  It is a fundamental paradigm that the physical effects induced by electric
fields are qualitatively different from those induced by magnetic fields. Here
we show that electrons at a Dirac point in bilayer graphene experience an
unusual type of electromagnetism where magnetic and electric fields are
virtually equivalent: every coupling of an electron's degrees of freedom to a
magnetic field is matched by an analogous coupling of the same degrees of
freedom to an electric field. This counter-intuitive duality of matter-field
interactions enables novel ways to create and manipulate spin and pseudo-spin
polarizations in bilayer graphene via external fields and leads to the
emergence of a valley-contrasting axion electrodynamics, where the traditional
association of charges at rest with electric fields and charge currents with
magnetic fields is reversed.
