A property that is not an electron’s but behaves exactly like one: something with two possible values that the mathematics treats as ‘up’ and ‘down’. In graphene it records which of the two kinds of carbon site – the two sublattices of the – an electron’s wave sits on, and it is locked to the direction the electron moves, which is why electrons in graphene rarely bounce straight back. Which layer of a , or which , can serve as a pseudospin in the same way.
As the site uses it
Strong spin–orbit coupling gives the local moments a multipolar character, so the effective pseudospins are not simple spin-1/2, and first-principles work has to supply Kondo-lattice parameters rather than assume them.
In twisted 2H-MoTe2 the topmost moiré valence bands carry nonzero Chern numbers with layer-pseudospin skyrmion textures, and exact diagonalisation of projected continuum models reproduces the fractional states.
In graphene the share of an electron on the two sublattices acts as a spin, and near a Dirac point it points along the electron’s motion.
Two sublattices, one ‘spin’
Graphene’s honeycomb is made of two interpenetrating , A and B. Near the an electron’s wave has a share on each, and those two shares can be written as the two parts of a spin: all on A is ‘up’, all on B is ‘down’, and an equal mix points somewhere in between. Nothing magnetic is involved, but the mathematics is that of a spin, which is why the name stuck.
In graphene this pseudospin is tied to the direction of motion: an electron moving one way has its pseudospin pointing along its path, and one moving the opposite way has it reversed. This locking is what physicists mean when they call graphene’s electrons .
What the locking does
Turning an electron round reverses its momentum, so it would also have to flip its pseudospin – and a potential that varies smoothly over many atoms cannot do that. Electrons in graphene therefore rarely scatter straight back, they pass through potential barriers that would stop ordinary electrons (Klein tunnelling), and going once around a Dirac point gives their wave an extra phase of π. That phase shifts graphene’s steps by a half, the signature that identified its electrons as massless Dirac particles in 2005. In bilayer graphene the pseudospin turns twice as fast, and the phase is 2π.
Other pseudospins
The idea travels. In bilayer graphene and in stacks of two layers, which layer an electron sits in behaves as a pseudospin that an electric field across the stack can tilt, and in materials this layer pseudospin can wind into -like textures. Valleys are treated the same way in valleytronics. In magnets built from heavy ions such as ruthenium or iridium, spin and orbital motion combine into a two-level state that acts as an effective spin of one half – a pseudospin – and models of are written in it.
For specialists
Any two-component degree of freedom described by Pauli matrices, independent of real spin. In monolayer graphene the sublattice amplitudes form a pseudospin locked parallel or antiparallel to the momentum (chirality), giving the Dirac Hamiltonian v σ·p, a Berry phase of π, suppressed backscattering and Klein tunnelling; in bilayer graphene it winds twice, with a Berry phase of 2π. Layer and valley indices act as pseudospins in bilayers and moiré systems, and in magnetism the term names the effective low-energy doublet of an ion with strong , such as the effective spin-½ moments of α-RuCl3.