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Register a new userDiscovery of ^C$_2$ rotation anomaly in topological crystalline insulator SrPb
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Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries ^C$_n$, which have surface rotation anomaly evading the fermion doubling theorem, i.e. n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the ^C$_2$ rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry ^T and ^C$_{2y}$ on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the ^C$_2$ rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behaviour of the new classes of TCIs.
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Based on first-principles calculations and symmetry-based indicator analysis, we find a class of topological crystalline insulators (TCIs) with $C_2$ rotation anomaly in a family of Zintl compounds, including $mathrm{Ba}_{3}mathrm{Cd}_{2}mathrm{As}_{4}$, $mathrm{Ba}_{3}mathrm{Zn}_{2}mathrm{As}_{4}$ and $mathrm{Ba}_{3}mathrm{Cd}_{2}mathrm{Sb}_{4}$. The nontrivial band topology protected by coexistence of $C_2$ rotation symmetry and time-reversal symmetry $T$ leads to two surface Dirac cones at generic momenta on both top and bottom surfaces perpendicular to the rotation axis. In addition, ($d-2$)-dimensional helical hinge states are also protected along the hinge formed by two side surfaces parallel with the rotation axis. We develop a method based on Wilson loop technique to prove the existence of these surface Dirac cones due to $C_2$ anomaly and precisely locate them as demonstrated in studying these TCIs. The helical hinge states are also calculated. Finally, we show that external strain can be used to tune topological phase transitions among TCIs, strong Z$_2$ topological insulators and trivial insulators.
Recent theoretical advances have proposed a new class of topological crystalline insulator (TCI) phases protected by rotational symmetries. Distinct from topological insulators (TIs), rotational symmetry-protected TCIs are expected to show unique topologically protected boundary modes: First, the surface normal to the rotational axis features unpinned Dirac surface states whose Dirac points are located at generic k points. Second, due to the higher-order bulk boundary correspondence, a 3D TCI also supports 1D helical edge states. Despite the unique topological electronic properties, to date, purely rotational symmetry-protected TCIs remain elusive in real materials. Using first-principles band calculations and theoretical modeling, we identify the van der Waals material $alpha$-Bi4Br4 as a TCI purely protected by rotation symmetry. We show that the Bi4Br4s (010) surface exhibits a pair of unpinned topological Dirac fermions protected by the two-fold rotational axis. These unpinned Dirac fermions show an exotic spin texture highly favorable for spin transport and a band structure consisting of van Hove singularities due to Lifshitz transition. We also identify 1D topological hinge states along the edges of an $alpha$-Bi4Br4 rod. We further discuss how the proposed topological electronic properties in $alpha$-Bi4Br4 can be observed by various experimental techniques.
A new class of materials, Topological Crystalline Insulators (TCIs) have been shown to possess exotic surface state properties that are protected by mirror symmetry. These surface features can be enhanced if the surface-area-to-volume ratio of the material increases, or the signal arising from the bulk of the material can be suppressed. We report the experimental procedures to obtain high quality crystal boules of the TCI, SnTe, from which nanowires and microcrystals can be produced by the vapour-liquid-solid (VLS) technique. Detailed characterisation measurements of the bulk crystals as well as of the nanowires and microcrystals produced are presented. The nanomaterials produced were found to be stoichiometrically similar to the source material used. Electron back-scatter diffraction (EBSD) shows that the majority of the nanocrystals grow in the vicinal {001} direction to the growth normal. The growth conditions to produce the different nanostructures of SnTe have been optimised.
Topological insulators (TIs) host novel states of quantum matter, distinguished from trivial insulators by the presence of nontrivial conducting boundary states connecting the valence and conduction bulk bands. Up to date, all the TIs discovered experimentally rely on the presence of either time reversal or symmorphic mirror symmetry to protect massless Dirac-like boundary states. Very recently, it has been theoretically proposed that several materials are a new type of TIs protected by nonsymmorphic symmetry, where glide-mirror can protect novel exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of such new nonsymmorphic TI (NSTI) is still missing. Using angle-resolved photoemission spectroscopy, we reveal that such hourglass topology exists on the (010) surface of crystalline KHgSb while the (001) surface has no boundary state, which is fully consistent with first-principles calculations. We thus experimentally demonstrate that KHgSb is a NSTI hosting hourglass fermions. By expanding the classification of topological insulators, this discovery opens a new direction in the research of nonsymmorphic topological properties of materials.
We show that in the presence of $n$-fold rotation symmetries and time-reversal symmetry, the number of fermion flavors must be a multiple of $2n$ ($n=2,3,4,6$) on two-dimensional lattices, a stronger version of the well-known fermion doubling theorem in the presence of only time-reversal symmetry. The violation of the multiplication theorems indicates anomalies, and may only occur on the surface of new classes of topological crystalline insulators. Put on a cylinder, these states have $n$ Dirac cones on the top and on the bottom surfaces, connected by $n$ helical edge modes on the side surface.
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