  Crystal symmetry governs the nature of electronic Bloch states. For example,
in the presence of time reversal symmetry, the orbital magnetic moment and
Berry curvature of the Bloch states must vanish unless inversion symmetry is
broken. In certain 2D electron systems such as bilayer graphene, the intrinsic
inversion symmetry can be broken simply by applying a perpendicular electric
field. In principle, this offers the remarkable possibility of switching on/off
and continuously tuning the magnetic moment and Berry curvature near the Dirac
valleys by reversible electrical control. Here we demonstrate this principle
for the first time using bilayer MoS2, which has the same symmetry as bilayer
graphene but has a bandgap in the visible that allows direct optical probing of
these Berry-phase related properties. We show that the optical circular
dichroism, which reflects the orbital magnetic moment in the valleys, can be
continuously tuned from -15% to 15% as a function of gate voltage in bilayer
MoS2 field-effect transistors. In contrast, the dichroism is gate-independent
in monolayer MoS2, which is structurally non-centrosymmetric. Our work
demonstrates the ability to continuously vary orbital magnetic moments between
positive and negative values via symmetry control. This represents a new
approach to manipulating Berry-phase effects for applications in quantum
electronics associated with 2D electronic materials.
