Electromagnetic coupling of spins and pseudospins in bilayer graphene

Abstract

We present a detailed theoretical study of bilayer-graphene's electronic properties in the presence of electric and magnetic fields. Using group-theoretical methods, we derive an invariant expansion of the Hamiltonian for electron states near the K point of the Brillouin zone. In contrast to known materials, including single-layer graphene, any possible coupling of physical quantities to components of the external electric (magnetic) field has a counterpart where the analogous component of the magnetic (electric) field couples to exactly the same combination of quantities. For example, a purely electric spin splitting appears as the magneto-electric analogue of the familiar magnetic Zeeman spin splitting. The measurable thermodynamic response induced by magnetic and electric fields is thus completely symmetric. The Pauli magnetization induced by a magnetic field takes exactly the same functional form as the polarization induced by an electric field. Our findings thus reveal unconventional behavior of spin and pseudospin degrees of freedom in their coupling to external fields. We explain how these counterintuitive couplings are consistent with fundamental principles such as time reversal symmetry. For example, only a magnetic field can give rise to a macroscopic spin polarization, whereas only a perpendicular electric field can induce a macroscopic polarization of the sublattice-related pseudospin degree of freedom characterizing the intravalley orbital motion in bilayer graphene. These rules enforced by symmetry for the matter-field interactions clarify the nature of spins versus pseudospins. We also provide numerical values of prefactors for relevant coupling terms. While our theoretical arguments use bilayer graphene as an example, they are generally valid for any material with similar symmetries.

arXiv comment15 pages, 2 figures. revised final version, supersedes arXiv:1206.4761

References in corpus (20)

• The electronic properties of graphene
• Topological Field Theory of Time-Reversal Invariant Insulators
• Valley contrasting physics in graphene: magnetic moment and topological transport
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• The electronic properties of bilayer graphene
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Existence and topological stability of Fermi points in multilayered graphene
• Spin-orbit coupling in hydrogenated graphene
• Orbital magnetoelectric coupling in band insulators
• Theory of spin-orbit coupling in bilayer graphene
• Parity and valley degeneracy in multilayer graphene
• Invariant expansion for the trigonal band structure of graphene
• Relativistic analysis of magnetoelectric crystals: extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr_2 O_3 data
• Group theoretical and topological analysis of the quantum spin Hall effect in silicene
• Magnetoelectric coupling, Berry phase, and Landau level dispersion in a biased bilayer graphene
• Valley symmetry breaking in bilayer graphene: a test to the minimal model
• Time reversal of pseudo-spin 1/2 degrees of freedom
• Magnetoelectric effect in bilayer graphene controlled by valley-isospin density

Cited by in corpus (6)

• Tunable Berry curvature, valley and spin Hall effect in Bilayer MoS${}_2$
• Chirality-induced spin texture switching in twisted bilayer graphene
• Spintronics with graphene quantum dots
• Effective Dynamics of 2D Bloch Electrons in External Fields Derived From Symmetry
• In-plane magnetoelectric response in bilayer graphene
• Longitudinal magnetoconductivity and magnetodielectric effect in bilayer graphene