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arXiv:0711.1294 · Physical Review B

Spin susceptibility of interacting two-dimensional electrons with anisotropic effective mass

Tayfun Gokmen, Medini Padmanabhan, Emanuel Tutuc, MANSOUR SHAYEGAN, S. De Palo, Saverio Moroni, Gaetano Senatore

Published Dec 10, 2007• 28 citations
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Abstract

We report measurements of the spin susceptibility in dilute (${r}_{s}$ up to $\ensuremath{\approx}10$) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses ${m}_{l}$ and ${m}_{t}$. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to $\sqrt{{m}_{l}.{m}_{t}}$. Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.

DOI
10.1103/physrevb.76.233301

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We report measurements of the spin susceptibility in dilute (rs{r}_{s}rs​ up to \ensuremath≈10\ensuremath{\approx}10\ensuremath≈10) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses ml{m}_{l}ml​ and mt{m}_{t}mt​. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to ml.mt\sqrt{{m}_{l}.{m}_{t}}ml​.mt​​. Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.
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We determine the spin susceptibility $\ensuremath{\chi}$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs heterostructure. The band structure effects, modifying mass and ggg-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime. When properly normalized, $\ensuremath{\chi}$ decreases monotonically from 3 to 1.1 with increasing density over our experimental range from 0.1 to $4\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. In the high density limit, $\ensuremath{\chi}$ tends correctly towards $\ensuremath{\chi}\ensuremath{\rightarrow}1$ and compare well with recent theory.
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The nature of the ground state of degenerate two dimensional (2D) fermions at zero magnetic field is an outstanding open problem, which has not been deciphered despite decades of research. In the absence of disorder, the ground state is believed to be determined by the interplay between the kinetic energy, E f, and the inter-particle interaction energy, Ec = e2/ica, where a = (nn)~1^ 2 is the typical inter-particle distance, n is the areal particle density, and k is the host dielectric constant. The relative importance of the two energy scales is characterized by rs = a/ao, with ao being the Bohr radius. For electrons in a single band, rs = Ec/ E f while for the (100) surface of silicon rs = Ec/2E p , due to the two-fold valley degeneracy. At very high densities (rs <£ 1) a 2D system approaches the paramagnetic limit of a non-interacting degenerate gas characterized by the Pauli susceptibility, xo • As the density is reduced, the growing ferromagnetic correlations lead to substantial enhancement of the spin susceptibility, The system is predicted to remain paramagnetic up to rs « 20, where numerical calculations [1] find a quantum phase transition to a ferromagnetic liquid phase [2]. At lower density, rs & 37 [3], the Coulomb correlations are predicted to lead to a second phase transition to an anti-ferromagnetic quantum Wigner crystal. The energy balance between the ferro and paramagnetic states is very subtle, therefore the density window where ferromagnetism can take place is small [1].