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arXiv:1607.07382 · Physical review. B./Physical review. B

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Shiqi Li, Myriam P. Sarachik

Published Jan 11, 2017• 6 citations
arXivHTMLPDF

Abstract

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 ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density ${n}_{\text{c}}$ reported earlier. With and without magnetic field, the parameters ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.

DOI
10.1103/physrevb.95.041301

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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 \ensuremathρ(T)=\ensuremathρ0exp[(TES/T)1/2]\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\text{exp}[{({T}_{ES}/T)}^{1/2}]\ensuremathρ(T)=\ensuremathρ0​exp[(TES​/T)1/2], with TES{T}_{ES}TES​ and 1/\ensuremathρ01/{\ensuremath{\rho}}_{0}1/\ensuremathρ0​ 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/\ensuremathρ0=\ensuremathσ01/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}1/\ensuremathρ0​=\ensuremathσ0​ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.
This chapter focuses on experimental results obtained in low-disordered strongly interacting two-dimensional (2D) electron systems; in particular in (100)-silicon metal-oxide-semiconductor field-effect transistors (MOSFET). It describes the additional confirmation in favor of zero-temperature zero-field metal-insulator transition is provided by magnetic and thermopower measurements. The chapter argues that the metal-insulator transition in silicon samples with very low level of disorder is driven by interactions. In a low-disordered 2D electron system in silicon MOSFETs, the resistivity at a certain "critical" electron density shows virtually no temperature dependence over a wide range of temperatures. In 2000, it was experimentally found that the ratio between the spin and the cyclotron splittings in silicon MOSFETs strongly increases at low electron densities. The strong enhancement of the spin susceptibility has indicated that at low electron densities, the system behaves well beyond the weakly interacting Fermi liquid.
The in-plane magnetoconductance of the strongly interacting two-dimensional electron system in a silicon MOSFET (metal-oxide-semiconductor-field-effect transistor) exhibits an unmistakable kink at a well-defined electron density, nk{n}_{k}nk​. The kink at nk{n}_{k}nk​ is near, but not at the critical density nc{n}_{c}nc​ determined from resistivity measurements, and the density at which nk{n}_{k}nk​ occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.
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.
The increase in the resistivity with decreasing temperature followed by a drop by more than one order of magnitude is observed on the metallic side near the zero-magnetic-field metal-insulator transition in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells. We find that the temperature [Formula: see text], at which the resistivity exhibits a maximum, is close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value [Formula: see text] decreases appreciably for spinless electrons in spin-polarizing (parallel) magnetic fields. The observed behaviour of [Formula: see text] cannot be described by existing theories. The results indicate the spin-related origin of the effect.
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.