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Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Satos complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys. Rev. B {bf 90}, 165114 (2014)], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.
We identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy Fermi arcs at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hi
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten
We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of higher-order topological insulators and superconductors which possess surface states that propagate alo
We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-pa
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity.