Topological insulators and Hall effect

Topological insulators are partial insulators that are insulators inside themselves but are very good conductors on their sides or edges. Quality of topological insulators (TI) usually improves if internal content is not conductive and surface should preferrably have higher density of electrons than inside. Some researchers even consider TIs potential room temperature superconductors. Mostly they are combination of different elements like most insulators but at least in case of graphene, which is conductor, can also become topological insulator which only conducts on edges but for that it has to be cooled to 0,3C above absolute zero and also be in 35 Tesla magnetic field. 

Kawazulite is natural example of TI. Like artificial ones they commonly have a metallic reflective appearance. Like many TIs it contains bismuth, tellurium and selenium.

Overview of Hall effect which is related topic to TIs. When current goes through magnetic field (B) then electrons get pushed to one side due to Lorentz force. If electrodes get connected to these sides then these gathering of electron on one side causes measurable voltage difference (VH) between sides.

Above illustration shows quantum Hall effect in semiconductor but it also describes closely how electrons behave in TI. Inside electrons orbit in circles but near border they skip along like stones on water as they keep on trying to circle but keep deflecting from edge. Inner structure of material can push electrons to move and when this moving is in circles then material may get enough internal magnetic field to start moving other electrons around these magnetic field lines and in TI's it is called spin quantum Hall effect. One difference between this and usual Hall effect is that spin quantum version causes oppositely moving electrons on sides.

Applying high pressure (~100 000 atmospheres) to semiconductors turns at least one of them to topological insulator.

TI could be superconducting unless there are excess electrons inside material but doping surface with electronegative substance to attract electrons there can reduce that problem.

Bismuth tellurochloride (BiTeCl) is maybe 1st topological insulator discovered which has one side positive and other negative due to inner structure.  Electrical currents flowed on upper side but not on other sides. Semiconducting transistors and most TIs materials are either n or p type but by layering many alternating layers of bismuth, tellurium and chlorine on top of each other, BiTeCl starts to have those charge differences within same piece. One of the hopes with such material is that their sides could function as p-n junctions where current is one directional. Outside magnetic fields can create channels on the sides that seem to conduct electricity with no resistance.

Illustration of graphene in conditions that make it TI. Electrons with certain spin can move along edge (shown with blue arrows) but electrons with opposite spins (red arrows) get blocked on these sides so in general currents flow around graphene flakes either clockwise or counterclockwise.

While graphene is conductor in room temperature it could behave slightly like TI under intense (35 tesla) magnetic field (to cause Hall effect) and 0,3 C above absolute zero which allows it to transport electrons with different spins in different directions. Magnetic field lines could be perpendicular to surface graphene or also parallel to surface and both caused these spin dependent flow current.

Common use for TIs according to maybe most articles i read about TIs is their supposed good use in quantum computers or spintronics devices. So far the only example of spin use in any computer part i could understand is illustrated below.

(source)
A) with usual current there is similar amount of up and down spins which spread evenly on both sides but voltage between these sides stays 0 because there is even number of electron on both sides. B) by using ferromagnet (FM) electrons can be sent with same spin. Opposite spin electrons shown red are created on other side (maybe also with ferromagnets but turned 180 degrees) and electrons with opposite spins can flow on same edge if they are going in opposite direction. This way electrons can concentrate on same side and create voltage differences. According to authors this time spins were separated due to Spin Hall effect, where opposite spins move to opposite sign of material without need for outside magnetic field. In this case outer magnetic field not needed and it can even disrupt electron flow by making them rotate in small circles. These spin differences can be measured with light as different electron spins give differently polarized light.

Above example with spins influencing light polarization may be usable in computer security by pushing certain secret amount of electron on certain regions and letting suitably polarized light expose data (maybe with interference exposing data on some screen or letting light push important electron on transistors in direction to some other transistor that gives data signal). Circular polarization keeps rotating its polarization direction depending how much it has traveled so bumpy surface may shine with differently polarized light on different heights which has potential for secret data storage.