  Bloch states of electrons in honeycomb two-dimensional crystals with
multi-valley band structure and broken inversion symmetry have orbital magnetic
moments of a topological nature. In crystals with two degenerate valleys, a
perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect
due to these magnetic moments, leading to magnetoelectric effects which can be
leveraged for creating valleytronic devices. In this work, we demonstrate that
trilayer graphene with Bernal stacking, (ABA TLG) hosts topological magnetic
moments with a large and widely tunable valley g-factor, reaching a value 1050
at the extreme of the studied parametric range. The reported experiment
consists in sublattice-resolved scanning tunneling spectroscopy under
perpendicular electric and magnetic fields that control the TLG bands. The
tunneling spectra agree very well with the results of theoretical modeling that
includes the full details of the TLG tight-binding model and accounts for a
quantum-dot-like potential profile formed electrostatically under the scanning
tunneling microscope tip.
