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Register a new userEnhanced Superconductivity in Monolayer $T_d$-MoTe$_2$ with Tilted Ising Spin Texture
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Crystalline two-dimensional (2D) superconductors with low carrier density are an exciting new class of materials in which superconductivity coexists with strong interactions, the effects of complex topology are not obscured by disorder, and electronic properties can be strongly tuned by electrostatic gating. Very recently, two such materials, magic-angle twisted bilayer graphene and monolayer $T_d$-WTe$_2$, have been reported to show superconductivity at temperatures near 1 K. Here we report superconductivity in semimetallic monolayer $T_d$-MoTe$_2$. The critical temperature $T_textrm{c}$ reaches 8 K, a sixty-fold enhancement as compared to the bulk. This anomalous increase in $T_textrm{c}$ is only observed in monolayers, and may be indicative of electronically mediated pairing. Reflecting the low carrier density, the critical temperature, magnetic field, and current density are all tunable by an applied gate voltage, revealing a superconducting dome that extends across both hole and electron pockets. The temperature dependence of the in-plane upper critical field is distinct from that of $2H$ transition metal dichalcogenides (TMDs), consistent with a tilted spin texture as predicted by textit{ab initio} theory.
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We examine anharmonic contributions to the optical phonon modes in bulk $T_d$-MoTe$_2$ through temperature-dependent Raman spectroscopy. At temperatures ranging from 100 K to 200 K, we find that all modes redshift linearly with temperature in agreement with the Gr{u}neisen model. However, below 100 K we observe nonlinear temperature-dependent frequency shifts in some modes. We demonstrate that this anharmonic behavior is consistent with the decay of an optical phonon into multiple acoustic phonons. Furthermore, the highest frequency Raman modes show large changes in intensity and linewidth near $Tapprox 250$ K that correlate well with the $T_d to 1T^prime$ structural phase transition. These results suggest that phonon-phonon interactions can dominate anharmonic contributions at low temperatures in bulk $T_d$-MoTe$_2$, an experimental regime that is currently receiving attention in efforts to understand Weyl semimetals.
Using van der Waals tunnel junctions, we perform spectroscopy of superconducting $mathrm{NbSe_2}$ flakes, of thicknesses ranging from 2--25 monolayers, measuring the quasiparticle density of states as a function of applied in-plane magnetic field up to 33T. In flakes up to $approx$ 15 monolayers thick, we find that the density of states is well-described by a single band superconductor. In these thin samples, the magnetic field acts primarily on the spin (vs orbital) degree of freedom of the electrons, and superconductivity is further protected by Ising spin-orbit coupling (ISOC), which pins Cooper pair spins out-of-plane. The superconducting energy gap, extracted from our tunnelling spectra, decreases as a function of the applied magnetic field. However, in bilayer $mathrm{NbSe_2}$, close to the critical field (up to 30T, much larger than the Pauli limit), superconductivity appears to be even more robust than expected if only ISOC is considered. This can be explained by a predicted subdominant triplet component of the order parameter, coupled to the dominant singlet component at finite field. This equal-spin, odd-parity triplet state arises from the non-colinearity between the applied magnetic field and the Ising field.
Monolayer WTe$_2$, a centrosymmetric transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topological nature of superconducting WTe$_2$ with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate in-plane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring higher-order topology from the boundary perspective: Generally a superconducting inversion-symmetric quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe$_2$, hosts Majorana corner modes if the superconductivity is parity-odd. We further point out that this higher-order phase is an inversion-protected topological crystalline superconductor and study the bulk-boundary correspondence. Finally, we discuss possible experiments for probing the Majorana corner modes. Our findings suggest superconducting monolayer WTe$_2$ is a playground for higher-order topological superconductivity, and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.
NbSe$_{2}$ and NbS$_{2}$ are isostructural two-dimensional materials that exhibit contrasting superconducting properties when reduced to the single monolayer limit. Monolayer NbSe$_{2}$ is an Ising superconductor, while there have been no reports of superconductivity in monolayer NbS$_{2}$. NbS$_{x}$Se$_{2-x}$ alloys exhibit an intriguing non-monotonic dependence of the superconducting transition temperature with sulfur content, which has been interpreted as a manifestation of fractal superconductivity. However, several key questions about this result are not known: (1) Does the electronic structure of the alloy differ from the parent compounds, (2) Are spin fluctuations which have been shown to be prominent in monolayer NbSe$_{2}$ also present in the alloys? Using first-principles calculations, we show that the density of states at the Fermi level and the proximity to magnetism in NbS$_{x}$Se$_{2-x}$ alloys are both reduced compared to the parent compound; the former would decrease the transition temperature while the latter would increase it. We also show that Se vacancies, which are likely magnetic pair-breaking defects, may form in large concentrations in NbSe$_{2}$. Based on our results, we suggest an alternative explanation of the non-monotonic behavior the superconducting transition temperature in NbS$_{x}$Se$_{2-x}$ alloys, which does not require the conjecture of multifractality.
Recent discovery of Ising superconductivity protected against in-plane magnetic field by spin-orbit coupling (SOC) has stimulated intensive research interests. The effect, however, was only expected to appear in two-dimensional (2D) noncentrosymmetric materials with spin-valley locking. In this work, we proposed a new type of Ising superconductivity in 2D materials with $C_{nz}$ rotational symmetry ($n=3,4,6$). This mechanism, dubbed as type-II Ising superconductivity, is applicable for centrosymmetric materials. Type-II Ising superconductivity relies on the SOC-induced spin-orbital locking characterized by Ising-type Zeeman-like fields displaying opposite signs for opposing orbitals. We found that type-II Ising superconductivity are most prominent around time-reversal invariant momenta and is not sensitive to inversion symmetry breaking. By performing high-throughput first-principles calculations, about one hundred candidate materials were identified. Our work significantly enriches the physics and materials of Ising superconductor, opening new opportunities for fundamental research and practical applications of 2D materials.
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