We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution v_F(k_F) of tungsten. The 4D spectral function ρ(E_B; k) in the entire bulk Brillouin zone and 6 eV binding-energy (E_B) 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.

中文翻译：

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费米表面和费米速度的直接3D映射

我们对包括费米表面和钨的费米速度分布v _F（k _F）的体电子结构进行了完整的映射。得益于新的多维光发射数据记录技术（结合全场k），在约3小时内获得了整个布里渊区的4D光谱函数ρ（E _B ; k）和6  eV结合能（E _B）区间。 显微镜，具有飞行时间并行能量记录）和所用软X射线的高亮度。直接比较体和表面光谱函数（在低光子能量下拍摄）揭示了（110）投影体带结构中局部带隙的时间反转不变表面状态。表面状态连接空穴和电子袋，否则它们将被间接的局部带隙分开。我们通过自旋滤波动量成像确认了其类似Dirac的自旋纹理。所测量的4D数据阵列可通过简单的算法（无需近​​似值）提取所有波段，所有能量等值面，电子速度，空穴或电子电导率，有效质量和内部电势的3D色散。