The Benalcazar-Bernevig-Hughes(BBH) model is one of the most representative higher-order topological insulators with different bulk-edge correspondence comparing conventional topological states. In this work, we propose to realize a couple-BBH model with glide reflection symmetry by coupling two topologically distinct BBH models. Such a system gives rise to intriguing properties beyond the traditional BBH model. A topological phase transition from higher-order topological phase to a semimetal has been predicted in this system. Furthermore, the band crossing points and nodal ring protected by glide reflection symmetry has also been explored. Our work provides a viewpoint to demonstrate the versatile phenomena induced by the interplay between higher-order topology and nonsymmorphic symmetries.
We study the topological crystalline insulator phase protected by the glide symmetry, which is characterized by the Z2 topological number. In the present paper, we derive a formula for the Z2 topological invariant protected by glide symmetry in a nonprimitive lattice, from that in a primitive lattice. We establish a formula for the glide-Z2 invariant for the space group No. 9 with glide symmetry in the base-centered lattice, by folding the Brillouin zone into that of the primitive lattice where the formula for the glide-Z2 invariant is known. The formula is written in terms of integrals of the…
It is known that three-dimensional magnetic systems with glide symmetry can be characterized by a $Z_2$ topological invariant together with the Chern number associated with the normal vector of the glide plane, and they are expressed in terms of integrals of the Berry curvature. In the present paper, we study the fate of this topological invariant when inversion symmetry is added while time-reversal symmetry is not enforced. There are two ways to add inversion symmetry, leading to space groups No.~13 and No.~14. In space group No.~13, we find that the glide-$Z_2$ invariant is expressed solely …
We propose a systematic way of constructing Floquet second-order topological insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time symmetry that is unique in Floquet systems. In particular, we are able to show that the static enlarged Hamiltonian in the frequency domain acquires the reflection symmetry, which is inherited from the time-glide symmetry of the original system. As a consequence, one can construct a variety of time-glide symmetric Floquet SOTIs using the knowledge of static SOTIs. Moreover, the time-glide symmetry only needs to be implemented approximately in …
Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of topological materials have led us to a new paradigm in surface science, and one can expect that topological surface states may affect surface energies and crystal facets in an unconventional way. Here we show that the surface energy of glide-symmetric topological crystalline insulators (TCI) depends on the surface orientation in a singular way via the parity of the Mi…
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
We theoretically demonstrate that a ferromagnetic/superconductor junction on the surface of three-dimensional topological insulators (3D TIs) has an anisotropic angle-dependent Andreev reflection when the in-plane magnetization has a component perpendicular to the junction. In the presence of in-plane magnetization, the Dirac cone's location adjusts in the $k$-space, whereas its out-of-plane component induces a gap. This movement leads to the anisotropic angle-dependent Andreev reflection and creates transverse conductance flows parallel to the interface. Also, an indirect gap induces in the j…
Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic ban…
Traditional ionic/covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum hall effect systems, do not typically display such a commensuration. Tnstead, they can undergo a phase transition to a trivial insulator that preserves the electron filling. Nevertheless, in some crystalline insulators, termed filling-enforced quantum band insulators (feQBIs), electron filling can dictate nontrivial topology in the insulating ground state. Currently, little is known about the relation bet…
Superconducting proximity junctions made of topological insulator (TI) nanoribbons (NRs) provide a useful platform for studying topological superconductivity. We report on the fabrication and measurement of Josephson junctions (JJs) using Sb doped Bi$_2$Se$_3$ NRs in contact with Al electrodes. Aharonov$-$Bohm and Altshuler$-$Aronov$-$Spivak oscillations of the axial magneto-conductance of TI NR were observed, indicating the existence of metallic surface states along the circumference of the TI NR. We observed the supercurrent in the TI NR JJ and subharmonic gap structures of the differential …
In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase supporting a single chiral edge state. We show that as the system de-magnetizes, disorder from randomly oriented magnetic moments can produce a `quantum anomalous parity Hall' phase with \emph{helical} edge modes protected by a unitary reflection symmetry. We further show that introducing superconductivity, combined with selective breaking of reflection symmetry by a gate, allows for creation and manipulation of Majorana zero modes via purely electrical means and at ze…
Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach
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