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Higher order topological insulators are a new class of topological insulators in dimensions $\rm d>1$. These higher-order topological insulators possess $\rm (d - 1)$-dimensional boundaries that, unlike those of conventional topological…
Acoustic traps are used to capture and handle suspended microparticles and cells in microfluidic applications. A particular simple and much-used acoustic trap consists of a commercially available, millimeter-sized, liquid-filled glass…
Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity…
Higher-order topological phases of matter have been extensively studied in various areas of physics. While the Aubry-Andr\'e-Harper model provides a paradigmatic example to study topological phases, it has not been explored whether a…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well…
Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
Topological insulators (TIs) are expected to be a promising platform for novel quantum phenomena, whose experimental realizations require sophisticated devices. In this Technical Review, we discuss four topics of particular interest for TI…
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…
Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted…
Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
A $t_{2g}^5$ system with a honeycomb lattice structure such as Na$_2$IrO$_3$ was firstly proposed as a topological insulator even though Na$_2$IrO$_3$ and its isostructural materials in nature have been turned out to be a Mott insulator…
The discovery of the topological insulators has fueled a surge of interests in the topological phases in periodic systems. Topological insulators have bulk energy gap and topologically protected gapless edge states. The edge states in…
Ternary half-Heusler compounds with widely tunable electronic structures, present a new platform to discover topological insulators. Due to time-consuming computations and synthesis procedures, the identification of new topological…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…