Local and Tunable Geometric Phase of Dirac Fermions in a Topological Junction

We discover a new type of geometric phase of Dirac fermions in solids, which is an electronic analogue of the Pancharatnam phase of polarized light. The geometric phase occurs in a local and nonadiabatic scattering event of Dirac fermions at a junction, unveiling topological aspects of scattering of chiral particles, and it is experimentally tunable to an arbitrary value. It provides a unique approach of detecting the topological order of the insulator in a metal-insulator junction of Dirac fermions, establishing new bulk-edge correspondence. The geometric phase also modifies the fundamental quantization rule of Dirac fermions, suggesting topological devices with nontrivial charge and spin transport such as a topological wave guide and a topological transistor.