Measurements of Correlated 2D Electrons in the Lowest Landau Level on Silicon-(111)

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Kott, Tomasz Maria
Kane, Bruce E
Einstein, Theodore L
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.