Metal-Insulator Transition at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mspace /><mml:mo>=</mml:mo><mml:mspace /><mml:mn>0</mml:mn><mml:mn /></mml:math>in a Dilute Two Dimensional GaAs-AlGaAs Hole Gas

Simmons, M. Y.; Hamilton, A. R.; Pepper, M.; Linfield, Edmund H.; Rose, P. D.; Ritchie, D. A.; Savchenko, A. K.; Griffiths, Tom

doi:10.1103/physrevlett.80.1292

Cited by 246 publications

(248 citation statements)

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“…While behavior similar to that of Ref. [2] has now been reported for a wide variety of 2D carrier systems such as n-AlAs [4], n-GaAs [5], n-Si/SiGe [6,7], p-GaAs [8,9,10], and p-Si/SiGe [11,12], the origin of the metallic state and its transition into the insulating phase remain major puzzles in solid state physics.…”

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confidence: 99%

Spin–valley phase diagram of the two-dimensional metal–insulator transition

et al. 2007

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Using symmetry breaking strain to tune the valley occupation of a two-dimensional (2D) electron system in an AlAs quantum well, together with an applied in-plane magnetic field to tune the spin polarization, we independently control the system's valley and spin degrees of freedom and map out a spin-valley phase diagram for the 2D metal-insulator transition. The insulating phase occurs in the quadrant where the system is both spin-and valley-polarized. This observation establishes the equivalent roles of spin and valley degrees of freedom in the 2D metal-insulator transition.PACS numbers: 71.30.+h, 73.43.Qt, 73.50.Dn, The scaling theory of localization in two dimensions [1], which predicts an insulating phase for two-dimensional electron systems (2DESs) with arbitrarily weak disorder, was challenged by the observation of a metallic temperature dependence (dρ/dT > 0) of the resistivity, ρ, in low-disorder Si metal-oxide-semiconductor field-effect transistors (Si-MOSFETs) [2]. The associated metal-toinsulator transition (MIT) has subsequently become the subject of intense interest and controversy [3]. While behavior similar to that of Ref.[2] has now been reported for a wide variety of 2D carrier systems such as n-AlAs, 10], and p-Si/SiGe [11,12], the origin of the metallic state and its transition into the insulating phase remain major puzzles in solid state physics.Several experiments have demonstrated the important role of the spin degree of freedom in the MIT problem, either in systems with a strong spin-orbit interaction [10,13,14], or via the application of an external magnetic field to spin polarize the carriers [15,16,17,18,19]. The latter experiments have shown that a magnetic field applied parallel to the 2DES plane suppresses the metallic temperature dependence, ultimately driving the 2DES into the insulating regime as the 2DES is spin polarized. The relevance of multiple conduction-band valleys, on the other hand, is less known. Although it has been discussed theoretically that the occupation of multiple valleys may also be important [20,21], there has been no direct experimental demonstration. Here we show that the electrons' valley degree of freedom indeed plays a crucial role, analogous to that of spin. We study a 2DES, confined to an AlAs quantum well, in which we can independently tune both the spin and valley degrees of freedom. By studying the temperature dependence of ρ at various degrees of spin and valley polarization, we map out the metal-insulator phase diagram in this system at a constant density. The 2DES exhibits a metallic behavior when either the valley or spin are left fully unpolarized, and a minimum amount of both spin and valley polarization is required to enter the insulating phase.We performed experiments on 2DESs confined to modulation-doped, AlAs quantum wells of width 11 nm and 15 nm [22]. In these systems, the electrons occupy two conduction-band valleys of AlAs centered at the edges of the Brillouin zone along the [100] and [010] directions. We denote these valleys as X and Y...

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Spin–valley phase diagram of the two-dimensional metal–insulator transition

et al. 2007

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“…It consists in comparing the real part of anisotropic self-energy (30) and the magnetic part of the trial mode energy (19). Under WMS condition (22), both of these energy items are of the same order of magnitude, save the case of the magnetic field oriented nearly parallel to the direction of current. We thus expect the conductance anisotropy to be expressed, at most, moderately.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 90%

“…As shown in the Appendix, under WS conditions which imply that WDS inequalities (21) and WMS inequality (22) are satisfied simultaneously, the averaging of the trial Green function results in the asymptotic expression…”

Section: Spectral Peculiarities Of Renormalized Mode Statesmentioning

confidence: 99%

“…Inasmuch as magnetic fields appropriate for such a transition are strong enough to completely polarize electron spins, this prompted many of the researchers (see, e. g., Refs. [22,23,24]) to assert categorically that it is exactly the spin polarization that should be regarded as a physical origin of 2D MIT in a parallel magnetic field. This point of view is also supported by the lack of a comprehensive theory of the electron transport in real quasi-two-dimensional (Q2D) systems, i. e. planar systems of finite, though rather small, thickness.…”

Section: Introductionmentioning

confidence: 99%

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One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect

Tarasov¹

2006

Phys. Rev. B

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The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three partsthe system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.

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“…Our analysis of compressibility and thermopower points to thermodynamic nature of metal-insulator transition in 2D systems. Recently, a great deal of interest has been focussed on the anomalous transport behavior of a wide variety of low-density 2D electron [1,2] and hole [3,4,5] systems. It has been found that, below some critical density, the cooling causes an increase in resistivity, whereas in the opposite high density case the resistivity decreases.…”

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confidence: 99%

Thermal correction to resistivity in dilute 2D Si-based systems

Cheremisin

2005

Physica E: Low-dimensional Systems and Nanostructures

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We calculate the resistivity of 2D electron (hole) gas, taking into account the degeneracy and the thermal correction due to the combined Peltier and Seebeck effects. The resistivity is found to be universal function of temperature, expressed in units of h e 2 (kF l) −1 . The giant parallel magnetiresistivity found to result from the spin and, if exists, valley splitting of the energy spectrum. Our analysis of compressibility and thermopower points to thermodynamic nature of metal-insulator transition in 2D systems. PACS numbers: 73.40.Qv, 71.30+h, 73.20.Fz Recently, a great deal of interest has been focussed on the anomalous transport behavior of a wide variety of low-density 2D electron [1,2] and hole [3,4,5] systems. It has been found that, below some critical density, the cooling causes an increase in resistivity, whereas in the opposite high density case the resistivity decreases. Another unusual property of dilute 2D systems is their enormous response to parallel magnetic field. At low temperatures the magnetic field found to suppress the metallic behavior of 2D electron(hole) gas and result in strong increasing of resistivity upon enhancement of spin polarization degree [6,7]. At high temperatures the parallel magnetoresistivity starts to be unaffected by magnetic field when the temperature exceeds a value being of the order of Zeeman energy. A strong perpendicular magnetic field, if applied simultaneously with the parallel one, results in suppression of parallel magnetoresistivity [8]. Although numerous theories have been put forward to account for these effects, the origin of the above behavior is still the subject of a heated debate.The ohmic measurements known to be carried out at low current I → 0 in order to prevent heating. Usually, only the Joule heat is considered to be important. In contrast to the Joule heat, the Peltier and Thomson effects are linear in current. As shown in Refs. [9,10,11], the Peltier effect influences ohmic measurements and results in a correction to a measured resistance. When current is flowing, one of the sample contacts is heated, and the other cooled, because of the Peltier effect. The contact temperatures are different. The voltage drop across the circuit includes the Seebeck thermoelectromotive force, which is linear in current. Finally, there exists a thermal correction ∆ρ, to the ohmic resistivity, ρ, of the sample. For degenerate electrons, ∆ρ/ρ ∼ (kT /µ) 2 , where µ is the Fermi energy. Hence, the correction may be comparable with the ohmic resistance of a sample when kT ∼ µ.In the present paper, we report on a study of low-T transport in 2D electron(hole) gas, taking into account both the electron degeneracy and the Peltier-effectinduced correction to resistivity. [9,10]. The parallel magnetoresistivity found to originate from the spin and,if exists, valley splitting of 2D energy spectrum.Let us consider, for clarity, the (100) MOSFET 2DEG system. The electrons are assumed to occupy the first quantum-well subband with isotropic energy spectrum ε(k) =h 2 k 2 2m...

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Metal-Insulator Transition atB=0in a Dilute Two Dimensional GaAs-AlGaAs Hole Gas

Cited by 246 publications

References 22 publications

Spin–valley phase diagram of the two-dimensional metal–insulator transition

Spin–valley phase diagram of the two-dimensional metal–insulator transition

One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect

Thermal correction to resistivity in dilute 2D Si-based systems

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