Observation of the topological surface state in the nonsymmorphic topological insulator KHgSb

Abstract

, KHgX are insulating in the bulk but possess robust gapless surface states (see Fig. 1a), forming the unique "hourglass Fermions"on the (010) surface. The surface fermion contains four branches (quadruplets) dispersions and unbreakable zigzag chain-like patterns 49 (Fig. 1b). These surface states can also be understood as two copies of surface states of weak topological insulators 53 . The nonsymmorphic glide mirror protects these two copies from annihilating with each other inside the mirror plane. In order to visualize the intriguing hourglass fermion surface states and confirm the nonsymmorphic topological insulator nature of KHgX, ARPES is the natural experimental tool.In this work, we report comprehensive ARPES study on the electronic structures of KHgSb on both (001) and (010) Basic information of KHgSbHigh quality KHgSb crystals was synthesized by the flux method (see Appendix for details).The crystal structure of KHgSb is shown in Fig. 1c with space group P63/mmc and the lattice constants a=b=4.78 Å , c=10.225 Å . The in-plane Hg and Sb atoms show strong bonding, forming in-plane honeycomb lattices. The off-plane K atoms sit above the center of each honeycomb, sandwiched loosely by the two adjacent layers and serve as their inversion center.The natural cleavage surface is along the (001) and (010) surface (parallel to the diagonal of the in-plane honeycomb and preserves the glide reflection). The bulk Brillouin zone (BZ) and the surface BZs of both (001) and (010) surfaces are shown in Fig. 1d. Fig. 1e, f illustrate the broad Fermi surface mapping across multiple BZs on the (001) and (010) surfaces, respectively, confirming the cleavage surfaces with correct lattice parameters (the momentum direction of kx is defined along Γ − X; ky along Γ ̅ − K ̅ and kz along Γ − Z, respectively, see Fig. 1d). The core level photoemission spectra (Fig. 1g) show sharp characteristic Sb4d, K3p and Hg5d levels. The electronic structures on the (001) surfaceWe first focus on the electronic structures on the (001) According to the band structure calculation 49, KHgSb is a fully gapped nonsymmorphic crystalline topological insulator with no surface states residing on the (001) surfaces. In order to prove this, we tuned the Fermi surface by introducing potassium atoms in situ onto the sample surface so that the absorbed potassium atoms on the surface would donate free electrons.After K-dosing, we could clearly observe the bottom of the conduction band and the top of the valence band simultaneously along both (Fig. 2g(i)-(ii)). An indirect band gap of ~200 meV is observed with no signatures of in-gap surface states (Fig. 2h), agreeing with the calculations (Fig. 2e). The electronic structures on the (010) surfaceNext we demonstrate the detailed electronic structure on the (010) surface in Figure 3. Fig. 3a shows the stacking CECs. After inspecting CECs ranging from Eb=0~400meV, one could observe (see Fig. 3a,b) the quasi-one-dimensional Fermi surface disperses into two pieces when going to higher binding energies until ...

A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb

“…S15). Moreover, photoemission [12,13] and ab initio band calculations do not see 3 bands. In addition, we distinguish our results from the anomalous Hall effect [19] in ferromagnets and conventional semimetals (see Sec.…”

“…Hall measurements in a field B ẑ, with current in the x-y plane can detect the QSH states, provided the chemical potential µ lies inside the bulk gap. (Our measurements do not couple to the hourglass modes [12,13] because they disperse alongΓZ with v g ẑ. )We report results from two batches of crystals (Supplementary Secs.…”

Z4 Topological Superconductivity in UCoGe

“…In this Letter, we propose that UCoGe under pressure may be a Z 4 nontrivial TNCS. In the context of topological insulators, such Z 4 nontrivial phases have already been proposed [62,63], and experimental implication has recently been reported [76,77]. However, its counterpart in superconductors has remained unknown, although Z 2 nontrivial glide-even TNCS has been proposed in the Aphase of UPt 3 [51].…”

Acoustic Möbius insulators from projective symmetry

“…The Möbius twisted boundary states were predicted in fractional Josephson effect 16,24 , KHgX (X = As, Sb, Bi) 25 , Kondo insulators (CeXSn with X = Ni, Rh, Ir) 26 , and axion insulators (MnBi2nTe3n+1) 20 . However, they have been elusive in experiment to date [27][28][29] . For the first time, we provide compelling experimental evidence for the Möbius edge and hinge states in position, momentum, energy, and phase domains.…”