2018
DOI: 10.1126/science.aan2802
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Wallpaper fermions and the nonsymmorphic Dirac insulator

Abstract: Materials whose gapless surface states are protected by crystal symmetries include mirror topological crystalline insulators and nonsymmorphic hourglass insulators. There exists only a very limited set of possible surface crystal symmetries, captured by the 17 "wallpaper groups." Here we show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples. In … Show more

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Cited by 175 publications
(198 citation statements)
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“…If the bulk is insulating, in rare cases the bulk bands can be connected in a special way that forces surface states to appear, which are topological. 200 There are a few cases of such nonsymmorphic topological insulators, but only one, exhibiting the "hourglass" surfaces state 201 (called this way because it is shaped like an hourglass), has been seen experimentally. 202 Semimetals that are nonsymmorphic can also show surface states: ZrSiS and related materials all show very prominent surface states in their ARPES spectra.…”
Section: Surface Statesmentioning
confidence: 99%
“…If the bulk is insulating, in rare cases the bulk bands can be connected in a special way that forces surface states to appear, which are topological. 200 There are a few cases of such nonsymmorphic topological insulators, but only one, exhibiting the "hourglass" surfaces state 201 (called this way because it is shaped like an hourglass), has been seen experimentally. 202 Semimetals that are nonsymmorphic can also show surface states: ZrSiS and related materials all show very prominent surface states in their ARPES spectra.…”
Section: Surface Statesmentioning
confidence: 99%
“…In this work, we propose that the surface states of ZrSiS are not derived from the nonsymmorphic bulk band topology, such as hourglass [36] and Dirac [37] surface states, nor are they due to a structural surface modification, but instead are the result of a reduced symmetry at the surface.…”
Section: Introductionmentioning
confidence: 99%
“…Following the discoveries of time-reversal symmetry-protected Z 2 topological insulator states in both 2D and 3D [1][2][3], intensive efforts have been devoted to searching for new types of topological band insulators protected by crystal symmetries, or topological crystalline insulators (TCI) [4]. Although the large number of crystalline space group symmetries suggests the possibility of a wealth of TCI states, for a long time, the theoretically known TCIs were largely limited to crystals with mirror reflections [4][5][6][7] and glide mirror reflections [8,9], such as the SnTe family of IV-VI semiconductors [10][11][12][13][14][15][16][17][18].…”
mentioning
confidence: 99%