We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that upper critical field for a field along the c-axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c-axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that to get good agreement between theory and recent experimental measurements of Hc2, this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order. PACS numbers:The recently discovered heavy fermion superconductor CePt 3 Si 1 has triggered many experimental and theoretical studies 2,3,4,5,6,7,8,9 . There are two features which have caused this attention: the absence of inversion symmetry; and the comparatively high upper critical magnetic field (H c2 ). Broken inversion symmetry (parity) has a pronounced effect on the quasiparticle states through the splitting of the two spin degenerate bands. This influences the superconducting phase, which usually relies on the formation of pairs of electrons in degenerate quasiparticle states with opposite momentum. The availability of such quasiparticle states is usually guaranteed by time reversal and inversion symmetries (parity) 10,11 . It is relatively easy to remove time reversal symmetry, e.g. by a magnetic field, and the physical consequences of this have been well studied. However, parity is not so straightforwardly manipulated by external fields. Superconductivity in materials without inversion center therefore provides a unique opportunity in this respect.The large H c2 ≈ 4T in CePt 3 Si 1,8 implies that the Zeeman splitting must be non-negligible below T c = 0.75K (the estimated paramagnetic limit is at H P ≈ 1.2 T). In a magnetic field, this superconductor has to form Cooper pairs under rather odd circumstances. In particular, it is no longer guaranteed that a state with momentum k at the Fermi surface has a degenerate partner at −k. The state k would rather pair with a degenerate state −k + q and in this way generate an inhomogeneous superconducting phase. We argue below that recent H c2 measurements 8 suggest that this is the case in CePt 3 Si. These measurements show that, while the upper critical field is basically isotropic close to T c , a small anisotropy appears at lower temperature 8 (H c c2 /H ab c2 = 1.18 at T = 0). The apparent absence of a paramagnetic limit in CePt 3 Si can be explained by lack of inversion symmetry even if the pairing has s-wave symmetry 2,12,13 . However, these works indicate that suppression of paramagnetism is very anisotropic and the application of this theory to CePt 3 Si would indicate no paramagnetic suppression for the field along the c-axis, but a suppression fo...

Due to the lack of both parity and time-reversal symmetries, the Rashba superconductors CePt 3 Si, CeRhSi 3 , and CeIrSi 3 , in the presence of a magnetic field, are unstable to helical ͑single plane wave͒ order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field-temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-q phase ͑loosely called a stripe phase͒, in which both the magnitude and the phase of the order parameter are spatially varying. We find the position of this helical to multiple-q phase transition. We further examine the density of states and identify features unique to the helical phase.

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Recently, Kaminski et al. have reported that time-reversal symmetry is broken in the pseudogap phase in the high-temperature superconducting material Bi 2 Sr 2 CaCu 2 O 2ϩ␦ ͑Bi-2212͒. Here we examine the role of translationally invariant broken time-reversal states on d x 2 Ϫy 2 superconductors. In particular, we determine the change in the superconducting order parameter structure. We find that the broken time-reversal pseudogap state that is consistent with the experiment of Kaminski et al. gives rise to a mixed singlet-triplet pairing dϩip phase. This dϩip state is shown to give rise to a helical superconducting phase. Consequences of this d ϩip state on Josephson experiments are discussed.

We have carried out a determination of the magnetic-field-temperature (H-T) phase diagram for realistic models of the high field superconducting state of tetragonal Sr2RuO4 with fields oriented in the basal plane. This is done by a variational solution of the Eilenberger equations. This has been carried for spin-triplet gap functions with a d-vector along the c-axis (the chiral p-wave state) and with a d-vector that can rotate easily in the basal plane. We find that, using gap functions that arise from a combination of nearest and next nearest neighbor interactions, the upper critical field can be approximately isotropic as the field is rotated in the basal plane. For the chiral dvector, we find that this theory generically predicts an additional phase transition in the vortex state. For a narrow range of parameters, the chiral d-vector gives rise to a tetracritical point in the H-T phase diagram. When this tetracritical point exists, the resulting phase diagram closely resembles the experimentally measured phase diagram for which two transitions are only observed in the high field regime. For the freely rotating in-plane d-vector, we also find that additional phase transition exists in the vortex phase. However, this phase transition disappears as the in-plane d-vector becomes weakly pinned along certain directions in the basal plane.