Abstract

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 ${\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}\mathrm{Se}$ 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 ${\mathrm{Pb}}_{1\ensuremath{-}y}{\mathrm{Eu}}_{y}\mathrm{Se}$ 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 $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ 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.

Highlights

  • Multivalley semiconductors offer additional degrees of freedom for tuning of the electronic properties for valleytronics device applications because these properties significantly depend on the structure of the valleys as well as their interaction [1–5]

  • Using magnetooptical Landau level spectroscopy, we show that Topological interface states (TISs) and TIS are very sensitive to the valley anisotropy of the bulk barrier material due to their remarkable property of being localized mainly at the interface, contrary to trivial quantum wells (QWs) states found in ordinary semiconductor heterostructures

  • We have demonstrated significant interactions between topological and massive states in multivalley topological crystalline insulator (TCI) QW heterostructures

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Summary

INTRODUCTION

Multivalley semiconductors offer additional degrees of freedom for tuning of the electronic properties for valleytronics device applications because these properties significantly depend on the structure of the valleys as well as their interaction [1–5]. The surfaces of constant energy of these band minima are plotted for the two types of valleys with respect to [111]: the longitudinal valley depicted in black and the three equivalent oblique valleys in red, tilted by θ = 70.5 ◦ with respect to the surface normal [111] They both have an anisotropic factor K, defined as the ratio between the major and minor axis of the ellipsoids. Using magnetooptical Landau level spectroscopy, we show that TIS and TIS are very sensitive to the valley anisotropy of the bulk barrier material due to their remarkable property of being localized mainly at the interface, contrary to trivial QW states found in ordinary semiconductor heterostructures. Our spectroscopy allows us to quantify the strength of the interaction potential between different levels and to accurately deduce the in-plane anisotropy of the TIS Dirac cone dispersion [20,46]

PRESENTATION OF THE EXPERIMENTS
THEORY
Bulk Landau levels
QW Landau levels
RESULTS AND DISCUSSION
CONCLUSIONS

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