Related papers: Higher-order topology and corner triplon excitatio…
Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems…
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion…
In the quasi-two-dimensional (quasi-2D) copper- and iron-based superconductors, the onset of superconductivity is accompanied by a prominent peak in the magnetic spectrum at momenta close to the wave-vector of the nearby antiferromagnetic…
The 1D Kitaev model in the topological phase, with open boundary conditions, hosts strong Majorana zero modes. These are fermion parity-odd operators that almost commute with the Hamiltonian and manifest in long coherence times for edge…
We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion…
Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
Weyl semimetals and higher-order topological insulators represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition…
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…
Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary…
Quantized bulk quadrupole moment has unveiled a nontrivial boundary state, exhibiting lower-dimensional topological edge states and simultaneously hosting the in-gap corner modes of zero dimension. All state-of-the-art strategies for…
Topological properties of a certain class of spinless three-band Hamiltonians are shown to be summed up by the Skyrmion number in momentum space, analogous to the case of two-band Hamiltonian. Topological tight-binding Hamiltonian on a…
Topological superconductors are a class of unconventional superconducting materials featuring sub-gap zero-energy Majorana bound modes that hold promise as a building block for topological quantum computing. In this work, we study the…
We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at their boundary in agreement with the bulk-boundary…
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several…
Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order…
We introduce topological skyrmion semimetal phases of matter, characterized by bulk electronic structures with topological defects in ground state observable textures over the Brillouin zone (BZ), rather than topological degeneracies in…
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…