Researchers are very excited for TIs which show some unique properties such as spin momentum locking and large spin-orbit interaction. they say spins are 100% intrinsically polarized in TI.
I have one confusion. In TI spins transport in two opposite direction with one spin up and other spin down. then how will we get large spin polarization. because we have both spin up and spin down spins.
Please explain it
Thank you
If the transport is in just one direction, only one kind of spin can contribute to transport. That's the idea and the selling point.
As you write, spin is tied to mentum due to Rashba coupling. in particular, this kind of spin polarization is not to be confused with magnetization.
Dear Sir, Thank you
but transport is in both direction. How we can make it in one direction. do you mean that if we apply magnetic field in one direction , the spins in that direction will contribute to transport?
Is spin-momentum locking is due to Rashba coupling? As I know Rashba coupling has pair of spin up and spin down.
in particular, this kind of spin polarization is not to be confused with magnetization.
Could you please elaborate more?
(a) No. "transport" here means corrent flow due to application of a voltage (electric field). Since only electrons are mobile, the sign of momentum involved in transport is fixed. Then by spin momentum locking so is the sign of spin.
(b) yes, but these are tied to states with opposite sign of momentum. That's exactly the point. See link below for a quick explanation. As a result, spin polarization is the property of a current flow (due to spin Momentum locking) and not of a volume (or surface) density (states of all momentum and hence spin orientations exist in the material).
https://www.researchgate.net/post/Can_anyone_explain_spin-momentum_locking_in_3D_topological_insulator#view=50f1acc8e5438f0b1100003e
The spin polarization in the bulk of topological insulator is definitely zero due to time-reversal symmetry. Spin polarization mentioned here is not to be confused with magnetization. Generally in the momentum space for any single-particle state labelled by momentum \vec{k}, spin direction is also arbitrary. But in topological insulator, the spin direction for momentum \vec{k} is not arbitrary, but determined by spin-orbit coupling. This should be the meaning of spin polarization in topological insulator.
Time reversal symmetry has it (Kramers Theorem) that single electron (in general: states with an uneven number of fermions) states must be (at least) two-fold degenerate. For a 'normal' electron state this implies spin degeneracy (and hence arbitrary spin dierection as Beibing Huang pointed out. See below, however for a slightly more stringent argument.)
The normal notion is that the presence of magnetic flux density destroys time reversal symmetry. One can think of time reversal symmetry by considering waht it would mean to let time flow backwards: an object in motion will be at the same place immediately after time reversal but move in opposite direction, so the sign of momentum is reversed. This automatically implies that angular momentum is also subject to time reversal. You shall find this confirmed when considering the trajectory of an electron in a magnetic field.
Quantum mechanically you will know that applying a magnetic field leads to Zeeman splitting and so the 2-fold degeneracy is lifted.
So, in the field free case, the spin degeneracy implies zero magnetization (spin polarization).
In the theoretical description, time reversal symmetry is represented by an antiunitary operator, which involves komplex conjugation. [For an all-time textbook classic on the subject you may want to consider Messiah's text, Volume 2, chapter XV, but similar treatments an be found at other places, e.g. the document linked below.]
Now how about electron/Bloch states in periodic solids? Complex conjugation of a Bloch state describes a state with opposite momentum (just as time reversal did in the classical noteion). So time reversal implies degeneracy of {k,\sigma} with {-k,-\sigma} (where \sigma symbolizes spin). That is still exactly the case in the topological surface state. What is lifted is the degeneracy between {k,\sigma} and {k,-\sigma}. But that, to be precise, was not required by time reversal symmetry! It derives from other symmetries, and breaking those is what may lead to exotic states such as th TI surface states.
About visualizing time reversal symmetry: that is difficult I would say. It is more instructive to consider what can and what cannot induce breaking time reversal symmetry. As said above, presence of magnetic flux density does. Purely electrostatic potentials cannot and therefore never do.
http://bohr.physics.berkeley.edu/classes/221/9697/timerev.pdf
Thank you Sir for nice explanation.
I have one more question in my mind. as TIs show counter propagating spins with 100% spin polarization in one direction. since they are always counter-propagation, how these materials can be used in spintronics? because we need only one typr of spins and have to avoid other type.
Magnetically doped TIs are a hot and controversial topic. And what seems simple (magnetism opend a gap in the surface state) is not necessarily easily usable. You may take a look at the linked manuscript which should be published in a little while (albeit under new title: "Dual nature of magnetic dopants and competing trends in topological insulators")
Article Emergence of a two-fluid behavior in magnetically doped topo...
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