Magnetoresistance Anomalies in LaAlO$_{3}$/ SrTiO$_{3}$(110): Fingerprints of Flat $d_{yz}$/$d_{xz}$ Band along [1-10] zigzag chain

We report novel features in the in-plane magnetoresistance (MR) of anisotropic two-dimensional electron gas (2DEG) at LaAlO$_{3}$/SrTiO$_{3}$(110) heterostructures, which unveil the existence of a flat band in this system. One of the striking features is an anisotropy of the MR with a ``$\mbox{d}_{z^{2}} $-wave''-like symmetry upon rotating the magnetic field H within (110) plane at low temperature, which is caused by the existence of flat $d_{yz}$/$d_{zx}$ band. Combining with theoretical and experimental results, we confirm that a flat $d_{yz}$/$d_{xz}$ band formed along [1-10] Ti-O-Ti zigzag chain direction which might be very interesting for searching for topological state such as in superconducting regime.