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arXiv:1606.07914 · Physical review. B./Physical review. B

Novel energy scale in the interacting two-dimensional electron system evidenced from transport and thermodynamic measurements

L. A. Morgun, A. Yu. Kuntsevich, V. M. Pudalov

Published Jun 22, 2016• 19 citations
arXivHTMLPDF

Abstract

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 ${T}^{*}$ 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 ${T}_{\mathrm{kink}}(n)$, a high-energy behavior that ``mimics'' the low-temperature diffusive interaction regime. The zero-field resistivity temperature dependence exhibits an inflection point ${T}_{\mathrm{infl}}(n)$. In thermodynamic magnetization, the weak-field spin susceptibility per electron $\ensuremath{\partial}\ensuremath{\chi}/\ensuremath{\partial}n$ changes sign at ${T}_{dM/dn}(n)$. All three notable temperatures, ${T}_{\mathrm{kink}},\phantom{\rule{0.16em}{0ex}}{T}_{\mathrm{infl}}$, and ${T}_{dM/dn}$ 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 ${T}^{*}$ caused by interactions in the 2DE system.

DOI
10.1103/physrevb.93.235145

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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 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.
Exact numerical results for the dc magnetoconductivity tensor of the two-dimensional spatially disordered Yukawa-Sachdev-Ye-Kitaev (2D-YSYK) model on a square lattice, at first order in applied perpendicular magnetic field, are obtained from the self-consistent disorder-averaged solution of the 2D-YSYK saddle-point equations. This system describes fermions endowed with a Fermi surface and coupled to a bosonic scalar field through spatially random Yukawa interactions. The resulting local and energy-dependent fermionic self-energies are employed in the Kubo formalism to calculate the longitudinal and Hall conductivities, the Hall coefficient, the carrier mobility, and the cotangent of the Hall angle, at fixed fermion density. From the interplay between YSYK interactions and square-lattice embedding, and the non-Boltzmann frequency-dependent self-energies, we find nontrivial evolution of the magnetotransport coefficients as a function of temperature and YSYK interaction strength, notably a superlinear evolution of the Hall-angle cotangent and the inverse carrier mobility with temperature, concomitant with linear-in-temperature resistivity, in an extended crossover regime above the low-temperature marginal Fermi liquid ground state. Our model and results provide a controlled theoretical framework to interpret magnetotransport experiments, at linear order in applied magnetic field, in strange-metal phases found in strongly correlated solid-state electron systems.
The interpretation of the metal-insulator transition phenomena in disordered two-dimensional electron systems in terms of density-dependent scaling variables suggests the existence of a quantum critical point at some critical electron density. However a first principles scaling theory based on renormalization group (RG) methods predicts a strong temperature dependence of the dimensionless resistivity R(T)\mathcal{R}(T)R(T), even at small R(T)\mathcal{R}(T)R(T), that is not observed. The observed properties are in fact consistent with a weakly disordered Fermi liquid, and there are no indications of strong temperature dependence induced by scaling. While the RG expansion in a power series in R(T)\mathcal{R}(T)R(T) has only been evaluated to lowest order, this should be sufficient to describe experiments in the region of very small R\mathcal{R}R. A further apparent anomaly is a return from metal-like to insulating-like behavior for increasing density. We explain these fundamental discrepancies between the first principles theory and experiment. We find that the R⪡1\mathcal{R}⪡1R⪡1 data in the currently attainable temperature range are in a weak scaling regime described by the logarithmic approximation. We independently determine the density dependent prefactor of the logarithm using data for the spin susceptibility and effective mass. We find good agreement between theory and experiment for R(T)\mathcal{R}(T)R(T) in the diffusive regime. We point out that there are corrections to the leading logarithm approximation that should be observable at still lower temperatures.
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.
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.