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We start with the silicene or germanene single-particle Hamiltonian in buckled 2D hexagonal lattices expressed in terms of Dirac matrices in the Weyl basis. The Hamiltonian of these systems comprises of the Dirac kinetic energy, a mass gap…
The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such…
Searching for controllable topological phase by means of external stimuli in two-dimensional (2D) material-based van der Waals (vdW) heterostructures is currently an active field for both the underlying physics and practical applications.…
We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ ($n=0,1,2,3$) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the…
Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry.…
Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and…
We report on high-field magnetotransport (B up to 35 T) on a gated superlattice based on single-layer graphene aligned on top of hexagonal boron nitride. The large-period moir\'e modulation (15 nm) enables us to access the Hofstadter…
We study the role of the edges in determining the features of the topological phase in a quasicrystalline higher order topological insulator. We consider a specific model consisting of two stacked Haldane models with opposite Chern number…
In intrinsic magnetic topological insulators, Dirac surface state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however.…
A pair of Dirac points (analogous to a vortex-antivortex pair) associated with opposite topological numbers (with $\pm\pi$ Berry phases) can be merged together through parameter tuning and annihilated to gap the Dirac spectrum, offering a…
Altermagnets provide a natural platform for studying and exploiting piezomagnetism. In this paper, we introduce a class of insulating altermagnets in two dimensions (2D) referred to as Dirac quadrupole altermagnets, and show based on…
A single two-dimensional Dirac cone with a mass gap produces a quantized (spin-) Hall step in the absence of magnetic field. What happens in strong electric fields? This question is investigated by analyzing time evolution and dynamics of…
BiSbTeSe$_2$ is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low temperature surface transport in this material is heralded by…
The magnetic proximity effect is a fundamental feature of heterostructures composed of layers of topological insulators and magnetic materials since it underlies many potential applications in devices with novel quantum functionality.…
The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While…
The quantum magnetic oscillations are studied for planar condensed matter systems with a linear, Dirac-like spectrum of quasiparticle excitations. We derive analytical expressions for magnetic oscillations (de Haas - van Alphen effect) in…
We present the first determination of the topological susceptibility from lattice QCD in the presence of strong background magnetic fields. Our simulations employ 2+1 flavours of stout improved staggered quarks with physical masses and…
We study the emergence of gauge couplings in the surface states of topological insulators. We show that gauge fields arise when a three dimensional strong topological insulator is coated with an easy-plane ferromagnet with magnetization…
We consider the proximity effect in a Topological Insulator sandwiched between two conventional superconductors, by comparing s-wave spin singlet superconducting pairing correlations and odd-parity triplet pairing correlations with zero…
For many biotechnological applications it would be useful to better understand the effects produced by electric fields on lipid membranes. This review discusses several aspects of the electrostatic properties of a planar lipid membrane with…