Magnetic topological insulators are three dimensional
magnetic materials
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
with a non-trivial
topological index
In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compo ...
protected by a
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
other than
time-reversal. In contrast with a
non-magnetic topological insulator, a magnetic topological insulator can have naturally gapped
surface states
Surface states are electronic states found at the surface of materials. They are formed due to the sharp transition from solid material that ends with a surface and are found only at the atom layers closest to the surface. The termination of a mate ...
as long as the quantizing symmetry is broken at the surface. These gapped surfaces exhibit a topologically protected half-quantized surface
anomalous Hall conductivity (
) perpendicular to the surface. The sign of the half-quantized surface anomalous Hall conductivity depends on the specific surface termination.
Theory
Axion coupling
The
classification of a 3D crystalline topological insulator can be understood in terms of the axion coupling
. A scalar quantity that is determined from the ground state wavefunction
: