agreement with numerical simulations.
We study the current-voltage characteristics of a superconducting Wheatstone bridge in the presence of radio frequency current sources. Besides the regular integer Shapiro steps in the current-voltage characteristics observed when the voltage is measured between the input and output leads of the dc biasing current, we also found additional integer steps in the transverse voltage for large value of the dc biasing current. An explanation for these steps is given in terms of competing circulating currents in the bridge.
Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.
Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.