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arXiv:cond-mat/0403191 · Physical Review Letters

Spin Susceptibility of Two-Dimensional Electrons in Narrow AlAs Quantum Wells

K. Vakili, Y. P. Shkolnikov, Emanuel Tutuc, Etienne P. De Poortere, MANSOUR SHAYEGAN

Published Jun 1, 2004• 106 citations
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Abstract

We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45 A wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.

DOI
10.1103/physrevlett.92.226401

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We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45 A wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.
We report measurements of the spin susceptibility in dilute (rs{r}_{s}rs​ 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 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.
Starting from the quantum Monte Carlo (QMC) prediction for the ground-state energy of a clean two-dimensional one-valley (2D1V) electron gas, we estimate the energy correction due to scattering sources present in actual devices such as AlAs quantum wells and GaAs heterostructures. We find that the effect of uncorrelated disorder, in the lowest (second) order in perturbation theory, is to enhance the spin susceptibility leading to its eventual divergence. In the density region where the Born approximation is able to reproduce the experimental mobility, the prediction for the spin susceptibility yielded by perturbation theory is in very good agreement with the available experimental evidence.
Abstract Using several independent methods, we find that the metal-insulator transition occurs in the strongly-interacting two-valley two-dimensional electron system in ultra-high mobility SiGe/Si/SiGe quantum wells in zero magnetic field. The transition survives in this system in parallel magnetic fields strong enough to completely polarize the electrons’ spins, thus making the electron system “spinless.” In both cases, the resistivity on the metallic side near the transition increases with decreasing temperature, reaches a maximum at a temperature Tmax, and then decreases. The decrease reaches more than an order of magnitude in zero magnetic field. The value of Tmax in zero magnetic field is found to be close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value Tmax decreases appreciably for spinless electrons in spin-polarizing magnetic fields. The observed behavior of Tmax cannot be described by existing theories. The results indicate the spin-related origin of the effect. At the same time, the low-temperature resistivity drop in both spin-unpolarized and spinless electron systems is described quantitatively by the dynamical mean-field theory.
We report temperature and density dependences of the spin susceptibility of strongly interacting electrons in Si inversion layers. We measured (i) the itinerant electron susceptibility ${\ensuremath{\chi}}^{*}$ from the Shubnikov-de Haas oscillations in crossed magnetic fields and (ii) thermodynamic susceptibility ${\ensuremath{\chi}}_{\mathrm{T}}$ sensitive to all the electrons in the layer. Both ${\ensuremath{\chi}}^{*}$ and ${\ensuremath{\chi}}_{\mathrm{T}}$ are strongly enhanced with lowering the electron density in the metallic phase. However, there is no sign of divergency of either quantity at the density of the metal-insulator transition nc{n}_{c}nc​. Moreover, the value of ${\ensuremath{\chi}}_{\mathrm{T}}$, which can be measured across the transition down to very low densities deep in the insulating phase, increases with density at n<ncn<{n}_{c}n<nc​, as expected. In the absence of magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be consistent with Fermi-liquid-based predictions, and to be much weaker than the power law predicted by non-Fermi-liquid models. We attribute a much stronger temperature dependence of ${\ensuremath{\chi}}_{\mathrm{T}}$ to localized spin droplets. In strong enough in-plane magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be stronger than that expected for the Fermi liquid interaction corrections.
The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.
The resistivities of the dilute, strongly interacting two-dimensional electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\text{exp}[{({T}_{ES}/T)}^{1/2}]$, with TES{T}_{ES}TES​ and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density nc{n}_{\text{c}}nc​ reported earlier. With and without magnetic field, the parameters TES{T}_{ES}TES​ and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.