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International Journal of Modern Physics B

EFFECTS OF PARALLEL MAGNETIC FIELDS ON THE UNUSUAL METALLIC BEHAVIOR IN TWO DIMENSIONS

Dragana Popović

Published Aug 30, 2002• 0 citations
Publisher

Abstract

The fate of the metallic phase in parallel magnetic fields represents one of the major open issues in the studies of dilute, strongly interacting systems in two dimensions (2D). In this experiment, the temperature dependence of conductivity σ(T) of a 2D electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a new and unexpected kind of metallic behavior with dσ/dT > 0, and a novel type of a metal-insulator transition,1 which occurs at a critical electron density nc(0). At low fields (B ≤ 2 T ), nc increases as nc(B) - nc(0) ∝ Bβ(β ≈ 0.9), and the zero-temperature conductivity scales as σ(ns, B, 0)/σ (ns, 0, 0) = f(Bβ/δn) (where δn = (ns - nc(0))/nc(0), and ns is electron density) as expected for a quantum phase transition. The metallic phase persists in fields up to 18 T, consistent with the saturation of nc at high fields. These results strongly suggest that the 2D metal may exist even for spinless electrons.

DOI
10.1142/s0217979202014164

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The fate of the metallic phase in parallel magnetic fields represents one of the major open issues in the studies of dilute, strongly interacting systems in two dimensions (2D). In this experiment, the temperature dependence of conductivity σ(T) of a 2D electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a new and unexpected kind of metallic behavior with dσ/dT > 0, and a novel type of a metal-insulator transition,1 which occurs at a critical electron density nc(0). At low fields (B ≤ 2 T ), nc increases as nc(B) - nc(0) ∝ Bβ(β ≈ 0.9), and the zero-temperature conductivity scales as σ(ns, B, 0)/σ (ns, 0, 0) = f(Bβ/δn) (where δn = (ns - nc(0))/nc(0), and ns is electron density) as expected for a quantum phase transition. The metallic phase persists in fields up to 18 T, consistent with the saturation of nc at high fields. These results strongly suggest that the 2D metal may exist even for spinless electrons.
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 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.
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.
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.
The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization in two-dimensional systems of non-interacting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from the insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.