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Topological insulators are a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship…
The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i)…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
We report appearance of non-trivial zero energy corner modes in the form of topological defects (trimers) in a carefully designed 2D crystalline topological insulator. The proposed scenario is developed via an unconventional stacking of 1D…
Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility…
A two-dimensional quadrupole topological insulator on a square lattice is a typical example of a higher-order topological insulator. It hosts an edge state localized near each of its $90^{\circ}$ corners at an energy $E$ inside the band…
Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…
Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects…
Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here,…
Control of topological edge modes is desirable for encoding quantum information resiliently against external noise. Their implementation on quantum hardware, however, remains a long-standing problem due to current limitations of circuit…
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional…
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…
Recent topological band theory distinguishes electronic band insulators with respect to various symmetries and topological invariants, most commonly, the time reversal symmetry and the $\rm Z_2$ invariant. The interface of two topologically…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
We build Floquet-driven capactive circuit networks to realize topological states of matter in the frequency domain. We find the Floquet circuit network equations of motion to reveal a potential barrier which effectively acts as a boundary…
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…
Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner…
Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge…
We study the orbital magnetic quadrupole moment (MQM) in three dimensional higher-order topological phases. Much like electric quadrupole moment, which is associated with a charge response on the boundaries of a finite sample, the diagonal…
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although significant progress on topological phenomena has been achieved in the classical domain, the…