Multi-Valley Physics of Two-Dimensional Electron Systemson Hydrogen-Terminated Silicon (111) Surfaces

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Recent work on two dimensional electron systems (2DES) has focused increasingly on understanding the way the presence of additional degrees of freedom (e.g. spin, valleys, subbands, and multiple charge layers) affect transport as such effects may be critical to the development of nanoscale and quantum devices and may lead to the discovery of new physics . In particular, conduction band valley degeneracy opens up a rich parameter space for observing and controlling 2DES behavior. Among such systems, electrons on the (111) surface of silicon are especially notable because effective mass theory predicts the conduction band to be sixfold degenerate, for a total degeneracy (spin ×valley) of 12 in the absence of a magnetic field B. Previous investigations of Si(111) transport using Metal-Oxide-Semiconductor Field Effect Transistors (MOSFETs) observed a valley degeneracy gv of 2 except in certain specially prepared samples with low mobility.

We have developed a novel device architecture for investigating transport on a H-Si(111)-vacuum interface free from the complications created by intrinsic disorder at Si-SiO2 interfaces. The resulting devices display very high mobilities (up to 110,000 cm2/Vs at 70 mK, more than twice as large as the best silicon MOSFETs), enabling us to probe valley-dependent transport to a much greater degree than previously possible. In particular, we observed detailed Integer Quantum Hall structure with hints of Fractional states as well. These devices display clear evidence of six occupied valleys, including strongly “metallic” temperature dependence expected for large gv. Some devices show strong sixfold degeneracy while others display a partial lifting of the degeneracy, resulting in unequal distribution of electrons among the six valleys. This symmetry breaking results in anisotropic transport at low B fields, but other observed anisotropies remain unexplained.

Finally, we apply this unusual valley structure to show how corrections to the low-B magnetoresistance and Hall effect can provide information about valley-valley interactions. We propose a model of valley drag, similar to Coulomb drag in bilayer systems, and find good agreement with our experimental data, though a small residual drag in the T→0 limit remains unexplained.