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arXiv:1810.03560 · Physical review. B./Physical review. B

Probing spin susceptibility of a correlated two-dimensional electron system by transport and magnetization measurements

V. M. Pudalov, A. Yu. Kuntsevich, M. E. Gershenson, I. S. Burmistrov, M. Reznikov

Published Oct 3, 2018• 17 citations
arXivHTMLPDF

Abstract

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 ${n}_{c}$. 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 $n<{n}_{c}$, 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.

DOI
10.1103/physrevb.98.155109

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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 \ensuremathχ∗{\ensuremath{\chi}}^{*}\ensuremathχ∗ from the Shubnikov-de Haas oscillations in crossed magnetic fields and (ii) thermodynamic susceptibility \ensuremathχT{\ensuremath{\chi}}_{\mathrm{T}}\ensuremathχT​ sensitive to all the electrons in the layer. Both \ensuremathχ∗{\ensuremath{\chi}}^{*}\ensuremathχ∗ and \ensuremathχT{\ensuremath{\chi}}_{\mathrm{T}}\ensuremathχT​ 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 \ensuremathχT{\ensuremath{\chi}}_{\mathrm{T}}\ensuremathχT​, 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 \ensuremathχ∗{\ensuremath{\chi}}^{*}\ensuremathχ∗ 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 \ensuremathχT{\ensuremath{\chi}}_{\mathrm{T}}\ensuremathχT​ to localized spin droplets. In strong enough in-plane magnetic field, we found the temperature dependence of \ensuremathχ∗{\ensuremath{\chi}}^{*}\ensuremathχ∗ to be stronger than that expected for the Fermi liquid interaction corrections.
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.
We report thermodynamic magnetization measurements of two-dimensional electrons in several high-mobility Si metal-oxide-semiconductor field-effect transistors. We provide evidence for an easily polarizable electron state in a wide density range from insulating to deep into the metallic phase. The temperature and magnetic field dependence of the magnetization is consistent with the formation of large-spin droplets in the insulating phase. These droplets melt in the metallic phase with increasing density and temperature, though they survive up to large densities.
We study how the non-Fermi-liquid two-phase state reveals itself in transport properties of high-mobility Si-MOSFETs. We have found features in zero-field transport, magnetotransport, and thermodynamic spin magnetization in a 2D correlated electron system that may be directly related with the two-phase state. The features manifest above a density-dependent temperature T∗{T}^{*}T∗ that represents a high-energy scale, apart from the Fermi energy. More specifically, in magnetoconductivity, we found a sharp onset of the regime $\ensuremath{\delta}\ensuremath{\sigma}(B,T)\ensuremath{\propto}{(B/T)}^{2}$ above a density-dependent temperature Tkink(n){T}_{\mathrm{kink}}(n)Tkink​(n), a high-energy behavior that ``mimics'' the low-temperature diffusive interaction regime. The zero-field resistivity temperature dependence exhibits an inflection point Tinfl(n){T}_{\mathrm{infl}}(n)Tinfl​(n). In thermodynamic magnetization, the weak-field spin susceptibility per electron $\ensuremath{\partial}\ensuremath{\chi}/\ensuremath{\partial}n$ changes sign at TdM/dn(n){T}_{dM/dn}(n)TdM/dn​(n). All three notable temperatures, Tkink,Tinfl{T}_{\mathrm{kink}},\phantom{\rule{0.16em}{0ex}}{T}_{\mathrm{infl}}Tkink​,Tinfl​, and TdM/dn{T}_{dM/dn}TdM/dn​ behave critically $\ensuremath{\propto}(n\ensuremath{-}{n}_{c})$, are close to each other, and are intrinsic to high-mobility samples solely; we therefore associate them with an energy scale T∗{T}^{*}T∗ caused by interactions in the 2DE system.
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 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].
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.