Experimental Realization of Type-II Dirac Fermions in a PdTe_{2} Superconductor

Planar Hall effect induced by anisotropic orbital magnetoresistance in type-II Dirac semimetal PdTe2

We measure planar Hall effect (PHE) and longitudinal anisotropic magnetoresistance (AMR) with a magnetic field rotating in the a-b plane in the type-II Dirac semimetal PdTe₂. The measured PHE and AMR curves can be fitted by the theoretical equations; however, a detailed analysis of the extracted data demonstrates that the parameter related to PHE and AMR has no relationship with the chiral anomaly due to the absence of negative longitudinal magnetoresistance (MR) when the electric and magnetic fields are parallel to each other. Meanwhile, we prove that the origin of PHE in PdTe₂ is the anisotropic orbital MR. Our work suggests that negative longitudinal MR is necessary to identify chiral anomaly, and we cannot in general use PHE as a signal for the presence of the chiral anomaly in Dirac/Weyl semimetals.

Quasi-1D Topological Nodal Vortex Line Phase in Doped Superconducting 3D Dirac Semimetals

We study vortex bound states in three-dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. We find that there exist robust gapless vortex bound states propagating along the vortex line in the s-wave superconducting state. We refer to this newly found phase as the quasi-1D nodal vortex line phase. According to the Altland-Zirnbauer classification, the phase is characterized by a topological index (ν;N) at k_{z}=0 and k_{z}=π, where ν is the Z_{2} topological invariant for a 0D class-D system and N is the Z topological invariant for a 0D class-A system. Furthermore, we show that the vortex end Majorana zero mode can coexist with the quasi-1D nodal phase in certain types of Dirac semimetals. The possible experimental observations and material realization of such nodal vortex line states are discussed.

Insight into the robust multiple Dirac-cones in perovskite R3¯c phase CuBO3 semimetal from first-principles

Motivated by a related recent study (Jiao et al. PRL 119, 016403 (2017)), in this work, a new R3¯c type semimetal has been calculated based on the first-principles method. We observed that CuBO₃ showed robust multiple Dirac-cones (DCs) near the Fermi level. Also, we found that these DCs were coming from the hybridization between O-p and Cu-d orbits. As a medium state between normal insulating state and topological insulating state, Dirac semimetal is a new class of materials due to its novel physical properties. Moreover, for CuBO₃, the Dirac-like band crossings are dispersed in a linear pattern across a very large energy range. In order to guide the experiment, the thermal stability of CuBO₃ has been studied through ab initio molecular dynamic simulations. Finally, we are keen to emphasize that the specific space of this group allows for the three-dimensional Dirac point to be used as a symmetric protection for degeneracy. There may be many other three-dimensional Dirac semimetals in the R3¯c phase of crystallization that have not yet been discovered. Thus, more attention to these materials is required in the future.

Defect-Mediated Phase Transformation in Anisotropic Two-Dimensional PdSe2 Crystals for Seamless Electrical Contacts

The failure to achieve stable Ohmic contacts in two-dimensional material devices currently limits their promised performance and integration. Here we demonstrate that a phase transformation in a region of a layered semiconductor, PdSe₂, can form a contiguous metallic Pd₁₇Se₁₅ phase, leading to the formation of seamless Ohmic contacts for field-effect transistors. This phase transition is driven by defects created by exposure to an argon plasma. Cross-sectional scanning transmission electron microscopy is combined with theoretical calculations to elucidate how plasma-induced Se vacancies mediate the phase transformation. The resulting Pd₁₇Se₁₅ phase is stable and shares the same native chemical bonds with the original PdSe₂ phase, thereby forming an atomically sharp Pd₁₇Se₁₅/PdSe₂ interface. These Pd₁₇Se₁₅ contacts exhibit a low contact resistance of ∼0.75 kΩ μm and Schottky barrier height of ∼3.3 meV, enabling nearly a 20-fold increase of carrier mobility in PdSe₂ transistors compared to that of traditional Ti/Au contacts. This finding opens new possibilities in the development of better electrical contacts for practical applications of 2D materials.

Single-component molecular conductor [Pt(dmdt)2]-a three-dimensional ambient-pressure molecular Dirac electron system

The single-component molecular conductor [Pt(dmdt)2] is a sought-after ambient-pressure molecular Dirac electron system, which exhibits a high temperature-insensitive conductivity and temperature-dependent magnetic susceptibility nearly vanishing below 120 K. First-principles DFT calculations reveal that Dirac cones emerge along the a* direction, and form Dirac nodal lines.

Mixed type I and type II superconductivity due to intrinsic electronic inhomogeneities in the type II Dirac semimetal PdTe2

The type II Dirac semimetal PdTe[Formula: see text] is unique in the family of topological parent materials because it displays a superconducting ground state below 1.7 K. Despite wide speculation on the possibility of an unconventional topological superconducting phase, tunneling and heat capacity measurements revealed that the superconducting phase of PdTe[Formula: see text] follows predictions of the microscopic theory of Bardeen, Cooper and Schrieffer for conventional superconductors. The superconducting phase in PdTe[Formula: see text] is further interesting because it also displays properties that are characteristic of type-I superconductors and are generally unexpected for binary compounds. Here, from scanning tunneling spectroscopic measurements we show that the surface of PdTe[Formula: see text] displays intrinsic electronic inhomogeneities in the normal state which leads to a mixed type I and type II superconducting behaviour along with a spatial distribution of critical fields in the superconducting state. Understanding of the origin of such inhomogeneities may be important for understanding the topological properties of PdTe[Formula: see text] in the normal state.

Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices

We've constructed a guide to the electronic properties and topological phases of Archimedean lattices. Within these lattices, a rich electronic structure emerges forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points.

Penetration depth study of the type-I superconductor PdTe2

Superconductivity in the topological non-trivial Dirac semimetal PdTe₂ was recently shown to be type-I. We hereby report measurements of the relative magnetic penetration depth, [Formula: see text], on several single crystals using a high precision tunnel diode oscillator technique. The temperature variation [Formula: see text] follows an exponential function for [Formula: see text], consistent with a fully-gapped superconducting state and weak or moderately coupling superconductivity. By fitting the data we extract a [Formula: see text]-value of  ∼500 nm. The normalized superfluid density is in good agreement with the computed curve for a type-I superconductor with nonlocal electrodynamics. Small steps are observed in [Formula: see text], which possibly relates to a locally lower [Formula: see text] due to defects in the single crystalline sample.

3D Dirac Plasmons in the Type-II Dirac Semimetal PtTe_{2}

Transition-metal dichalcogenides showing type-II Dirac fermions are emerging as innovative materials for nanoelectronics. However, their excitation spectrum is mostly unexplored yet. By means of high-resolution electron energy loss spectroscopy and density functional theory, here, we identify the collective excitations of type-II Dirac fermions (3D Dirac plasmons) in PtTe_{2} single crystals. The observed plasmon energy in the long-wavelength limit is ∼0.5  eV, which makes PtTe_{2} suitable for near-infrared optoelectronic applications. We also demonstrate that interband transitions between the two Dirac bands in PtTe_{2} give rise to additional excitations at ∼1 and ∼1.4  eV. Our results are crucial to bringing to fruition type-II Dirac semimetals in optoelectronics.

Type I superconductivity in Dirac materials

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals while in the PdTe₂, superconductivity is clearly of the first kind. This is very rare in Dirac semi-metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic. Therefore the 'hybrid' Dirac-parabolic material is intermediate between the two extremes. A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D cone and used to determine anisotropic coherence lengths, the penetration depths and applied to recent extensive experiments. Magnetic properties of these superconductors are then studied in the parallel to the layers magnetic field on the basis of microscopically derived Ginzburg-Landau effective theory for the order parameter.

Two-dimensional type-II Dirac fermions in layered oxides

Relativistic massless Dirac fermions can be probed with high-energy physics experiments, but appear also as low-energy quasi-particle excitations in electronic band structures. In condensed matter systems, their massless nature can be protected by crystal symmetries. Classification of such symmetry-protected relativistic band degeneracies has been fruitful, although many of the predicted quasi-particles still await their experimental discovery. Here we reveal, using angle-resolved photoemission spectroscopy, the existence of two-dimensional type-II Dirac fermions in the high-temperature superconductor La_1.77Sr_0.23CuO₄. The Dirac point, constituting the crossing of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{x^2 - y^2}$$\end{document}dx2-y2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{z^2}$$\end{document}dz2 bands, is found approximately one electronvolt below the Fermi level (E_F) and is protected by mirror symmetry. If spin-orbit coupling is considered, the Dirac point degeneracy is lifted and the bands acquire a topologically non-trivial character. In certain nickelate systems, band structure calculations suggest that the same type-II Dirac fermions can be realised near E_F.

Many predicted topological quasi-particles still await experimental discovery. Here, Horio et al. reveal the existence of two-dimensional type-II Dirac fermions in the high-temperature superconductor La_1.77Sr_0.23CuO₄, promoting layered oxides as promising topological materials.

Dirac semimetal in β-CuI without surface Fermi arcs

Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict that β-cuprous iodide (β-CuI) is a peculiar DSM whose surface states form closed Fermi pockets instead of Fermi arcs. In such a fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to Fermi pockets stems from a large cubic term preserving all crystal symmetries and from the small energy difference between the surface and bulk Dirac points. The cubic term in β-CuI, usually negligible in prototypical DSMs, becomes relevant because of the particular crystal structure. As such, we establish a concrete material example manifesting the lack of topological protection for surface Fermi arcs in DSMs.

Band Structure Perfection and Superconductivity in Type-II Dirac Semimetal Ir1-x Ptx Te2

The discovery of a new type-II Dirac semimetal in Ir_1-x Pt_x Te₂ with optimized band structure is described. Pt dopants protect the crystal structure holding the Dirac cones and tune the Fermi level close to the Dirac point. The type-II Dirac dispersion in Ir_1-x Pt_x Te₂ is confirmed by angle-resolved photoemission spectroscopy and first-principles calculations. Superconductivity is also observed and persists when the Fermi level aligns with the Dirac points. Ir_1-x Pt_x Te₂ is an ideal platform for further studies on the exotic properties and potential applications of type-II DSMs, and opens up a new route for the investigation of the possible topological superconductivity and Majorana physics.

Galvanomagnetic properties of the putative type-II Dirac semimetal PtTe2

Platinum ditelluride has recently been characterized, based on angle-resolved photoemission spectroscopy data and electronic band structure calculations, as a possible representative of type-II Dirac semimetals. Here, we report on the magnetotransport behavior (electrical resistivity, Hall effect) in this compound, investigated on high-quality single-crystalline specimens. The magnetoresistance (MR) of PtTe₂ is large (over 3000% at T = 1.8 K in B = 9 T) and unsaturated in strong fields in the entire temperature range studied. The MR isotherms obey a Kohler’s type scaling with the exponent m = 1.69, different from the case of ideal electron-hole compensation. In applied magnetic fields, the resistivity shows a low-temperature plateau, characteristic of topological semimetals. In strong fields, well-resolved Shubnikov – de Haas (SdH) oscillations with two principle frequencies were found, and their analysis yielded charge mobilities of the order of 10³ cm² V⁻¹ s⁻¹ and rather small effective masses of charge carriers, 0.11 m_e and 0.21 m_e. However, the extracted Berry phases point to trivial character of the electronic bands involved in the SdH oscillations. The Hall effect data corroborated a multi-band character of the electrical conductivity in PtTe₂, with moderate charge compensation.

Inducing Strong Superconductivity in WTe2 by a Proximity Effect

The search for proximity-induced superconductivity in topological materials has generated widespread interest in the condensed matter physics community. The superconducting states inheriting nontrivial topology at interfaces are expected to exhibit exotic phenomena such as topological superconductivity and Majorana zero modes, which hold promise for applications in quantum computation. However, a practical realization of such hybrid structures based on topological semimetals and superconductors has hitherto been limited. Here, we report the strong proximity-induced superconductivity in type-II Weyl semimetal WTe₂, in a van der Waals hybrid structure obtained by mechanically transferring NbSe₂ onto various thicknesses of WTe₂. When the WTe₂ thickness ( t_WTe2) reaches 21 nm, the superconducting transition occurs around the critical temperature ( T_c) of NbSe₂ with a gap amplitude (Δ_p) of 0.38 meV and an unexpected ultralong proximity length ( l_p) up to 7 μm. With the thicker 42 nm WTe₂ layer, however, the proximity effect yields T_c ≈ 1.2 K, Δ_p = 0.07 meV, and a short l_p of less than 1 μm. Our theoretical calculations, based on the Bogoliubov-de Gennes equations in the clean limit, predict that the induced superconducting gap is a sizable fraction of the NbSe₂ superconducting one when t_WTe2 is less than 30 nm and then decreases quickly as t_WTe2 increases. This agrees qualitatively well with the experiments. Such observations form a basis in the search for superconducting phases in topological semimetals.

Type-II Dirac Photons at Metasurfaces

Topological characteristics of energy bands, such as Dirac and Weyl nodes, have attracted substantial interest in condensed matter systems as well as in classical wave systems. Among these energy bands, the type-II Dirac point is a nodal degeneracy with tilted conical dispersion, leading to a peculiar crossing dispersion in the constant-energy plane. Such nodal points have recently been found in electronic materials. The analogous topological feature in photonic systems remains a theoretical curiosity, with experimental realization expected to be challenging. Here, we experimentally realize the type-II Dirac point using a planar metasurface architecture, where the band degeneracy point is protected by the underlying mirror symmetry of the metasurface. Gapless edge modes are found and measured at the boundary between the different domains of the symmetry-broken metasurface. Our Letter shows that metasurfaces are simple and practical platforms for realizing electromagnetic type-II Dirac points, and their planar structure is a distinct advantage that facilitates applications in two-dimensional topological photonics.

Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

k paths exactly with [Formula: see text] symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe₂ family materials also have the [Formula: see text] spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and [Formula: see text] method, we predict that PtSe₂ family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe₂ family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.

Bulk Fermi Surfaces of the Dirac Type-II Semimetallic Candidates MAl_{3} (Where M=V, Nb, and Ta)

We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates MAl_{3} (where, M=V, Nb and Ta). The angular dependence of their Fermi surface (FS) cross-sectional areas reveals a remarkably good agreement with our first-principles calculations. Therefore, dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level ϵ_{F} for VAl_{3}, NbAl_{3} and TaAl_{3} respectively, in agreement with the prediction of broken Lorentz invariance in these compounds. However, for all three compounds we find that the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We explain this via an analysis of the Berry phase where the position of this orbit, relative to the Dirac node, is adjusted within the error implied by the small disagreement between our calculations and the experiments. We suggest that a very small amount of doping could displace ϵ_{F} to produce topologically nontrivial orbits encircling their Dirac node(s).

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle-resolved photoemission, we find that these generically host a co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

From Type-II Triply Degenerate Nodal Points and Three-Band Nodal Rings to Type-II Dirac Points in Centrosymmetric Zirconium Oxide

Using first-principles calculations, we report that ZrO is a topological material with the coexistence of three pairs of type-II triply degenerate nodal points (TNPs) and three nodal rings (NRs), when spin-orbit coupling (SOC) is ignored. Noticeably, the TNPs reside around the Fermi energy with a large linear energy range along the tilt direction (>1 eV), and the NRs are formed by three strongly entangled bands. Under symmetry-preserving strain, each NR would evolve into four droplet-shaped NRs before fading away, producing distinct evolution compared with that in usual two-band NR. When SOC is included, TNPs would transform into type-II Dirac points while all of the NRs are gapped. Remarkably, the type-II Dirac points inherit the advantages of TNPs: residing around the Fermi energy and exhibiting a large linear energy range. Both features facilitate the observation of interesting phenomena induced by type-II dispersion. The symmetry protections and low-energy Hamiltonian for the nontrivial band crossings are discussed.