Abstract:

Two-level systems are routinely represented in terms of pseudo-spin-1/2 degrees of freedom, and such pseudo-spins are usually considered to be entirely analogous to the real spin angular momentum. Here we consider time reversal (TR) of pseudo-spins from a completely general perspective and find that there exist two different types. One type behaves like ordinary spin, for which all of its three Cartesian components are odd under TR. In addition, a second type of pseudo-spin exists, behaving counter-intuitively in that only one Cartesian component is odd and the other two are even under TR. The second type is not merely of academic interest, as it is realised, eg, by the pseudo-spin representation of the 2D isotropic harmonic oscillator (Schwinger model of spin-1/2). We show that the sublattice-related pseudospin of quasi-relativistic charge carriers in graphene also belongs to the second type and discuss observable implications of this fact.
 
 
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