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

TL;DR

This study analyzes the spin and valley effects in a two-dimensional low-density electron system in Si-MOSFETs, revealing the stability of the unpolarized phase and matching experimental data without fitting parameters.

Contribution

It introduces a self-consistent classical mapping approach to accurately compute the energy and response functions of the two-valley 2DES, showing the unpolarized phase remains stable up to Wigner crystallization.

Findings

Unpolarized phase is always stable in the two-valley system.

Calculated response functions agree with Quantum Monte Carlo data.

Results match experiments without fitting parameters.

Abstract

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 $\zeta$ 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, $\zeta=0$) and found to be in excellent agreement. However, unlike in the one-valley 2DES, it is shown that {\it the unpolarized phase is always the stable phase in the 2-valley system}, right up to Wigner Crystallization at $r_s=42$. 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 {\it ad hoc} fit parameters. They agree with experiments and do not invoke impurity effects or metal-insulator transition phenomenology.