Fig. 4

Non-symmorphic effect on a floating band surface state. a Schematics depicting the anomalous Umklapp process derived from the non-symmorphic P4/nmm group. The blue square surrounds the first surface BZ of ZrSiSe(001), in which only the floating band surface state contours are presented. Q₁ and Q₂ label two dominate scattering vectors. G_x and G_y represent the reciprocal unit vectors. Normal scattering (Q₁) and Umklapp scatterings (Q₁ + G_x, and Q₁ + G_y) are expected to generate the same shapes of QPI patterns in a conventional system with C_4v symmetry. b Sketch (not to scale) highlighting the QPI features which arising only from the floating band. The artificially added red dots in b, d–f mark Bragg points. The vectors Q₁, Q₂, G_x, and G_y are defined the same way and in the same directions as in a, but with different lengths. The central square (denoted by Q₁ and Q₂) originates from normal scatterings, while the double arcs near Bragg points are induced by Umklapp scatterings. Note the feature at Q₁ + G_y is absent, which leads to the half-missing anomalous Umklapp process. c The measured C_4v s-QPI pattern at 400 meV. d (e) is the simulated s-QPI pattern derived from a Zr vacancy by allowing (forbidding) inter-BZ scatterings without considering the non-symmorphic effect. f is same as e but with considering the non-symmorphic effect. From this, it appears that only f reproduces c, especially the half-missing Umklapp process. The \(\left( {\left. {M_z} \right|\frac{1}{2}\frac{1}{2}0} \right)\) symmetry leads to an extension of the first BZ (purple dotted square in a). This non-symmorphic effect naturally induces the half-missing Umklapp interference