Physics

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Measurements of Correlated 2D Electrons in the Lowest Landau Level on Silicon-(111)
(2012) Kott, Tomasz Maria; Kane, Bruce E; Einstein, Theodore L; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Degenerate, multicomponent systems in a single Landau level have generated interest due to the possibilities for novel correlated ground states in the integer and fractional quantum Hall (FQH) regimes. Early experiments focused on measurements of engineered GaAs materials with a tunable spin degeneracy. Subsequent development of AlAs quantum wells with tunable valley degeneracy allowed the study of a spin-like degeneracy in the same limit. Recently, there has been great interest in the sub-lattice (valley) degeneracy in graphene, where experiments show that the FQH hierarchy is affected by the underlying valley symmetry. Measurements on silicon had been hampered by high disorder at interfaces. Lately, however, Si(100)/SiGe heterostructures have shown mobilities up to ~ 10^6 cm^2/Vs. Nonetheless, Si(100) is known to have an intrinsic valley splitting due to surface effects. Si(100) is not the only face of silicon used in transport measurements. On (111) oriented silicon surfaces, 2D electrons have three pairs of opposite momentum valleys. In contrast to either AlAs or Si(100), the last pair of valleys in Si(111) cannot be broken within the effective mass approximation; valleys in graphene cannot be broken in this way either. Additionally, both AlAs and Si(111) exhibit anisotropic effective mass tensors, which also affects transport properties, adding interest to these cases. We present transport data on a very high mobility (µ = 3.25 × 10^5 cm^2/V sec at a temperature T = 90 mK and a carrier density n_s = 4.15 × 10^-11 cm^-2) hydrogen-terminated Si(111) surface. Using a novel device structure free from complications created by disorder at Si-SiO_2 , we have probed many-valley effects. In particular, we observe an anisotropy between orthogonal current directions that is consistent with an expected anisotropy due to the effective mass tensor. Additionally, we observe an extended fractional quantum Hall hierarchy around filling factor ν = 3/2. We argue that the FQH hierarchy is consistent with the SU(2) symmetry of a valley-degenerate ground state, and estimate the effective mass of composite fermions. Finally, we present evidence for many-body interactions affecting activation energies at integer filling factors. We find that the development of ν = 2 occurs in an unusually narrow temperature range and, thus, may be consistent with a transition to novel valley-symmetry-breaking states.
Multi-Valley Physics of Two-Dimensional Electron Systemson Hydrogen-Terminated Silicon (111) Surfaces
(2010) McFarland, Robert Nicholas; Kane, Bruce E; Drew, Howard D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
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 g_v 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 g_v. 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.