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Acknowledgment.-The authors wish to acknowledge the contribution of Robert C. Reid, who designed the capillary apparatus used here. Preliminary investigations of this problem were made

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. I. INTRODUCTIONThe narrow-gap III-V semiconductors InAs and InSb (InX) have attractive material parameters, including small effective mass, large Lande g-factor, and large spin-

Analysis of the electronic state of the CuO 2 planes of high-T c materials has been performed with special regard to the influence of the Coulomb interactions separated after moments. Using this analysis to derive the basic structure of the electronic states within the CuO 2 planes of the high-T c materials, different symmetry breaking effects were revealed. First of all, a commensurate charge and bonding fluctuation state (CBF) with the period (2a,2b) is established which exists collinearly with the antiferromagnetic spin state. It is concluded that the CBF state and the antiferromagnetic spin state are results of the same electronic renormalizations. Furthermore, the existence of localized topological hole states under hole doping is established. As a natural consequence of this local symmetry is broken. It is proven that a quadrupolar-polarization induced attractive hole-hole interaction can exist between such topological hole states. This interaction creates an ordered topological hole structure which leads to a global symmetry breaking. This highly ordered topological hole structure which will be referred as bonded holes (b-holes) can be characterized as parallel one-dimensional electronic states (stripes) along particular ..Cu-O-Cu.. bonding directions which are intrinsically coupled to each other. The highly ordered topological b-hole state exists undisturbed for hole concentrations n h in the range of 0.125 holes/copper ≤ n h ≤ 0.25 holes/copper. The total correlation energy per b-hole E C(tot)  was found to be greater than 160 meV. In addition to b-holes, holes which are not intrinsically bonded exist in the concentration range of n h > 0.125 holes/copper. These non-bonded holes are termed as free holes (f-holes). The inevitable consequence is an electronic two fluid behaviour (b-holes, f-holes) within the hole concentration range of 0.125 holes/copper < n h ≤ 0.25 holes/copper. A comparison with experimental results is given with particular respect to peculiarities of µSR experiments, neutron scattering results (1/8 problem), Hall-effect anomalies and scanning tunneling microscopy (STM). The characteristics of the electronic state deduced by the new methodology described here enable a more in depth understanding of these experimental results.