Understanding and control of spin degrees of freedom on the surfaces of topological materials are the key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi 2 Se 3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies which directly demonstrates the mechanics of timereversal symmetry breaking on the surface. We further show that an insulating gap induced by quantum tunneling between surfaces exhibits spin texture modulation at low energies but respects time-reversal invariance. These spin phenomena and the control of their Fermi surface geometrical phase first demonstrated in our experiments pave the way for future realization of many predicted exotic magnetic phenomena of topological origin.Since the discovery of three dimensional topological insulators [1][2][3][4][5], topological order proximity to ferromagnetism has been considered as one of the core interests of the field [6][7][8][9][10][11][12][13][14][15][16]. Such interest is strongly motivated by the proposed time-reversal (TR) breaking topological physics such as quantized anomalous chiral Hall current, spin current, axion electrodynamics, and inverse spin-galvanic effect [9][10][11][12], all of which critically rely on finding a way to break TR symmetry on the surface and utilize the unique TR broken spin texture for applications. Since quantum coherence is essential in many of these applications, devices need to be engineered into thin films in order to enhance or de-enhance surface-tosurface coupling or the quantum tunneling of the electrons. The experimental spin behavior of surface states under the two extreme limits, namely the doped magnetic groundstate and ultra-thin film quantum tunneling groundstate, is thus of central importance to the entire field. However, surprisingly, it is not known what happens to the spin configuration under these extreme conditions relevant for device fabrications. Fundamentally, TR symmetry is inherently connected to the Kramers' degeneracy theorem which states that when TR symmetry is preserved, the electronic states at the TR invariant momenta have to remain doubly spin degenerate. Therefore, the establishment of TR breaking effect fundamentally requires measurements of electronic groundstate with a spin-sensitive probe. Here we utilize spin-3 resolved angle-resolved photoemission spectroscopy to measure the momentum space spin configurations in systematically magnetically doped, non-magnetically doped, and ultra-thin quantum coherent topological insulator films [17], in order to understand the nature of electronic groundstates under two extreme limits vital for magnetic topological devices. These measurements allow us to make definitive conclusions regarding magnetism on to...

Methods to generate spin-polarised electronic states in non-magnetic solids are strongly desired to enable all-electrical manipulation of electron spins for new quantum devices. 1 This is generally accepted to require breaking global structural inversion symmetry. [1][2][3][4][5] In contrast, here we present direct evidence from spin-and angleresolved photoemission spectroscopy for a strong spin polarisation of bulk states in the centrosymmetric transition-metal dichalcogenide WSe 2 . We show how this arises due to a lack of inversion symmetry in constituent structural units of the bulk crystal where the electronic states are localised, leading to enormous spin splittings up to ∼ 0.5 eV, with a spin texture that is strongly modulated in both real and momentum space. As well as providing the first experimental evidence for a recently-predicted 'hidden' spin polarisation in inversion-symmetric materials, 6 our study sheds new light on a putative spin-valley coupling in transition-metal dichalcogenides, 7-9 of key importance for using these compounds in proposed valleytronic devices.The powerful combination of inversion symmetryensures that electronic states of non-magnetic centrosymmetric materials must be doubly spin-degenerate. If inversion symmetry is broken, however, relativistic spin-orbit interactions can induce a momentum-dependent spin splitting via an effective magnetic field imposed by spatially-varying potentials. If the * To whom correspondence should be addressed: philip.king@standrews.ac.uk resulting spin polarisations can be controllably created and manipulated, they hold enormous promise to enable a range of new quantum technologies. These include routes towards electrical control of spin precession for spin-based electronics, 1,10 new ways to engineer topological states 11,12 and possible hosts of Majorana fermions for use in quantum computation. 5 To date, there are two generally-accepted categories of materials in which spinpolarised states can be stabilised without magnetism. The first exploits the breaking of structural inversion symmetry of a centrosymmetric host by imposing an electrostatic potential gradient, for example within an asymmetric quantum well, leading to Rashba-split 13 states localised at surfaces or interfaces. [14][15][16][17] In the second, a lack of global inversion symmetry in the unit cell mediates spin splitting of the bulk electronic states, either through a Dresselhaus-type interaction, 18 or a recently discovered bulk form of the Rashba effect. 4,19 Here, we present the first experimental observation of a third distinct class: a material which has bulk inversion symmetry but nonetheless exhibits a large spin polarisation of its bulk electronic states. We demonstrate this for the transition-metal dichalcogenide 2H-WSe 2 . This layered compound is composed of stacked Se-W-Se planes (Fig. 1(a)), each of which contains an in-plane net dipole moment which is proposed to lead to a strong spin-valley coupling for an isolated monolayer. 7,8,20 The bulk unit cell contains two s...

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]