Orbital and interlayer skyrmion crystals in bilayer graphene

Abstract

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies E = ± N (N + 1)ℏω * c where ω * c is the effective cyclotron frequency and N = 0, 1, 2, ... All Landau levels but N = 0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N = 0 has an extra degeneracy due to the fact that orbitals n = 0 and n = 1 both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states 73.22.Gk,78.70.Gq

Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene

“…This orbital degeneracy brings about a new realm of quantum phenomena, [13][14][15][16][17][18] such as orbital mixing and orbital-pseudospin waves. The eightfold degeneracy of the zero-energy levels is partially or fully lifted in the presence of Zeeman coupling, interlayer bias and Coulomb interactions, and these levels evolve into a variety of pseudo-zero-mode levels, or brokensymmetry states, as discussed theoretically in the context of quantum-Hall ferromagnetism 13 and others.…”

Interaction-enhanced electron-hole and valley asymmetries in the lowest Landau level ofABA-stacked trilayer graphene

“…Trilayer graphene has 12 such levels with threefold "orbital" degeneracy, and so on. This orbital degeneracy is a new feature peculiar to the LLL in multilayer graphene, and leads to intriguing quantum phenomena [12][13][14][15][16][17] such as orbital mixing and orbitalpseudospin waves. In real samples these zero-energy levels evolve, due to general interactions, into a variety of pseudo-zero-mode (PZM) levels, or broken-symmetry states within the LLL, as discussed theoretically.…”

Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels inABC-stacked trilayer graphene

“…In the presence of Zeeman coupling, Coulomb interactions, etc., these zeroenergy levels evolve into a variety of pseudo-zero-mode (PZM) levels, or broken-symmetry states, as discussed theoretically. [9][10][11] The interplay of orbital degeneracy and Coulomb interactions brings about a new realm of quantum phenomena 9,[12][13][14][15][16] in the PZM sector, such as orbital mixing and orbital-pseudospin waves.…”