Josephson Effect for Superconductors Lacking Time-Reversal and Inversion Symmetries

Abstract

Because of the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave (or s) order parameter must exist. If time reversal is also violated, an allowed invariant is the product of the d wave (or s wave), p wave, and an appropriately directed current. We show that this leads to a new and remarkable property of the Josephson current for tunneling into a s-wave superconductor along the direction parallel to the axis of the p-wave component. These ideas are applied to the heavy-fermion compounds which lack center of inversion due to crystalline symmetry, as well as time-reversal symmetry, such as CePt 3 Si. They also apply to the superconducting state of the cuprates in the pseudogap region of the phase diagram where in the normal phase some experiments have detected a time-reversal and inversion symmetry broken phase. . These broken symmetries are expected to continue into the superconducting state, as indeed found in the experiments [2,4]. This should then also affect the symmetry of superconductivity [5,6].Some heavy-fermion superconductors such as CePt 3 Si lack center of inversion in their crystal structure and similar superconducting states are expected for them [7,8]. CePt 3 Si is noncentrosymmetric, antiferromagnetic below 2.2 K, and superconducting below 0.75 K. There is an ongoing debate about its order parameter symmetry [7,9], and the possibility of mixed spin-triplet and spin-singlet pairing has been suggested. Thermal conductivity measurements have demonstrated the existence of line nodes [10]. The relatively high value of H c2 (5 T) (above the Pauli-Clogston limit) seems to indicate a spin-triplet superconductor.Here we will show that the Josephson effect between a superconductor breaking inversion symmetry and timereversal symmetry and a conventional s-wave superconductor has a distinct signature from conventional Josephson effect. The clear observation of such effects will further substantiate the nature of the pseudogap phase for the cuprates and the nature of superconductivity in the relevant heavy-fermion compounds.Quite generally, if time-reversal and inversion symmetry are broken, a term in the free-energy of the form ( 1) is allowed. d is the dominant ''d-wave'' superconducting order parameter, px is a ''p-wave'' order parameter, and the coefficient is proportional to the order parameter associated to the symmetry breaking in the normal phase (for example, the crystal structure lacking center of inversion [7] or the spontaneous current loops [1] in cuprates). x corresponds to the (110) direction or the 1 10 direction depending on the domain for the cuprates, and to the c axis for CePt 3 Si. (We have introduced i explicitly in the coefficient so that is real.) In this case a superconducting state violating time-reversal and inversion symmetry and consistent with the proposed normal state is of the generic form d xy i 0 p x;y in zero magnetic field. 0 =2 d , where the leading term in the free energy for the d-wave component is d j d j 2 . Suc...

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