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The bulk band topology of symmetry invariant adiabatic systems in the thermodynamic limit are considered to be determined by the hopping energy. In this work, we present that in closed classical systems, due to generalized chiral symmetry…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant,…
We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the…
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…
Quantum material phases such as the Anderson insulator, diffusive metal, and Weyl/Dirac semimetal as well as topological insulators show specific wave functions both in real and Fourier spaces. These features are well captured by…
We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for…
Three dimensional topological insulators are bulk insulators with $\mathbf{Z}_2$ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by…
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…
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…
The introduction of structural defects in otherwise periodic media is well known to grant exceptional space control and localization of waves in various physical fields, including elasticity. Despite the variety of designs proposed so far,…
High-efficiency energy harvesting of ultrasonic elastic waves are crucial for powering electric gadgets in many emerging technologies such as wearable devices, wireless sensing, and biomedical implants. Although topological phononic…
Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems.…
We obtain the quantum phase diagram of the ionic Hubbard model including electron-hole symmetric density-dependent hopping. The boundaries of the phases are determined by crossing of excited levels with particular discrete symmetries, which…
We consider interface modes in block disordered subwavelength resonator chains in one dimension. Based on the capacitance operator formulation, which provides a first-order approximation of the spectral properties of dimer-type block…
A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological…
Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves…
A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak…