Suppose a topological insulator stripe, oppen boundary in Y direction, periodical boundary in X direction. If I add an electronic field in X direction, what will happen in Y direction?
Short answer is no. A stripe consisting of a topological insulator is characterised by protected conducting edge states. In the absence of magnetic field (i.e. in the presence of time-reversal invariance) and spin-orbit coupling, the edge states accommodate electrons of both spin species, but in the presence of spin-orbit coupling the removal of spin degeneracy outside some protected points of the Brillouin zone (i.e. the centre of the BZ and those points that upon inversion can be brought back to the original point through a translation by a reciprocal-lattice vector) gives rise to a system that shows quantum spin Hall effect, that is showing non-vanishing quantized Hall conductivity. Two interesting transport-measurement geometries (two-terminal and four-terminal geometries) on a stripe of a topological insulator (a stripe made of a graphene sheet) have been considered by Kane and Mele (Phys. Rev. Lett. 95, 226801 (2005)). For a review, consult Colloquium: Topological insulators, by Hasan and Kane (Rev. Mod. Phys. 82, 3045 (2010)). I attach the relevant links below.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.226801
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.3045
The electric field can destroy the mirror symmetry of topological crystalline insulator. As for the topologcial insulator stripe, i don not know= =
Electrical insulators as a new phase state of quantum matter with some bulk gap and some odd number of Dirac formations have recently been entangled with a two-dimensional model by us through an external magnetic field. The magnetic field used has its own impurities so much so that the eccentricity resulting from the turning point of magnetic critical insulation leads to aspects of compilation that have never been revealed by the “approximate approximation calculus” mostly used in a run under such circumstances.
Crystal and electronic structures have given us the topology that have made it likely for us to depend more on over-stuck service rather than on projections that go into manifolds and submanifolds of various dimensions. In additions, fulton heaters in this specific setting of complex systems where technique does not exist for efficient approximation, has led us to find even lower than submanifolds: something like up-submanifolds and down-submanifolds whereby the cloesed set of combining topological insulators itself has become the target in insulating the whole bulk without any regard for the gapless and/or edge services states. This means that the topological insulators that we are working on have been both gapless at surface and without such states so that they might be able to carry a pure spin current. However, this pure spin current is the point where we have made our own initiative provided through the closure of those areas where points cannot satisfy every path from one origin-set of the insulator to another point of it simulacrum. Therefore, we are actually depending on, so to speak, closure models for creating metainsulators, giving yet more models of simulations of magnetic insulators.
The surface of state of spin resolved ARPES works so that the focus of one direction is in Riemannian contrast to the zones that consequently appear throughout the folding holes as borderlines between submanifolds. For this, without any doubt, means that the dimensions of submanifolds where we are working on our different froms have been entangled with ergodicity as the totality of anisotropy that rises from insulation through coupling strength. The simplest form is, of course, happening within a two-dimensional partially anisotropic plane. In the most complex forms, they can even go into the quantum mechanic levels such as N-Hilbert dimension.
Roya Attarzadeh
Don Senior Prof. Reza Sanaye
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