Interaction between interface and massive states in multivalley topological heterostructures

Topological interface states (TISs) in multivalley systems are studied to unravel their valley sensitivity. For this purpose, multivalley IV-VI topological crystalline insulator (TCI) heterostructures are explored using magnetooptical Landau level spectroscopy up to 34 teslas. We characterize the TISs emerging from the distinct L valleys in Pb1-xSnxSe multiquantum wells grown along the [111] direction. It is shown that the shape of the two-dimensional (2D) Fermi surfaces of TISs residing at the TCI-trivial insulator interfaces are strongly affected by the valley anisotropy of topologically trivial Pb1-yEuySe barriers. This phenomenon is shown to be due to the deep penetration of the TISs into the barriers. For the valleys tilted with respect to the confinement direction, a significant interaction between topological states and the conventional massive quantum well states is observed, evidenced by the resulting large anticrossings between Landau levels. These are theoretically well described by a k . p model that considers tilt and anisotropy of the valleys in 2D. Therefore, in this paper, we provide a precise characterization of the TIS valley splitting as well as an accurate determination of the anisotropy of their Dirac cone dispersion.