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The motion of an electron and its spin are generally not coupled. However in a one dimensional material with strong spin-orbit interaction (SOI) a helical state may emerge at finite magnetic fields, where electrons of opposite spin will…

We consider a mesoscopic {\it ballistic} structure with Rashba spin-orbit splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which…

The investigation of topologically protected waves in classical media has opened unique opportunities to achieve exotic properties like one-way phonon transport, protection from backscattering and immunity to imperfections. Contrary to…

We study theoretically the two-dimensional topological electric state in a single band semiconductor with strong spin-orbit interactions under harmonic scalar electrostatic potentials. The electronic states described by the spin Landau…

Quasi--one dimensional edge channels are formed at the boundary of a two-dimensional electron system subject to a strong perpendicular magnetic field. We consider the effect of Rashba spin--orbit coupling, induced by structural inversion…

We explore the emergence of spin-polarised flat-bands at head-to-head domain walls in a recently predicted class of antiferromagnetic topological insulators hosting planar magnetisation. We show, in the framework of quantum well physics,…

We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice combining the cellular dynamical mean-field theory and its real space extension with analytical approaches. We provide a…

The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum…

The strength of the (Rashba-type) spin-orbit coupling in mesoscopic semiconductor rings can be tuned with external gate voltages. Here we consider the case of a periodically changing spin-orbit interaction strength as induced by sinusoidal…

Inverted-gap GaSb/InAs quantum wells have long been predicted to show quantum spin Hall insulator (QSHI) behavior. The experimental characterization of the QSHI phase in these systems has relied on the presence of quantized edge transport…

We demonstrate that a weak nonlinear magnetic entrance edge induces a tennis-racket (Dzhanibekov) instability in the shell-resolved orbital pseudospin dynamics of twisted electrons propagating in a nominally uniform solenoidal field.…

A substantial challenge in guiding elastic waves is the presence of reflection and scattering at sharp edges, defects, and disorders. Recently, mechanical topological insulators have sought to overcome this challenge by supporting…

Surfaces of topological insulators host a new class of states with Dirac dispersion and helical spin texture. Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at…

Topological insulators are unique devices supporting unidirectional edge states at their interfaces. Due to topological protection, such edge states persist in the presence of disorder and do not experience backscattering upon interaction…

Spin orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry…

Hall and diagonal resistances of bilayer fractional quantum Hall systems are discussed theoretically. The bilayers have electrodes attached separately to each layer. They are assumed to be coupled weakly by interlayer tunneling, while the…

Recent experiments by Hayashi et al. [Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit (qubit) in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate…

One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge of a three-dimensional second-order topological insulator. For…

We study roles of electron correlations on topological insulators on the honeycomb lattice with the spin-orbit interaction. Accurate variational Monte Carlo calculations show that the increasing on-site Coulomb interactions cause a strong…

A complicating factor in the realization and observation of quantum spin liquids in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons). These provide additional routes for…