Zeeman field induced midgap mode in two-dimensional node line semimetal

Two-dimensional node line semimetals protected by nonsymmorphic and parity-time symmetries are robust against weak perturbations. Since the topological invariant is not well defined, there is no edge states in the two-dimensional node line semimetal, which hinders the electronic device application. In this talk, we show that by introducing in-plane Zeeman field the two-dimensional node line semimetal can open an energy gap and generate midgap mode separated from bulk bands. The midgap state is protected by Berry phase π and well localized in each edge with fractional charge e/2. We also discuss the magnetic flux effects in such node line semimetal. Under magnetic flux field, the node line is split into one pair of Dirac points in the boundary of Brillouin zone. The location of the Dirac points is determined by the gauge chosen for the vector potential. Finally, we discuss the experimental realization of our model.