| In conventional superconductors, the Cooper pairs are formed from quasiparticles with opposite momentum and spins because of the degeneracy of the quasiparticles under time reversal and inversion. The absence of any of these symmetries will have pronounced effects on superconducting states. Time reversal symmetry can be broken in the presence of magnetic impurities or by the application of a magnetic field. Similarly, the dislocation of crystal ions from their higher symmetric positions can cause broken inversion symmetry. We studied the effects of broken time reversal and inversion symmetries on unconventional superconductors, such as high temperature cuprates, Sr2RuO 4, and CePt3Si. In the cuprates, the superconducting state exists near the antiferromagnetic order. Sr2RuO4 and CePt3Si do not have spatial inversion, and the superconducting states coexist with magnetic order. In cuprates, the broken time reversal symmetry has been reported in the pseudogap phase which will effect the d-wave superconducting state of underdoped regime. On the basis of symmetry analysis we found that a mixture of spin-singlet and -triplet state, d+ip, which is shown to give rise to a helical superconducting phase. Consequences of this d+ip state on Josephson experiments are also discussed. Sr2RuO 4 is known to be another broken time reversal superconductor with spin triplet superconductivity. The widely believed superconducting state, the chiral p wave state, has been extensively studied through Ginzburg Landau theory, but the predictions for this state contradict some experimental observations like anisotropy in the upper critical field, and the existence of a second vortex state. We have formalize quasiclassical theory to find the origin of these contradictions, and also extended the theory to study other possible super-conducting states. Surprisingly, we find that a superconducting state corresponding to freely rotating in-plane d-vector explains the existing experimental results.;The recently discovered broken inversion superconductors, CePt3 Si, Li2Pt3B, and Li2Pd3B, provide a unique opportunity to study the role of broken parity in the superconducting state. In these superconductors, the magnetic field leads to a novel inhomogeneous superconducting state, a helical pairing. Although the origin of helical phase is quite different from the other inhomogeneous superconducting phase in the Pauli paramagnetic limit of upper critical field, the Fulde-Ferrel-Larkin-Ovichinikov (FFLO) state, the consequences of both phases are same: the enhancement of transition temperature as a function of magnetic field. Usually, FFLO states are quite unstable and hard to observe experimentally as they exist only in the low-temperature, and high-magnetic field regime, within the clean limit. Till now, only in CeCoIn5 is the unusual magnetic field enhanced superconducting state near the quantum critical point believed to be the FFLO state. We have studied the consequences of helical phases on a macroscopic and microscopic levels. We found that the existence of the superconducting helical phases in broken parity superconductors as high as T c(H=0) make it favorable over the FFLO state. |
