  The electronic structure of surfaces plays a key role in the properties of
quantum devices. However, surfaces are also the most challenging to simulate
and engineer. Here, we study the electronic structure of InAs(001), InAs(111),
and InSb(110) surfaces using a combination of density functional theory (DFT)
and angle-resolved photoemission spectroscopy (ARPES). We were able to perform
large-scale first principles simulations and capture effects of different
surface reconstructions by using DFT calculations with a machine-learned
Hubbard U correction [npj Comput. Mater. 6, 180 (2020)]. To facilitate direct
comparison with ARPES results, we implemented a "bulk unfolding" scheme by
projecting the calculated band structure of a supercell surface slab model onto
the bulk primitive cell. For all three surfaces, we find a good agreement
between DFT calculations and ARPES. For InAs(001), the simulations clarify the
effect of the surface reconstruction. Different reconstructions are found to
produce distinctive surface states. For InAs(111) and InSb(110), the
simulations help elucidate the effect of oxidation. Owing to larger charge
transfer from As to O than from Sb to O, oxidation of InAs(111) leads to
significant band bending and produces an electron pocket, whereas oxidation of
InSb(110) does not. Our combined theoretical and experimental results may
inform the design of quantum devices based on InAs and InSb semiconductors,
e.g., topological qubits utilizing the Majorana zero modes.
