We study the superconducting pairing instabilities and gap functions for prototypical two-dimensional (2D) transition-metal dichalcogenides (TMDCs) WS$_2$, MoTe$_2$, and MoS$_2$ in the 2H phase under both hole and electron doping at 10 K. Our first-principles quantum many-body Green's function approach allows us to treat the full $d$ and $p$ manifold of orbitals with strong spin-orbit coupling, yielding pairing predictions with material specific detail. The resulting gap functions exhibit a variety of mixed-parity superconducting states, including $s$, $p$, $d$, $f$, $d\pm id$, and $p\pm ip$ pairing modes. In particular, we predict 3% and 4% hole-doped WS$_2$ to be a chiral $p\pm ip$ topological superconductor. For 1% hole-doped MoS$_2$, we find a competition between three doubly degenerate chiral and non-chiral instabilities. Overall, the relative pairing strengths are found to follow the Fermi surface topology, due to nesting between the Fermi surface sheets. Finally, we discuss our predictions in relation to available experimental data and classify the topology of the predicted superconducting pairing symmetries.
Monolayer NbSe$_2$ is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and ele…
Competing incommensurability, electronic correlations, and superconductivity in a hybrid transition metal dichalcogenide
Weizmann Institute of Science（魏茨曼科学研究所）；University of Hamburg（汉堡大学）；Bar Ilan University（巴伊兰大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Technion - Israel Institute of Technology（以色列理工学院）；Goethe Universität Frankfurt（法兰克福歌德大学）
Bilayer transition metal dichalcogenides (TMDs) belong to a class of materials with two unique features, the coupled spin-valley-layer degrees of freedom and the crystal structure that is globally centrosymmetric but locally non-centrosymmetric. In this work, we will show that the combination of these two features can lead to a rich phase diagram for unconventional superconductivity, including intra-layer and inter-layer singlet pairings and inter-layer triplet pairings, in bilayer superconducting TMDs. In particular, we predict that the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state can…
Theoretically it has been known that breaking spin-degeneracy and effectively realizing 'spinless fermions' is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here, we propose to realize spinless fermions by splitting the spin-degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is un…
Two-dimensional transition metal dichalcogenides entwine interaction, spin-orbit coupling, and topology. Hole-doped systems lack spin degeneracy: states are indexed with spin and valley specificity. This unique structure offers new possibilities for correlated phases and phenomena. We realize an unconventional superconducting pairing phase which is an equal mixture of a spin singlet and the $m = 0$ spin triplet. It is stable against large in-plane magnetic fields, and its topology allows quasiparticle excitations of net nonzero Berry curvature via pair-breaking circularly polarized light.
Time-reversal breaking topological superconductors are new states of matter which can support Majorana zero modes at the edge. In this paper, we propose a new realization of one-dimensional topological superconductivity and Majorana zero modes. The proposed system consists of a monolayer of transition metal dichalcogenides MX2 (M=Mo, W; X=S, Se) on top of a superconducting substrate. Based on first-principles calculations, we show that a zigzag edge of the monolayer MX2 terminated by metal atom M has edge states with strong spin-orbit coupling and spontaneous magnetization. By proximity coupli…
Metallic ferromagnets with strongly interacting electrons often exhibit remarkable electronic phases such as ferromagnetic superconductivity, complex spin textures, and nontrivial topology. In this report, we discuss the synthesis of a layered magnetic metal NiTa$_4$Se$_8$ (or Ni$_{1/4}$TaSe$_{2}$) with a Curie temperature of 58 Kelvin. Magnetization data and \textit{ab initio} calculations indicate that the nickel atoms host uniaxial ferromagnetic order of about 0.7$μ_{B}$ per atom, while an even smaller moment is generated in the itinerant tantalum conduction electrons. Strong correlations a…
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…
We report on specific heat and magnetotransport measurements performed on superconducting Cu$_{10\%}$TiSe$_2$ single crystals. We show that superconductivity persists in transport measurements up to magnetic fields $H_R$ well above the upper critical field $H_{c2}$ deduced from the calorimetric measurements. Surprisingly this "surface" superconductivity is present for all magnetic field orientations, either parallel or perpendicular to the layers. For $H\|ab$, the temperature dependence of the $H_R/H_{c2}$ ratio can be well reproduced by solving the Ginzburg-Landau equations in presence of a s…
In this paper, we propose a way to realize topological $s$-wave superconductivity with application of circularly polarized laser light in two-dimensional bilayer transition metal dichalcogenides (TMDs). Using Floquet theory, we analyze a tight-binding model of bilayer TMDs with time-periodic electric fields. After deriving an effective Hamiltonian, we investigate topological properties of the $s$-wave superconducting state. The laser light induces valley-dependent layer polarization and makes the system to be a topologically nontrivial superconducting state characterized by the Chern number. W…
In this work, we review the results of several recent works on the experimental and theoretical studies of monolayer superconducting transition metal dichalcogenides (TMD) such as superconducting MoS2 and NbSe2. We show how the strong Ising spin-orbit coupling (SOC), a special type of SOC which pins electron spins to out-of-plane directions, can affect the superconducting properties of the materials. Particularly, we discuss how the in-plane upper critical fields of the materials can be strongly enhanced by Ising SOC and how TMD materials can be used to engineer topological superconductors and…
We report on a novel mechanism of BCS-like superconductivity, mediated by a pair of Bogoliubov quasiparticles (bogolons). It takes place in hybrid systems consisting of a two-dimensional electron gas in a transition metal dichalcogenide monolayer in the vicinity of a Bose-Einstein condensate. Taking a system of two-dimensional indirect excitons as a testing ground we show, that the bogolon-pair-mediated electron pairing mechanism is stronger than phonon-mediated and single bogolon-mediated ones. We develop a microscopic theory of bogolon-pair-mediated superconductivity, based on the Schrieffer…
We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge density waves in two-dimensional transition metal dichalcogenides. In the case of particle-hole symmetry the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken electron (hole) pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasi-particles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave …
We introduce a McMillan-Ginzburg-Landau theory to describe the cooperative coexistence of charge-density and superconducting order in two-dimensional crystals. With a free-energy that explicitly accounts for the competition between commensurate and incommensurate ground states, we are able to map the transition between these phases and monitor the development of discommensurations in the near-commensurate regime. Attributing the enhancement of superconducting order to density-wave fluctuations, we propose a coupling scheme that yields a phase diagram in qualitative agreement with experiments i…
We study possible superconducting states in transition metal dichalcogenide (TMD) monolayers, assuming an on-site pairing potential that includes both intra- and inter-orbital terms. We find that if the mirror symmetry with respect to the system's plane is broken (e.g., by a substrate), this type of pairing can give rise to unconventional superconductivity, including time-reversal-invariant nodal and fully gapped topological phases. Using a multi-orbital renormalization group procedure, we show how these phases may result from the interplay between the local Coulomb repulsion, Hund's rule coup…
Two-dimensional transition metal dichalcogenide PdTe$_2$ recently attracts much attention due to its phase coexistence of type-II Dirac semimetal and type-I superconductivity. Here we report a 67 % enhancement of superconducting transition temperature in the 1T-PdSeTe in comparison to that of PdTe2 through partial substitution of Te atoms by Se. The superconductivity has been unambiguously confirmed by the magnetization, resistivity and specific heat measurements. 1T-PdSeTe shows type-II superconductivity with large anisotropy and non-bulk superconductivity nature with volume fraction ~ 20 % e…
The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem. Destruction of superconductivity and even superconductor-insulator transitions occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states. Because of the entanglement of various effects, the mechanism of enhancement is still under debate. Here we report well-controlled …
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 str…
In monolayer transition metal dichalcogenides (TMDs), electrons in opposite $K$ valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from in-plane mirror symmetry breaking pins the electron spins in out-of-plane directions, and results in the newly discovered Ising superconducting states with strongly enhanced upper critical fields. In this work, we show that the Ising SOC generates equal-spin triplet Cooper pairs with spin polarization in the in-plane directions. Importantly, the spin-triplet Cooper…
Topological superconductors (TSCs) are unconventional superconductors with bulk superconducting gap and in-gap Majorana states on the boundary that may be used as topological qubits for quantum computation. Despite their importance in both fundamental research and applications, natural TSCs are very rare. Here, combining state of the art synchrotron and laser-based angle-resolved photoemission spectroscopy, we investigated a stoichiometric transition metal dichalcogenide (TMD), 2M-WS2 with a superconducting transition temperature of 8.8 K (the highest among all TMDs in the natural form up to d…
We theoretically investigate the possibility of achieving a superconducting state in transition-metal dichalcogenide bilayers through intercalation, a process previously and widely used to achieve metallization and superconducting states in novel superconductors. For the Ca-intercalated bilayers MoS$_2$ and WS$_2$, we find that the superconducting state is characterized by an electron-phonon coupling constant larger than $1.0$ and a superconducting critical temperature of $13.3$ and $9.3$ K, respectively. These results are superior to other predicted or experimentally observed two-dimensional …
We investigate proximity-induced superconductivity in monolayers of transition metal dichalcogenides (TMDs) in the presence of an externally generated exchange field. A variety of superconducting order parameters is found to emerge from the interplay of magnetism and superconductivity, covering the entire spectrum of possibilities to be symmetric or antisymmetric with respect to the valley and spin degrees of freedom, as well as even or odd in frequency. More specifically, when a conventional \emph{s}-wave superconductor with singlet Copper pairs is tunnel-coupled to the TMD layer, both spin-s…
Pressure-induced Structural Phase Transition, Metallization, and Superconductivity in layered metalloid dichalcogenide 1T-SiTe$_2$
National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院，先进微结构协同创新中心）
Monolayer transition metal dichalcogenides (TMDs) host deeply bound excitons interacting with itinerant electrons, and as such they represent an exciting new quantum many-body Bose-Fermi mixture. Here, we demonstrate that electrons interacting with a Bose-Einstein condensate (BEC) of exciton-polaritons can realise a two-dimensional topological $p_x+ip_y$ superconductor. Using strong coupling Eliashberg theory, we show that this is caused by an attractive interaction mediated by the BEC, which overcompensates the repulsive Coulomb interaction between the electrons. The hybrid light-matter natur…
Systems that simultaneously exhibit superconductivity and spin-orbit coupling are predicted to provide a route toward topological superconductivity and unconventional electron pairing, driving significant contemporary interest in these materials. Monolayer transition-metal dichalcogenide (TMD) superconductors in particular lack inversion symmetry, enforcing a spin-triplet component of the superconducting wavefunction that increases with the strength of spin-orbit coupling. In this work, we present an experimental and theoretical study of two intrinsic TMD superconductors with large spin-orbit …
Recently, it was experimentally realized that 2D superconducting transition metal dichalcogenides (TMD) such as gated MoS$_2$ and monolayer NbSe$_2$ have in-plane upper critical magnetic fields much higher than the Pauli limit. This is due to the so-called Ising spin-orbit coupling (SOC) of TMD which pins the electron spins along the out-of-plane directions and protects the Cooper pairs from in-plane magnetic fields. However, many TMD materials with extremely large Ising SOC, in the order of a few hundred meV, are not superconducting. In this work, we show that TMD materials can induce strong …
Superconductivity occurs in electrochemically doped molybdenum dichalcogenides samples thicker than four layers. While the critical temperature (Tc) strongly depends on the field effect geometry (single or double gate) and on the sample (MoS2 or MoSe2), Tc always saturates at high doping. The pairing mechanism and the complicate dependence of Tc on doping, samples and field-effect geometry are currently not understood. Previous theoretical works assumed homogeneous doping of a single layer and attributed the Tc saturation to a charge density wave instability, however the calculated values of t…
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…
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2, in which a [100] rocksalt bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally non-superconducting layered transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc corresponding to the expected trivial to topological transition in the Pb1-xSnxSe bi-layer. We present a more detailed characterization of the superconductor at x = 0.…
Eigenstate multifractality is a distinctive feature of non-interacting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic weakly disordered single-layer NbSe$_2$ by means of low-temperature scanning tunneling microscopy/spectros…
The layered transition metal chalcogenides have been a fertile land in solid state physics for many decades. Various MX2-type transition metal dichalcogenides, such as WTe2, IrTe2, and MoS2, have triggered great attention recently, either for the discovery of novel phenomena or some extreme or exotic physical properties, or for their potential applications. PdTe2 is a superconductor in the class of transition metal dichalcogenides, and superconductivity is enhanced in its Cu-intercalated form, Cu0.05PdTe2. It is important to study the electronic structures of PdTe2 and its intercalated form in…
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $Γ- M$ lines of the Brillouin zone w…
In disordered transition-metal dichalcogenide (TMD) superconductor, both the strong spin-orbit coupling (SOC) and disorder show remarkable effects on superconductivity. However, the features of SOC and disorder were rarely detected directly. Here we report the quantum transport behaviors arising from the interplay of SOC and disorder in the TMD superconductor 1T-NbSeTe. Before entering the superconducting state, the single crystal at low temperature shows a resistivity upturn, which is T1/2 dependent and insensitive to the applied magnetic fields. The magnetoresistance (MR) at low temperatures…
Transition metal dichalcogenides (TMDCs) usually exhibit layered polytypic structures due to the weak interlayer coupling. 2H-NbSe2 is one of the most widely studied in the pristine TMDC family due to its high superconducting transition temperature (Tc = 7.3K) and the occurrence of a charge-density wave (CDW) order below 33 K. The coexistence of CDW with superconductivity poses an intriguing open question about the relationship between Fermi surface nesting and Cooper pairing. Past studies of this issue have mostly been focused on doping 2H-NbSe2 by 3d transition metals without significantly c…
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 compare the upper critical field of bulk single-crystalline samples of the two intrinsic transition metal dichalcogenide (TMD) superconductors, 2H-NbSe2 and 2H-NbS2, in high magnetic fields where their layer structure is aligned strictly parallel and perpendicular to the field, using magnetic torque experiments and a high-precision piezo-rotary positioner. While both superconductors show that orbital effects still have a significant impact when the layer structure is aligned parallel to the field, the upper critical field of NbS2 rises above the Pauli limiting field and forms a Fulde-Ferrel…
We report first principles calculations, within density functional theory, of copper intercalated titanium diselenides, CuxTiSe2, for values of x ranging from 0 to 0.11. The effect of intercalation on the energy bands and densities of states of the host material is studied in order to better understand the cause of the superconductivity that was recently observed in these structures. We find that charge transfer from the copper atoms to the metal dichalcogenide host layers causes a gradual reduction in the number of holes in the otherwise semi-metallic pristine TiSe2, thus suppressing the char…
When a Mott metal-insulator transition is inhibited by a small amount of disorder in the layered dichalcogenide 1T-TaS$_2$, an inhomogeneous superconducting state arises below T=2.1 K, and coexists with a nearly-commensurate charge-density-wave. By angle-resolved photoelectron spectroscopy (ARPES) we show that it emerges from a bad metal state with strongly damped quasiparticles. Superconductivity is almost entirely suppressed by an external magnetic field of 0.1 T.
Superconducting transition metal dichalcogenides emerged as a prime candidate for topological superconductivity. This work presents a detailed investigation of superconducting and transport properties on 2H-TaSeS single crystals using magnetization, transport, and specific heat measurements. These measurements suggest multigap anisotropic superconductivity with the upper critical field, breaking Pauli limiting field in both in-plane and out-of-plane directions. The angle dependence of the upper critical field suggests 2-dimensional superconducting nature in bulk 2H- TaSeS.
