We report superconductivity in Sn$_{x}$NbSe$_{2-δ}$, a topological nodal-line semimetal candidate with a noncentrosymmetric crystal structure. The superconducting transition temperature $T_{c}$ of this compound is extremely sensitive to Sn concentration $x$ and Se deficiency $δ$, 5.0 K for Sn$_{0.13}$NbSe$_{1.70}$ and 8.6 K for Sn$_{0.14}$NbSe$_{1.71}$ and Sn$_{0.15}$NbSe$_{1.69}$. In all samples, the temperature dependence of the upper critical field $H_{c2}(T)$ differs from the prediction of the Werthamer-Helfand-Hohenberg theory. While the zero-temperature value of the in-plane upper critical field of Sn$_{x}$NbSe$_{2-δ}$ with the higher $T_{c}$ is lower than the Pauli paramagnetic limit $H_{P}$, that of the lower $T_{c}$ sample exceeds $H_{P}$ by a factor of $\sim$2. Our observations suggest that odd-parity contribution dominates the superconducting gap function of Sn$_{x}$NbSe$_{2-δ}$, and it can be fine-tuned by the Sn concentration and Se deficiency.
Transition metal dichalcogenides like 2H-NbSe2 in their two-dimensional (2D) form exhibit Ising superconductivity with the quasiparticle spins are firmly pinned in the direction perpendicular to the basal plane. This enables them to withstand exceptionally high magnetic fields beyond the Pauli limit for superconductivity. Using field-angle-resolved magnetoresistance experiments for fields rotated in the basal plane we investigate the field-angle dependence of the upper critical field (Hc2), which directly reflects the symmetry of the superconducting order parameter. We observe a six-fold nodal…
Distinguishing nodal and nonunitary superconductivity in quasiparticle interference of an Ising superconductor with Rashba spin-orbit coupling: an example of NbSe$_2$
A search for the single material system that simultaneously exhibits topological phase and intrinsic superconductivity has been largely limited, although such a system is far more favorable especially for the quantum device applications. Except artificially engineered topological superconductivity in heterostructure systems, another alternative is to have superconductivity arising from the topological materials by pressure or other clean technology. Here, based on first-principles calculations, we first show that quasi-one-dimensional compound (NbSe4)2I represents a rare example of a chiral We…
We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_{2}$ in presence of both in-plane magnetic field and Rashba spin-orbit coupling (SOC). Repulsive interactions lead to two distinct instabilities, in singlet- and triplet- interaction channels. While we recover the previously predicted nodal topological superconducting state in the absence of Rashba SOC at large magnetic field with six pairs of nodes along \(Γ\)-\(M\) lines, a finite Rashba SOC breaks the symmetry that protects these nodes and therefore generally lifts them, resulting in a topologically …
We study the vortex bound states in three dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. Assuming two Dirac points on the kz-axis and bulk s-wave superconductivity, with a quantum vortex line parallel to the z-direction, we find that the superconducting vortex line has a robust quasi-1D nodal phase. The nodal phase stems from the symmetry protected Dirac points in the normal state bands, and it can be characterized by a topological index (ν; n) at kz = 0 and kz = π, where νis the Z2 topological invariant for a 0D class-D system and n is the Z topological invaria…
Hybridization between surface flat bands and bulk bands in the topological nodal-line semimetal Sn$_{0.15}$NbSe$_{1.75}$ probed via soft-point-contact spectroscopy
The combination with superconductivity and topological nontrivial band structure provides a promising route towards novel quantum states such as topological superconductivity. Here, we report the first observation of superconductivity (4.1 K) in Ba5In4Bi5 single crystal, a noncentrosymmetric topological semimetal featuring nodal chain loops at the high-symmetry points R and X. The magnetization, resistivity, and specific heat capacity measurements reveal that Ba5In4Bi5 is a moderately coupled type-II Bardeen-Cooper-Schrieffer superconductor. Bulk superconductivity is suggested from the magneti…
Weyl nodal loop semimetals (WNLs) host a closed nodal line loop Fermi surface in the bulk, protected zero-energy flat band, or drumhead, surface states, and strong spin-polarization. The large density of states of the drumhead states makes WNL semimetals exceedingly prone to electronic ordering. At the same time, the spin-polarization naively prevents conventional superconductivity due to its spin-singlet nature. Here we show the complete opposite: WNLs are extremely promising materials for superconducting Josephson junctions, entirely due to odd-frequency superconductivity. By sandwiching a W…
Nodal-line semimetals are topologically non-trivial states of matter featuring band crossings along a closed curve, i.e. nodal-line, in momentum space. Through a detailed analysis of the electronic structure, we show for the first time that the normal state of the superconductor NaAlSi, with a critical temperature of $T_{\rm c} \approx$ 7 K, is a nodal-line semimetal, where the complex nodal-line structure is protected by non-symmorphic mirror crystal symmetries. We further report on muon spin rotation experiments revealing that the superconductivity in NaAlSi is truly of bulk nature, featurin…
We investigate the impact of s-wave spin-singlet pairing on antiferromagnetic semimetals with Dirac points or nodal loops at the Fermi level. The electron pairing is generally shown to convert the semimetal into a tunable nodal superconductor. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the antiferromagnetic-superconducting state that set the occurrence of a large variety of electronic topological transitions. We provide a general criterion for predicting a series of transitions between nodal and fully gapped superconducting phases. Different types …
Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the wind…
We study impurity scattering in the normal and d-wave superconducting states of line nodal semimetals and show that, due to additional scattering phase space available for impurities on the surface, the quasiparticle interference pattern acquires an extended character instead of a discrete collection of delta function peaks. Moreover, using the T-matrix formalism, we demonstrate that the conventional behavior of a scalar impurity in a d-wave superconductor breaks down on the surface of a line nodal semimetal in the quasi flat band limit.
We observed quantum oscillations in thermoelectric and magnetic torque signals in non-centrosymmetric superconductor PbTaSe$_2$. One oscillatory frequency stems from the orbits formed by magnetic breakdown, while others are from two-dimensional-like Fermi surfaces near the topological nodal rings. Our comprehensive understanding of the Fermi surface topology of PbTaSe$_2$, including nailing down the Fermi level and detecting the Berry phases near the nodal rings, is crucial for searching plausible topological superconductivity in its bulk and surface states.
While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superco…
Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy "Fermi arcs" at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all …
Dirac nodal-line semimetals with the linear bands crossing along a line or loop, represent a new topological state of matter. Here, by carrying out magnetotransport measurements and performing first-principle calculations, we demonstrate that such a state has been realized in high-quality single crystals of SrAs3. We obtain the nontrivial pi Berry phase by analysing the Shubnikov-de Haas quantum oscillations. We also observe a robust negative longitudinal magnetoresistance induced by the chiral anomaly. Accompanying first-principles calculations identify that a single hole pocket enclosing the…
Topological semimetals with superconducting properties provide an emergent platform to explore the properties of topological superconductors. We report magnetization, and magneto-transport measurements on high quality single crystals of transition metal dichalcogenide SnTaS2. It is a nodal line semimetal with superconducting transition below Tc = 2.9 K. Moderate anisotropy (3.1) is observed in upper critical fields along H||c and H||ab plane. In the normal state we observe large magneto-resistance and weak anti-localization effect that provide unambiguous confirmation of topological features i…
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
