Spin and Valley dependent analysis of the two-dimensional low-density electron system in Si-MOSFETS

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The 2-D electron system (2DES) in Si metal-oxide field-effect transistors (MOSFETS) consists of two distinct electron fluids interacting with each other. We calculate the total energy as a function of the density n, and the spin polarization ζ in the strongly-correlated low-density regime, using a classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge terms. Here the ten distribution functions, arising from spin and valley indices, are self-consistently calculated to obtain the total free energy, the chemical potential, the compressibility and the spin susceptibility. The T=0 results are compared with the 2-valley Quantum Monte Carlo (QMC) data of Conti et al. (at T=0, ζ=0) and found to be in excellent agreement. However, unlike in the one-valley 2DES, it is shown that the unpolarized phase is always the stable phase in the 2-valley system, right up to Wigner Crystallization at rₛ=42. This leads to the insensitivity of g* to the spin polarization and to the density. The compressibility and the spin-susceptibility enhancement calculated from the free energy confirm the validity of a simple approach to the two-valley response based on coupled-mode formation. The three methods, QMC, CHNC, and Coupled-mode theory agree closely. Our results contain no ad hoc fit parameters. They agree with experiments and do not invoke impurity effects or metal-insulator transition phenomenology.