▎ 摘　　要

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies E = +/- root N(N+1)(h) over bar omega(c)*, where omega(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 contains an octet of degenerate states spanned by the layer spinors [0, h(n,X,sigma)(r)] in valley K and [h(n,X,sigma)(r), 0] in valley K', where h(n,X,sigma)(r) is the electronic wave function (or orbital) in Landau level n=0,1 with guiding center index X and spin sigma in the Landau gauge. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignment in space of the valley and orbital pseudospins. These quantum Hall pseudoferromagnetic 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. The modulation of electronic density in the crystalline phases is experimentally accessible through a scanning tunneling microscope measurement of their local density of states.