Helical edge states exist in the mixed spin-singlet and -triplet phase of a noncentrosymmetric superconductor (NCSS) when the pair amplitude (PA) in the negative helicity band, $Δ_-$, is smaller than the PA in the positive helicity band, $Δ_+$, i.e., when the PA in the triplet component is more than the same in the singlet component. We numerically determine energies of these edge states as a function of $γ= Δ_-/Δ_+$. The presence of these edge states is reflected in the tunneling process from a normal metal to an NCSS across a bias energy $eV$: (i) Angle resolved spin conductance (SC) obeying the symmetry $g_s(ϕ) =-g_s(-ϕ)$ shows peaks when the bias energy equals the available quasiparticle edge state energy provided $|eV| \lesssim Δ_-$. (ii) The total SC, $G_s$, is zero but modulates with $eV$ for finite magnetic field $H$. (iii) The zero bias peaks of $G_s$ and total charge conductance, $G_c$, at finite $H$ split into two at finite $eV$ for moderate $H$. (iv) At zero bias, $G_c$ and $G_s$ increase with $H$ and show peaks at $|H|\sim γH_0$ where $H_0$ is a characteristic field.
We consider the role of magnetic fields on the broken inversion superconductor CePt_3Si. 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 H_{c2}, this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particul…
Domains in non-centrosymmetric materials represent regions of different crystal structure and spin-orbit coupling. Twin boundaries separating such domains display unusual properties in non-centrosymmetric superconductors (NCS), where magneto-electric effects influence the local lower and upper critical magnetic fields. As a model system, we investigate NCS with tetragonal crystal structure and Rashba spin-orbit coupling (RSOC), and with twin boundaries parallel to their basal planes. There, we report that there are two types of such twin boundaries which separate domains of opposite RSOC. In a…
We study non-centrosymmetric topological superconductivity in correlated doped quantum spin-Hall insulators (QSHI) on honeycomb lattice without inversion symmetry where the intrinsic (Kane-Mele) and Rashba spin-orbit couplings can in general exist. We explore the generic topologically non-trivial superconducting phase diagram of the model system. Over a certain parameter space, the parity-mixing superconducting state with co-existing spin-singlet $d$+$id$ and spin-triplet $p$+$ip$-wave pairing is found. On a zigzag nanoribbon, the parity-mixing superconducting state shows co-existing helical a…
We study the spin transport properties of the non-centrosymmetric superconductor with time-reversal-symmetry where spin-triplet $(p_{x} \pm i p_{y})$-wave and spin-singlet s-wave pair potential can mix each other. We show that when the amplitude of $(p_{x} \pm ip_{y})$-wave pair potential is larger than that of s-wave one, the superconducting state belongs to the topologically nontrivial class analogous to the quantum spin Hall system, and the resulting helical edge modes as Andreev bound states are topologically protected. We find that the incident angle dependent spin polarized current flows…
Tunneling spectroscopy at surfaces of unconventional superconductors has proven an invaluable tool for obtaining information about the pairing symmetry. It is known that mid gap Andreev bound states manifest itself as a zero bias conductance peak in tunneling spectroscopy. The zero bias conductance peak is a signature for a non-trivial pair potential that exhibits different signs on different regions of the Fermi surface. Here, we review recent theoretical results on the spectrum of Andreev bound states near interfaces and surfaces in non-centrosymmetric superconductors. We introduce a theoret…
We study edge states of non-centrosymmetric superconductors where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spin-orbit coupling. For dxy-wave pairing, the obtained Andreev bound state has an anomalous dispersion as compared to conventional helical edge modes. A unique topologically protected time-reversal invariant Majorana fermion appears at the edge. The charge conductance in the non-centrosymmetric superconductor junctions reflects the anomalous structures of the dispersions, particularly the time-reversal invariant Majorana fermion is manifested as a zero bia…
An SNN-junction in which the superconducting potential is a mixture between s-wave and p-wave potentials is investigated using the Usadel equation equipped with Tanaka-Nazarov boundary conditions. The article provides several ways to distinguish between s + chiral and s + helical p-wave superconductors and a way to determine whether a superconductor has a mixed pair potential. Thus, it is of great importance in the determination of the pair potential of superconductors. It is shown that the different spin sectors satisfy independent equations and can thus be calculated separately even if the d…
We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4Pi-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that signatures of this effect can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestatio…
Non-centrosymmetric superconductors exhibit the magnetoelectric effect which manifests itself in the appearance of the magnetic spin polarization in response to a dissipationless electric current (supercurrent). While much attention has been dedicated to the thermodynamic version of this phenomenon (Edelstein effect), non-equilibrium transport magnetoelectric effects have not been explored yet. We propose the magnetoelectric Andreev effect (MAE) which consists in the generation of spin-polarized triplet Andreev conductance by an electric supercurrent. The MAE stems from the spin polarization o…
Vortex lattice structures to occur in Rashba non-centrosymmetric superconductors under a magnetic field parallel to the basal plane are studied by assuming a singlet Cooper pairing and taking account of both the paramagnetic and orbital depairings. A vortex lattice of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type with modulation perpendicular to the field is expected to occur in the limit of vanishing ${\tilde η}$, where ${\tilde η}$ is the spin-orbit coupling {\it normalized} by Fermi energy. As ${\tilde η}$ increases, however, this state tends to be replaced by another new vortex lattice with…
Motivated by recent experiments on FeTe$_{1-x}$Se$_{x}$, we construct an explicit minimal model of an iron-based superconductor with band inversion at the $Z$ point and non-topological bulk $s_{\pm}$ pairing. While there has been considerable interest in Majorana zero modes localized at vortices in such systems, we find that our model - without any vortices - intrinsically supports 1D helical Majorana modes localized at the hinges between (001) and (100) or (010) surfaces, suggesting that this is a viable platform for observing "higher-order" topological superconductivity. We provide a general…
Superconductivity and magnetism in the non-centrosymmetric heavy fermion compound CePt$_3$Si and related materials are theoretically investigated. Based on the randam phase approximation (RPA) analysis for the extended Hubbard model we describe the helical spin fluctuation induced by the Rashba-type anti-symmetric spin-orbit coupling and identify the two stable superconducting phases with either dominantly p-wave ($s$ + $P$-wave) or d-wave ($p$ + $D$ + $f$-wave) symmetry. The influcnce of the coexistent anti-ferromagnetic order is investigated in both states. The SC order parameter, quasiparti…
The paramagnetic properties in non-centrosymmetric superconductors with and without antiferromagnetic (AFM) order are investigated with focus on the heavy Fermion superconductors, CePt_3Si, CeRhSi_3 and CeIrSi_3. First, we investigate the spin susceptibility in the linear response regime and elucidate the role of AFM order. The spin susceptibility at T=0 is independent of the pairing symmetry and increases in the AFM state. Second, the non-linear response to the magnetic field are investigated on the basis of an effective model for CePt_3Si which may be also applicable to CeRhSi_3 and CeIrSi_3…
We calculate the upper critical field in superconductors without inversion symmetry at arbitrary temperatures, in the presence of scalar impurities. Both orbital and spin (paramagnetic) mechanisms of pair breaking are considered. The superconducting phase transition at nonzero field occurs into a helical vortex state, in which the order parameter is modulated along the applied field (in a cubic crystal). The helical state is stable with respect to disorder. However, if the difference between the densities of states in the electron bands split by spin-orbit coupling is neglected, then the order…
Symmetry-breaking has been known to play a key role in noncentrosymmetric superconductors with strong spin-orbit-interaction (SOI). The studies, however, have been so far mainly focused on a particular type of SOI, known as Rashba SOI, whereby the electron spin is locked to its momentum at a right-angle, thereby leading to an in-planar helical spin texture. Here we discuss electric-field-induced superconductivity in molybdenum disulphide (MoS2), which exhibits a fundamentally different type of intrinsic SOI manifested by an out-of-plane Zeeman-type spin polarization of energy valleys. We find …
The random spin-orbit coupling in multicomponent superconductors is investigated focusing on the non-centrosymmetric superconductor CePt_3Si and the spin triplet superconductor Sr_2RuO_4. We find novel manifestations of the random spin-orbit coupling in the multicomponent superconductors with directional disorders, such as stacking faults. The presence of stacking faults is indicated for the disordered phase of CePt_3Si and Sr_2RuO_4. It is shown that the d-vector of spin triplet superconductivity is locked to be d = k_y x - k_x y with the anisotropy ΔT_c/T_c0 \sim \barα^2/T_c0 W_z, where \bar…
