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arXiv:cond-mat/0011523 · Physical review. B, Condensed matter

Fate of the extended states in a vanishing magnetic field: The role of spins in strongly interacting two-dimensional electron systems

Mohammed R. Sakr, Maryam Rahimi, S. V. Kravchenko

Published Dec 14, 2001• 5 citations
arXivHTMLPDF

Abstract

In noninteracting two-dimensional (2D) electron systems, the extended states ``float up'' in energy in the vanishing perpendicular magnetic field ${B}_{\ensuremath{\perp}},$ giving rise to an insulator. However, in strongly interacting 2D systems, the extended states remain at a finite energy as ${B}_{\ensuremath{\perp}}\ensuremath{\rightarrow}0,$ thus allowing conduction. Here we show that polarizing the electrons' spins in strongly interacting systems causes the extended states to once more ``float up'' in energy, as they do for noninteracting electrons. The difference between extended states that float up (an insulator) or remain at a constant energy (a metal) is thus unambiguously tied to the existence of the spins.

DOI
10.1103/physrevb.65.041303

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In noninteracting two-dimensional (2D) electron systems, the extended states float up'' in energy in the vanishing perpendicular magnetic field ${B}_{\ensuremath{\perp}},$ giving rise to an insulator. However, in strongly interacting 2D systems, the extended states remain at a finite energy as ${B}_{\ensuremath{\perp}}\ensuremath{\rightarrow}0,$ thus allowing conduction. Here we show that polarizing the electrons' spins in strongly interacting systems causes the extended states to once more float up'' in energy, as they do for noninteracting electrons. The difference between extended states that float up (an insulator) or remain at a constant energy (a metal) is thus unambiguously tied to the existence of the spins.
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.
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 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.
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.
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.
Based on recent experimental evidence for a spin-polarized ground state in the insulating phase of the two-dimensional electron system, we propose that ferromagnetic spin fluctuations lead to an attractive interaction in the triplet channel and cause p-wave pairing in the conducting phase. We use the Landau-Fermi liquid phenomenology to explain how the enhanced spin susceptibility near the critical density yields an attractive potential, in a similar mechanism to superfluidity in 3He.{}^{3}\mathrm{He}.3He. As the density is decreased, the p-wave order parameter undergoes a transition from a unitary to a nonunitary state, in which it coexists with ferromagnetism for a range of densities. As the density is further reduced, the pairing amplitude vanishes and the system is described by a ferromagnetic insulator. Thus, we find two quantum critical points as a function of density associated with the polarization of the paired state and ferromagnetism. We explain the magnetotransport measurements in parallel and perpendicular magnetic fields and propose a shot-noise experiment to measure the pair charge.