Related papers: Octupole topological insulating phase in Brillouin…
The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane ($\mathrm{RP}^2$) and the appearance of quadrupole…
Recent theoretical studies have extended the Berry phase framework to account for higher electric multipole moments, quadrupole and octupole topological phases have been proposed. Although the two-dimensional quantized quadrupole insulators…
The Berry phase associated with energy bands in crystals can lead to quantized quantities, such as the quantization of electric dipole polarization in an insulator, known as a one-dimensional (1D) topological insulator (TI) phase. Recent…
Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice…
We report high pressure studies of the structural stability of Ru2Sn3, a new type of three dimensional topological insulator (3D-TI) with unique quasi-one dimensional Dirac electron states throughout the surface Brillouin zone of its…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
The manifold of the fundamental domain of the Brillouin zone is always considered to be a torus. However, under the synthetic gauge field, the Brillouin manifold can be modified by the projective symmetries, resulting in unprecedented…
Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional (2D) quadrupole and…
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order…
In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a…
We describe a three-dimensional crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat…
We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional…
Three dimensional (3D) third-order topological insulators (TIs) have zero-dimensional (0D) corner states, which are three dimensions lower than bulk. Here we investigate the third-order TIs on breathing pyrochlore lattices with p-orbital…
Three-dimensional (3D) two-band Hopf insulators are a paradigmatic example of topological phases beyond the topological classifications based on powerful methods like $K$-theory and symmetry indicators.Since this class of topological…
One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…
Topological quantum phase transition in electron gas systems is an enthralling phenomena. This phase transition has a unique property in that it is associated with a quantum phase transition point, which separates different regions with…
Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…