Shapiro Step Response of Intrinsic Josephson Junctions With High Critical Currents of ${({\rm Bi}_{1-{\rm x}}{\rm Pb}_{\rm x})}_{2}{\rm Sr}_{2}{\rm CaCu}_{2}{\rm O}_{\rm y}$

Abstract

We have studied the response of intrinsic Josephson junctions (IJJs) in cross-shaped samples of (Bi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Pb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CaCu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> (x=0.15) with high critical currents <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ic</i> at 4.2 K to injection of microwave with frequencies <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rf</sub> of 2-20 GHz. At the early stage of measurements Josephson vortex flow is induced in the IJJs by supplying high currents to them. After that, by injection of microwave power <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> to them clear constant voltage steps are successfully observed on their current-voltage characteristics, although their plasma frequency <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pl</sub> is much higher than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rf</sub> and they are not resistively shunted. The constant voltage steps appear so as to satisfy the Josephson frequency-voltage relation and behave like Shapiro steps depending on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> . Such behavior of steps is well reproduced by numerical simulations on Shapiro step response of JJs with shunt resistivity which is equal to the Josephson-vortex flow resistivity under microwave injection. Consequently, the observed constant voltage steps may be Shapiro steps out of the IJJs with the Josephson-vortex flow resistivity.