Group theory arguments have been invoked to argue that odd parity order parameters cannot have line nodes in the presence of spin-orbit coupling. In this paper we show that these arguments do not hold for certain non-symmorphic superconductors. Specifically, we demonstrate that when the underlying crystal has a twofold screw axis, half of the odd parity representations vanish on the Brillouin zone face perpendicular to this axis. Many unconventional superconductors have non-symmorphic space groups, and we discuss implications for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.
Recently, evidence has emerged for a field-induced even- to odd-parity superconducting phase transition in CeRh$_2$As$_2$ [S. Khim et al., Science 373 1012 (2021)]. Here we argue that the P4/nmm non-symmorphic crystal structure of CeRh$_2$As$_2$ plays a key role in enabling this transition by ensuring large spin-orbit interactions near the Brillouin zone boundaries, which naturally leads to the required near-degeneracy of the even- and odd-parity channels. We further comment on the relevance of our theory to FeSe, which crystallizes in the same structure.
We discuss the nodal structure of odd-parity superconductors in the presence of non-symmorphic crystal symmetries, both with and without spin-orbit coupling, and with and without time reversal symmetry. We comment on the relation of our work to previous work in the literature, and also the implications for unconventional superconductors such as UPt$_3$.
We demonstrate that, quite generally, the spin-singlet even-parity (spin-triplet odd-parity) pair potential in a superconductor induces the odd-frequency pairing component with spin-singlet odd-parity (spin-triplet even-parity) near interfaces. The magnitude of the induced odd-frequency component is enhanced in the presence of the midgap Andreev resonant state due to the sign change of the anisotropic pair potential at the interface. The Josephson effect should therefore occur between odd- and even-frequency superconductors, contrary to the standard wisdom. A method to probe the odd-frequency …
The topological property of a gapped odd-parity superconductor is jointly determined by its pairing nodes and Fermi surfaces in normal state. We reveal that the contractibility of Fermi surfaces without crossing any time-reversal invariant momentum and the presence of nontrivial Berry phase on Fermi surfaces are two key conditions for the realization of higher-order topological odd-parity superconductors (HOTOPSCs). When the normal state is a normal metal, we reveal the necessity of removable Dirac pairing nodes and provide a general and simple principle to realize HOTOPSCs. Our findings can n…
Parity is a fundamental quantum number to classify a state of matter. Materials rarely possess ground states with odd parity. We show that the superconducting state in iron-based superconductors is classified as an odd parity s-wave spin-singlet pairing state in a single trilayer FeAs/Se, the building block of the materials. In a low energy effective model constructed on the Fe square bipartite lattice, the superconducting order parameter in this state is a combination of a s-wave normal pairing between two sublattices and a s-wave $η$-pairing within the sublattices. Parity conservation was vi…
Under the assumption that superconducting pairing is driven by local d-p hybridization, we show that the superconducting state in iron-based superconductors is classified as an odd parity s-wave spin-singlet pairing state in a single trilayer FeAs/Se, the building block of the materials. In a low energy effective model with only d-orbitals in an iron square bipartite lattice, the superconducting order parameter in this state is a combination of a s-wave normal pairing between two sublattices and a s-wave $η$-pairing within the sublattices. Parity conservation was violated in proposed supercond…
We propose a route to achieve odd-parity spin-triplet superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin-degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfa…
Charge-transfer effect under odd-parity crystalline electric field (CEF) is analyzed theoretically. In quantum-critical metal $β$-YbAlB$_4$, seven-fold configuration of B atoms surrounding Yb atom breaks local inversion symmetry at the Yb site, giving rise to the odd-parity CEF. Analysis of the CEF on the basis of hybridization picture shows that admixture of 4f and 5d wave functions at Yb with pure imaginary coefficient occurs, which makes magnetic-toroidal (MT) and electric-dipole (ED) degrees of freedom active. By constructing the minimal model for periodic crystal $β$-YbAlB$_4$, we show th…
The discovery of the multiple $H$-$T$ phase diagram of CeRh$_2$As$_2$ offers a new route to designing topological superconductors. Although weak-coupling theories explain the experimental phase diagram qualitatively, a quantitative discrepancy between them has discouraged conclusive interpretation. In this Letter, we thoroughly study the effect of Coulomb interaction and the phase diagrams of locally noncentrosymmetric superconductors. We reveal even-odd parity transition and the enhancement of the parity transition field in strongly correlated superconductors, and an issue of CeRh$_2$As$_2$ i…
Using the functional renormalization group technique we demonstrate a route for potentially high-temperature odd-parity superconductivity in ferromagnetic materials caused by repulsive electron interactions, where the superconducting pairing is driven by charge-density wave fluctuations. Our model is directly applicable to a lightly cobalt-doped LaNiO$_3$ bilayer grown in the (111) direction. As the on-site repulsive interaction grows, a charge-density wave state with a charge pattern that respects all point-group symmetries of the bilayer is replaced by a superconducting state with an f-wave …
We investigate a model where superconducting electrons are coupled to a frequency dependent charge-density wave (CDW) order parameter Delta(w). Our approach can reconcile the simultaneous existence of low energy Bogoljubov quasiparticles and high energy electronic order as observed in scanning tunneling microscopy (STM) experiments. The theory accounts for the contrast reversal in the STM spectra between positive and negative bias observed above the pairing gap. An intrinsic relation between scattering rate and inhomogeneities follows naturally.
In this letter, we investigate topological phases of full-gapped odd-parity superconductors, which are distinguished by the bulk topological invariants and the topologically protected gapless boundary states. Using the particle-hole symmetry, we introduce Z_2 invariants characterizing topological odd-parity superconductors without or with time-reversal invariance. For odd-parity superconductors, a combination of the inversion and the U(1) gauge symmetry is manifestly preserved, and the combined symmetry enables us to evaluate the Z_2 invariants from the knowledge of the Fermi surface structure…
From the group theoretical ground, the Blount's theorem prohibits the existence of line nodes for odd-parity superconductors (SCs) in the presence of spin-orbit coupling (SOC). We study the topological stability of line nodes under inversion symmetry. From the topological point of view, we renovate the stability condition of line nodes, in which we not only generalize the original statement, but also establish the relation to zero-energy surface flat dispersions. The topological instability of line nodes in odd-parity SCs implies not the absence of bulk line nodes but the disappearance of the …
We study superconductivity in spin-orbit-coupled systems in the vicinity of inversion symmetry breaking. We find that due to the presence of spin-orbit coupling, fluctuations of the incipient parity-breaking order generate an attractive pairing interaction in an odd-parity pairing channel, which competes with the s-wave pairing. We show that applying a Zeeman field suppresses the s-wave pairing and promotes the odd-parity superconducting state. Our work provides a new mechanism for odd-parity pairing and opens a route to novel topological superconductivity.
A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. An augmented cluster magnetic multipole order in a crystal lacking local space inversion parity may break global inversion symmetry, and then, it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by Sr$_2$IrO$_4$. We find that even-parity superconductivity is more significantly suppressed by a spin-orbit coupl…
Unconventional superconductors host a plethora of interesting physical phenomena. However, the standard theory of superconductivity suggests that unconventional pairing is highly sensitive to disorder, and hence can only be observed in ultraclean systems. We find that due to an emergent chiral symmetry, spin-orbital locking can parametrically suppress pair decoherence introduced by impurity scattering in odd-parity superconductors. Our work demonstrates that disorder is not an obstacle to realize odd-parity superconductivity in materials with strong spin-orbit coupling.
Recent experiments indicate that superconductivity in Bi$_2$Se$_3$ intercalated with Cu, Nb or Sr is nematic with rotational symmetry breaking. Motivated by this observation, we present a model study of nematic and chiral superconductivity induced by odd-parity fluctuations. We show that odd-parity fluctuations in the two-component $E_u$ representation of $D_{3d}$ crystal point group can generate attractive interaction in both the even-parity $s$-wave and odd-parity $E_u$ pairing channels, but repulsive interaction in other odd-parity pairing channels. Coulomb repulsion can suppress $s$-wave p…
We show that mixed-parity superconductors may exhibit equal-spin pair correlations that are odd-in-time and can be tuned by means of an applied field. The direction and the amplitude of the pair correlator in the spin space turn out to be strongly dependent on the symmetry of the order parameter, and thus provide a tool to identify different types of singlet-triplet mixed configurations. We find that odd-in-time spin-polarized pair correlations can be generated without magnetic inhomogeneities in superconducting/ferromagnetic hybrids when parity mixing is induced at the interface.
We study unconventional superconductivity in a two-dimensional locally noncentrosymmetric triangular lattice. The model is relevant to bilayer transition metal dichalcogenides with 2H$_b$ stacking structure, for example. The superconducting instability is analyzed by solving the linearized Eliashberg equation within the random phase approximation. We show that ferromagnetic fluctuations are dominant owing to the existence of disconnected Fermi pockets near van Hove singularity, and hence odd-parity spin-triplet superconductivity is favored. In the absence of the spin-orbit coupling, we find th…
CuxBi2Se3 was recently proposed as a promising candidate for time-reversal-invariant topological superconductors[1]. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng[2], taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional E_u representation of the D3d crystal point group[1], which spontaneously breaks the three-fold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays …
Spin-orbit coupling in transition metal dichalcogenides (TMDCs) causes spin-valley locking giving rise to unconventional optical, transport, and superconducting properties. In this paper, we propose exotic superconductivity in bilayer group-IV TMDCs by symmetry control. The sublattice-dependent hidden spin-orbit coupling arising from local inversion symmetry breaking in the crystal structure may stabilize the odd-parity superconductivity by purely $s$-wave local pairing interaction. The stability of the odd-parity superconducting state depends on the bilayer stacking. The 2H$_b$ stacking in Mo…
The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band p…
Superconductive properties of the two-leg ladder compounds are studied theoretically. The antiferromagnetic fluctuations are considered because of the good nesting of the Fermi surfaces. The attractive interaction which is most likely due to the electron-phonon coupling is also taken into account. Under this circumstance, it is shown that the superconductivity has two sets of spin-triplet pairings. The gaps for both pairings have no node.
We report observation of the enhancement of superconductivity near lattice dislocations and the absence of the strengthening of vortex pinning in odd-parity superconductor Sr$_2$RuO$_4$, both surprising results in direct contrast to the well known sensitivity of superconductivity in Sr$_2$RuO$_4$ to disorder. The enhanced superconductivity appears to be related fundamentally to the two-component nature of the superconducting order parameter, as revealed in our phenomenological theory taking into account the effect of symmetry reduction near a dislocation.
We investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the local spin susceptibility, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments. Because of their different decay lengths, the Majorana modes can be observed and clearly distinguished from the Dirac modes of the topological insulator by local pro…
We show that odd-parity superconductivity occurs in multilayer Rashba systems without requiring spin-triplet Cooper pairs. A pairing interaction in the spin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state in the magnetic field parallel to the two-dimensional conducting plane. It is shown that the layer-dependent Rashba spin-orbit coupling and the orbital effect play essential roles for the PDW state in binary and tricolor heterostructures. We demonstrate that the odd-parity PDW state is a symmetry-protected topological superconducting state characterized by the one-dime…
Quantum dots are gate-defined within InSb nanowires, in proximity to NbTiN superconducting contacts. As the coupling between the dot and the superconductor is increased, the odd-parity occupations become non-discernible (erased) both above and below the induced superconducting gap. Above the gap, conductance in the odd Coulomb valleys increases until the valleys are lifted. Below the gap, Andreev bound states undergo quantum phase transitions to singlet ground states at odd occupancy. We observe that the apparent erasure of odd-parity regimes coincides at low-bias and at high-bias. This observ…
Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum sp…
Topological superconductors have been theoretically predicted as a new class of time-reversal-invariant superconductors which are fully gapped in the bulk but have protected gapless surface Andreev bound states. In this work, we provide a simple criterion that directly identifies this topological phase in \textit{odd-parity} superconductors. We next propose a two-orbital $U-V$ pairing model for the newly discovered superconductor Cu$_x$Bi$_2$Se$_3$%. Due to its peculiar three-dimensional Dirac band structure, we find that an inter-orbital triplet pairing with odd-parity is favored in a signifi…
We study odd-parity nematic superconductivity in doped topological insulators in presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flatband, nodal cones and the surface states of the parent topological insulator, gives rise to an overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface …
