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Topological superconductors are an intriguing and elusive quantum phase, characterized by topologically protected gapless surface/edge states residing in a bulk superconducting gap, which hosts Majorana fermions. Unfortunately, all…
By first-principles calculations, we find that Ba2X(X=Si, Ge) hosts a topological semimetal phase with one nodal ring in the kx=0 plane, which is protected by the glide mirror symmetry when spin-orbit coupling (SOC) is ignored. The…
In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim…
In a Dirac semimetal, the conduction and valence bands contact only at discrete (Dirac) points in the Brillouin zone (BZ) and disperse linearly in all directions around these critical points. Including spin, the low energy effective theory…
A grand challenge underlies the entire field of topology-enabled quantum logic and information science: how to establish topological control principles driven by quantum coherence and understand the time-dependence of such periodic driving?…
Planar topological superconductors with power-law-decaying pairing display different kinds of topological phase transitions where quasiparticles dubbed nonlocal-massive Dirac fermions emerge. These exotic particles form through long-range…
Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moir\'e materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions…
Type-II semi-Dirac fermions in two dimensions have been proposed to describe topologically nontrivial low-energy excitations in titanium/vanadium oxide heterostructures. These quasiparticles appear at the merger of three Dirac cones,…
We investigate Dirac fermions in the antifferomagnetic metallic state of iron-based superconduc- tors. Deriving an effective Hamiltonian for Dirac fermions, we reveal that there exist two Dirac cones carrying the same chirality, contrary to…
Topological insulators (TIs) are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of TIs have been well…
Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems…
We consider the three-dimensional Hamiltonian for Bi$_2$Se$_3$, a second-generation topological insulator, under the effect of a periodic drive for both in-plane and out-of-plane fields. As it will be shown by means of high-frequency…
We analyze the non-Hermitian Haldane model where the spin-orbit interaction is made non-Hermitian. The Dirac mass becomes complex. We propose to realize it by an $LC$ circuit with operational amplifiers. A topological phase transition is…
We unveil a topological phase of interacting fermions on a two-leg ladder of unequal parity orbitals, derived from the experimentally realized double-well lattices by dimension reduction. $Z_2$ topological invariant originates simply from…
Several proposed applications and exotic effects in topological insulators rely on the presence of helical Dirac states at the interface between a topological and a normal insulator. In the present work, we have used low-energy…
Using spin- and angle-resolved spectroscopy and relativistic many-body calculations, we investigate the evolution of the electronic structure of (Bi$_{1-x}$In$_x$)$_2$Se$_3$ bulk single crystals around the critical point of the trivial to…
Topological semimetals, known for their intriguing properties arising from band degeneracies, have garnered significant attention. However, the discovery of a material realization and the detailed characterization of spinless Dirac…
The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong…
Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or…
Topological insulators (TIs) are a unique class of materials characterized by a surface (edge) Dirac cone state of helical Dirac fermions in the middle of bulk (surface) gap. When the thickness (width) of TIs is reduced, however,…