An Aharonov-Bohm interferometer for determining Bloch band topology
Nailing down graphene's topology An electron traveling along a closed path in the momentum space of the graphene crystal lattice may not end up exactly the way it started. If its path happens to include one of the special points in momentum space, it will acquire a phase shift. Physicists can detect the signatures of this process by studying the transport properties of graphene. Duca et al. used interferometry to directly measure this so-called Berry flux in a hexagonal optical lattice, where intersecting laser beams simulate the environment that electrons experience in graphene (see the Perspective by Lamacraft). The high-precision technique may be useful in characterizing other topological structures. Science, this issue p. 288; see also p. 232 Interferometric techniques are used to measure the Berry flux in the momentum space of a hexagonal optical lattice. [Also see Perspective by Lamacraft] The geometric structure of a single-particle energy band in a solid is fundamental for a wide range of many-body phenomena and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. We realize an atomic interferometer to measure Berry flux in momentum space, in analogy to an Aharonov-Bohm interferometer that measures magnetic flux in real space. We demonstrate the interferometer for a graphene-type hexagonal optical lattice loaded with bosonic atoms. By detecting the singular π Berry flux localized at each Dirac point, we establish the high momentum resolution of this interferometric technique. Our work forms the basis for a general framework to fully characterize topological band structures.