Ultraclean two-dimensional hole systems with mobilities exceeding 107cm2/Vs

Owing to their large effective mass, strong and tunable spin-orbit coupling, and complex band structure, two-dimensional hole systems (2DHSs) in GaAs quantum wells provide rich platforms to probe exotic many-body physics, while also offering potential applications in ballistic and spintronics devices, and fault-tolerant topological quantum computing. We present here a systematic study of molecular-beam-epitaxy grown, modulation-doped, GaAs (001) 2DHSs where we explore the limits of low-temperature 2DHS mobility by optimizing two parameters, the GaAs quantum well width, and the alloy fraction ($x$) of the flanking ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ barriers. We obtain a breakthrough in 2DHS mobility, with a peak value $\ensuremath{\simeq}18\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$ at a density of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.16em}{0ex}}/{\mathrm{cm}}^{2}$, implying a mean free path of $\ensuremath{\simeq}57\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{m}$. Using transport calculations tailored to our structures, we analyze the operating scattering mechanisms to explain the nonmonotonic evolution of mobility with density. We find it imperative to include the dependence of effective mass on 2DHS density, well width, and $x$. We observe concomitant improvement in quality as evinced by the appearance of delicate fractional quantum Hall states at very low density.