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Abstract |
Two-dimensional electron gases under a strong magnetic field have tremendously expanded our
understanding of many-body physics, with the discovery of integer and fractional quantum Hall effects,
together with chiral edge states, fractional excitations, anyons. Another striking effect is the strong
coupling between charge and spin and valley degrees of freedom, which takes place near integer filling M
of the magnetic Landau levels. More precisely, because of the large energy gap associated to cyclotron
motion, any slow spatial variation of the spin background induces a variation of the electronic density
proportional to the topological density of the spin background. Minimizing Coulomb energy leads to an
exotic class of two-dimensional crystals, which exhibit a periodic non-collinear spin texture called a
Skyrmion lattice. Magnon propagation through such lattice has been recently investigated experimentally
in a graphene layer.
I will focus on the limit where we neglect coupling anisotropies in the N-dimensional spin and valley
internal space, so that a perfect SU(N) symmetry is assumed to hold. In this case, minimal energy
Skyrmion lattices may be described in terms of holomorphic maps from a torus (unit cell) to the
Grassmannian manifold Gr(M,N), such that the associated topological charge density is as uniform as
possible. The case of an undoped graphene layer corresponds to N = 4 and M = 2. The main outcome of
this analysis is the existence of two regimes depending on whether the topological charge on the unit cell
is smaller (unfrustrated case) or larger (frustrated case) than the number of internal states N accessible to
electrons. I will show that we can, to a large extent, identify minimal energy Skyrmion lattices by
combining the solution of the M = 1 case with Atiyah’s explicit description of rank M vector bundles on a
torus.
https://cnrs.zoom.us/j/92858575727?pwd=cFZqMjNOVUQ3dnJZb0FWak5RVEZTdz09
ID de réunion : 928 5857 5727
Code secret : A5J1NK |
