Quantum anomalous Hall state with Chern number C=2 in wurtzite quantum wells

Abstract

Quantum anomalous Hall (QAH) effect in topological insulators (TIs) is known to have involved energy bands with Chern numbers $C=\ifmmode\pm\else\textpm\fi{}1$. The QAH edge current would be electrically more accessible if one suppressed the edge-channel resistance, $h/C{e}^{2}$. That is why topological states $|C|>1$ are preferable for connecting them to an external circuit in device applications. The search for topological systems with a high Chern number is ongoing. This paper points to a semiconductor material system well developed for optoelectronic applications----III-nitrides. Polarization field in a compressed InN quantum well (QW) has two effects: it inverts conduction and valence energy bands, thus creating a prerequisite for topological insulator (TI), and generates Rashba spin splitting in conduction and valence bands. We calculate topological indexes in GaN/InN/GaN QW. In the QAH setting, value $|C|>1$ follows from the phase structure of interband coupling in III--V materials, providing Rashba and Zeeman fields act simultaneously. In nonmagnetic samples, explicitly calculated topological index ${Z}_{2}=1$ manifests the quantum spin Hall state.