¦ van der Waals gap Septuple layer J § J || T 1/2 J 0,1 || J 0,2 || J 0,3 || J 0,4 ||

We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution v(k) of tungsten. The 4D spectral function ρ(E; k) in the entire bulk Brillouin zone and 6 eV binding-energy (E) interval was acquired in ∼3 h thanks to a new multidimensional photoemission data-recording technique (combining full-field k-microscopy with time-of-flight parallel energy recording) and the high brilliance of the soft X-rays used. A direct comparison of bulk and surface spectral functions (taken at low photon energies) reveals a time-reversal-invariant surface state in a local bandgap in the (110)-projected bulk band structure. The surface state connects hole and electron pockets that would otherwise be separated by an indirect local bandgap. We confirmed its Dirac-like spin texture by spin-filtered momentum imaging. The measured 4D data array enables extraction of the 3D dispersion of all bands, all energy isosurfaces, electron velocities, hole or electron conductivity, effective mass and inner potential by simple algorithms without approximations. The high-Z bcc metals with large spin-orbit-induced bandgaps are discussed as candidates for topologically non-trivial surface states.

The layered van der Waals antiferromagnet MnBi2Te4 has been predicted to combine the band ordering of archetypical topological insulators like Bi2Te3 with the magnetism of Mn, making this material a viable candidate for the realization of various magnetic topological states. We have systematically investigated the surface electronic structure of MnBi2Te4(0001) single crystals by use of spin-and angle-resolved photoelectron spectroscopy (ARPES) experiments. In line with theoretical predictions, the results reveal a surface state in the bulk band gap and they provide evidence for the influence of exchange interaction and spin-orbit coupling on the surface electronic structure.The hallmark of a topological insulator is a single spinpolarized Dirac cone at the surface which is protected by time reversal-symmetry and originates from a band inversion in the bulk [1,2]. Notably, breaking time-reversal symmetry by magnetic order does not necessarily destroy the non-trivial topology but instead may drive the system into another topological phase. One example is the quantum anomalous Hall (QAH) state that has been observed in magnetically doped topological insulators [3]. The QAH state, in turn, may form the basis for yet more exotic electronic states, such as axion insulators [4,5] and chiral Majorana fermions [6]. Another example is the antiferromagnetic topological insulator state which is protected by a combination of time-reversal and lattice translational symmetries [7].Magnetic order in a topological insulator has mainly been achieved by doping with 3d impurities [3,8], which however inevitably gives rise to increased disorder. By contrast, the layered van der Waals material MnBi 2 Te 4 [9, 10] has recently been proposed to realize an intrinsic magnetic topological insulator [11][12][13][14], i.e. a compound that features magnetic order and a topologically non-trivial bulk band structure at the arXiv:1903.11826v2 [cond-mat.str-el]

Typical Kondo insulators (KIs) can have a nontrivial Z_{2} topology because the energy gap opens at the Fermi energy (E_{F}) by a hybridization between odd- and even-parity bands. SmB_{6} deviates from such KI behavior, and it has been unclear how the insulating phase occurs. Here, we demonstrate that charge fluctuations are the origin of the topological insulating phase in SmB_{6}. Our angle-resolved photoemission spectroscopy results reveal that with decreasing temperature the bottom of the d-f hybridized band at the X[over ¯] point, which is predicted to have odd parity and is required for a topological phase, gradually shifts from below to above E_{F}. We conclude that SmB_{6} is a charge-fluctuating topological insulator.