Related papers: Non-unique connection between bulk topological inv…
We have constructed a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter1-5 where exotic electronic phases of Dirac particles should arise1,6-8. Here we report a discovery of surface…
Axial vectors, such as current or magnetization, are commonly used order parameters in time-reversal symmetry breaking systems. These vectors also break isotropy in three dimensional systems, lowering the spatial symmetry. We demonstrate…
We analyze numerically the critical properties of a two-dimensional discretized random surface with extrinsic curvature embedded in a three-dimensional space. The use of the toroidal topology enables us to enforce the non-zero external…
For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of…
Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase…
The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of…
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…
We review the contributions of surface science methods to discover and improve 3D topological insulator materials, while illustrating with examples from our own work. In particular, we demonstrate that spin-polarized angular-resolved…
The surface states of 3D topological insulators in general have negligible quantum oscillations when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators can support surface states with…
We study the equilibrium and non-equilibrium properties of topological dipolar intersurface exciton condensates within time-reversal invariant topological insulators in three spatial dimensions without a magnetic field. We elucidate that,…
Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of…
We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi$_2$Te$_3$ by using a low temperature scanning tunneling microscope. The interference fringes are caused by the scattering of the…
We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends…
Topological insulators are insulating bulk materials hosting conducting surface states. Their magnetic doping breaks time-reversal symmetry and generates numerous interesting effects such as dissipationless transport. Nonetheless, their…
Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…