Topological order in a broken symmetry state
In contrast to an ordinary topological insulator, in an antiferromagnetic topological insulator (AFTI) the presence of magnetic order breaks time reversal symmetry as well as primitive-lattice translational symmetry, yet the product of both symmetry operations is preserved. This allows the definition of a new topological invariant that characterizes a topological state with antiferromagnetic order. Depending on hether the surface breaks this combined symmetry or not, metallic surface states may arise within the band gap and a half-integer quantum Hall effect is expected. Moreover, the presence of the topological phase is bound to the antiferromagnetic
phase and so vanishes above the Néel temperature. This makes the AFTI articularly interesting, as the topological state appears only after the system undergoes a lassical phase transition. Therefore, changing the temperature allows one to turn the topological phase on or off, resulting in a quantum phase transition at the Néel temperature. Within this framework we have investigated two possible candidate materials of the half-Heusler, REBiPt family, for this new ground state of matter.
The REBiPt family shows many interesting properties such as superconductivity, antiferromagnetic order, and super-heavy-fermion behaviour. Band structure calculations and ARPES experiments on Lu, Nd, and GdBiPt indicate the presence of metallic surface states that differ strongly from the band structure in the bulk.
On this background we have carried out single crystal and powder neutron and X-ray diffraction experiments, to determine the magnetic structure of GdBiPt and NdBiPt, as their crystalline structure have the necessary symmetries for being AFTI.
