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 coexistence 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.The classification of electronic structures based on their topological properties has opened powerful routes for understanding solid state materials. 1 The nowfamiliar Z 2 topological insulators are most renowned for their spin-polarised Dirac surface states residing in inverted bulk band gaps. 1 In systems with rotational invariance, a band inversion on the rotation axis can generate protected Dirac cones with a point-like Fermi surface of the bulk electronic structure. 2-8 If either inversion or time-reversal symmetry is broken, a bulk Dirac point can split into a pair of spin-polarised Weyl points. 9-15 Unlike for elementary particles, Lorentz-violating Weyl fermions can also exist in the solid state, manifested as a tilting of the Weyl cone. If this tilt is sufficiently large, so-called type-II Weyl points can occur, now formed at the touching of open electron and hole pockets. [15][16][17][18][19][20][21][22] Realising such phases in solid-state materials not only offers unique environments and opportunities for studying the fundamental properties of fermions, but also holds potential for applications exploiting their exotic surface excitations and bulk electric and thermal transport properties. [23][24][25][26][27] Consequently, there is an intense current effort focused on identifying compounds which host the requisite band inversions. In many cases, however, this arXiv:1702.08177v2 [cond-mat.mtrl-sci]

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.

Engineering and enhancing inversion symmetry breaking in solids is a major goal in condensed matter physics and materials science, as a route to advancing new physics and applications ranging from improved ferroelectrics for memory devices to materials hosting Majorana zero modes for quantum computing. Here, we uncover a new mechanism for realising a much larger energy scale of inversion symmetry breaking at surfaces and interfaces than is typically achieved. The key ingredient is a pronounced asymmetry of surface hopping energies, i.e. a kinetic energy-driven inversion symmetry breaking, whose energy scale is pinned at a significant fraction of the bandwidth. We show, from spin-and angle-resolved photoemission, how this enables surface states of 3d and 4d-based transition-metal oxides to surprisingly develop some of the largest Rashba-like spin splittings that are known. Our findings open new possibilities to produce spin textured states in oxides which exploit the full potential of the bare atomic spin-orbit coupling, raising exciting prospects for oxide spintronics. More generally, the core structural building blocks which enable this are common to numerous materials, providing the prospect of enhanced inversion symmetry breaking at judiciously-chosen surfaces of a plethora of compounds, and suggesting routes to interfacial control of inversion symmetry breaking in designer heterostructures.The lifting of inversion symmetry is a key prerequisite for stabilising a wide range of striking physical properties such as chiral magnetism, ferroelectricity, odd-parity multipolar orders, and the creation of Weyl fermions and other spin-split electronic states without magnetism [1][2][3][4][5][6][7] . Inversion symmetry is naturally broken at surfaces and interfaces of materials, opening exciting routes to stabilise electronic structures distinct from those of the bulk [8][9][10][11][12][13][14][15] . A striking example is found in materials which also host significant spin-orbit interactions, where inversion symmetry breaking (ISB) underpins the formation of topologically-protected surface states 11,16 and Rashba 10,17 spin splitting of surface or interfacelocalised two-dimensional electron gases 14,15,[18][19][20][21][22] , generically characterised by a locking of the quasiparticle spin perpendicular to its momentum. Such effects lie at the heart of a variety of proposed applications in spin-based electronics 10,[23][24][25][26][27] , and provide new routes to stabilise novel physical regimes such as spiral RKKY interactions, enhanced electron-phonon coupling, localisation by a weak potential, large spin-transfer torques, and mixed singlet-triplet superconductivity [28][29][30][31][32][33][34][35] . Conventional wisdom about how to maximize the Rashba effect has been to work with heavy elements whose atomic spin-orbit coupling is large. However, the energetic spin splittings obtained are usually only a small fraction of the atomic spin-orbit energy scale. This is because the key physics is not exclusively that of spi...