Superconducting Current-Phase Dependence in High-T_c Symmetrical Bicrystal Junctions

Abstract

The dependence of the superconducting current Is on the phase difference φ between the order parameters of the two superconductors forming a Josephson junction (current phase relation - CPR) determines dynamic parameters of the Josephson junctions (JJ) such as the Josephson inductance, the microwave impedance, the spectrum of the Josephson generation and so on. Calculations of Josephson circuits behaviour are usually made assuming ¹ a sinusoidal CPR I_s(φ)=I_csin φ (I_c is the critical current of the JJ). On other side the superconducting phase qubits for the quantum computing included Josephson junctions with double periodic (2 φ) CPR with minima at phase values φ=0. Pure sinusoidal CPR is observed in tunnel junctions between ordinary s-wave superconductors (SIS) over a wide range of temperatures². However, in JJ with direct (nontunnel) conductivity, like point contacts (ScS), a nearly sawtooth dependence of Is(φ) is observed at low temperature, which may be expressed in terms of Fourier components:

$$ {{\rm{I}}_{\rm{S}}}\left( \varphi \right) = {{\rm{I}}_{\rm{c}}}\sum {{\delta _n}\sin \left( {n\varphi } \right)} , $$

(1)

where n£1 and δ_n are the amplitudes of the Fourier components. The possible reason for the complex dependence of I_s(φ) is the contribution of multiple Andreev reflections to the current transport. For most types of JJs the Andreev’s levels are described by the formula²’3:

$$ {E_b} = \pm \Delta \surd \left( {1 - \overline D {{\sin }^2}\left( {{\varphi \mathord{\left/ {\vphantom {\varphi 2}} \right. \kern-\nulldelimiterspace} 2}} \right)} \right), $$

(2)

where Δ is the superconducting gap and ̄D is the barrier transparency.