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Near-surface InAs two-dimensional electron gas (2DEG) systems have greatpotential for realizing networks of multiple Majorana zero modes towards ascalable topological quantum computer. Improving mobility in the near-surface2DEGs is beneficial for stable topological superconducting states as well asfor correlation of multiple Majorana zero modes in a complex network. Here, weinvestigate near-surface InAs 2DEGs (13 nm away from the surface) grown onGaSb(001) substrates, whose lattice constant is closely matched to InAs, bymolecular beam epitaxy. The effect of 10-nm-thick top barrier to the mobilityis studied by comparing Al$_{0.9}$Ga$_{0.1}$Sb and In$_{0.75}$Ga$_{0.25}$As asa top barrier on otherwise identical InAs quantum wells grown with identicalbottom barrier and buffer layers. A 3-nm-thick capping layer onAl$_{0.9}$Ga$_{0.1}$Sb top barrier also affects the 2DEG electronic transportproperties by modifying scattering from 2D remote ionized impurities at thesurface. The highest transport mobility of 650,000 cm$^2$/Vs with an electrondensity of 3.81 $\times$ 10$^{11}$ cm$^{-2}$ was observed in an InAs 2DEG withan Al$_{0.9}$Ga$_{0.1}$Sb top barrier and an In$_{0.75}$Ga$_{0.25}$As cappinglayer. Analysis of Shubnikov-de Haas oscillations in the high mobility samplesuggests that long-range scattering, such as remote ionized impurityscattering, is the dominant scattering mechanism in the InAs 2DEGs grown onGaSb(001) substrates. In comparison to InAs quantum wells grown onlattice-mismatched InP, the ones grown on GaSb show smoother surface morphologyand higher quantum mobility. However, In$_{0.75}$Ga$_{0.25}$As top barrier inInAs quantum well grown on GaSb limits the transport mobility by chargeddislocations formed in it, in addition to the major contribution to scatteringfrom the alloy scattering.

Contribution of top barrier materials to high mobility in near-surface InAs quantum wells grown on GaSb(001)