Scaling and the metal-insulator transition in Si/SiGe quantum wells

Abstract. We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. PACS. 72.15.-v Electronic conduction in metals and alloy -73.20.Dx Electron states in low-dimensional structures -72.10.Bg General formulation of transport theory -05.60.Gg Quantum transport

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“…20.Dx Electron states in low-dimensional structures -72. 10.Bg General formulation of transport theory -05.60.Gg Quantum transport…”

Section: November 6 2000mentioning

confidence: 99%

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

Weinmann

Schmitteckert²,

Jalabert³

et al. 2001

Eur. Phys. J. B

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“…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.…”

mentioning

confidence: 99%

“…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%

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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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“…The 2D systems that show the MIT [1][2][3][4][5][6] are characterized by strong Coulomb interaction between electrons. The mean Coulomb energy per electron U = (πN s ) 1/2 e 2 /4πε 0 κ is larger than the mean kinetic energy K = πh 2 N s /m * by an order of the magnitude around the critical point for the MIT.…”

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Spin Degree of Freedom in a Two-Dimensional Electron Liquid

et al. 1999

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We have investigated correlation between spin polarization and magnetotransport in a high mobility silicon inversion layer which shows the metal-insulator transition. Increase in the resistivity in a parallel magnetic field reaches saturation at the critical field for the full polarization evaluated from an analysis of low-field Shubnikov-de Haas oscillations. By rotating the sample at various total strength of the magnetic field, we found that the normal component of the magnetic field at minima in the diagonal resistivity increases linearly with the concentration of "spin-up" electrons. 71.30.+h, 73.40.Qv, 73.40.Hm A metal-insulator transition (MIT) observed in Si metal-oxide-semiconductor field-effect transistors [1,2] (Si-MOSFET's) and other systems [3-6] attracts a great deal of attention since it seems to contradict an important result of the scaling theory by Abrahams et al. [7] that the conductance of a disordered two-dimensional (2D) system at zero magnetic field goes to zero for T → 0. In the metallic phase in Si-MOSFET's with high peak electron mobilities of µ peak > ∼ 2 m 2 /V s, the diagonal resistivity ρ xx shows a sharp drop with decreasing temperature from about 2 K [1]. Recent experiments [8,9] show that magnetic fields applied parallel to the 2D plane suppress the low temperature metallic conduction in Si-MOSFET's. Since the parallel magnetic field does not couple the orbital motion of electrons, this fact suggests an important role of the spin of electrons. However, the mechanism of the conduction in the anomalous metallic phase is not clear yet.The 2D systems that show the MIT [1-6] are characterized by strong Coulomb interaction between electrons. The mean Coulomb energy per electron U = (πN s ) 1/2 e 2 /4πε 0 κ is larger than the mean kinetic energy K = πh 2 N s /m * by an order of the magnitude around the critical point for the MIT. Here, N s is the electron concentration, κ is the relative dielectric constant at the interface, and m * is the effective mass of electron. It is estimated that U = 120 K, K = 14 K and the ratio r s = U/K = 8.3 for κ = 7.7 and m * = 0.19m e at N s = 1 × 10 15 m −2 in Si-MOSFET's. The ground state of the insulating phase of high mobility Si-MOSFET's is considered to be a pinned Wigner solid (WS) [10,11]. Magnetic field dependence of the thermal activation energy observed for various angles of the magnetic field was essentially explained by a model based on magnetic interactions in the pinned WS [12,13]. Although the quantum fluctuations change the 2D system into a liquid at higher-N s , electron-electron (e-e) interaction is expected to be still important.In the conduction band of silicon, the spin-orbit interaction is negligible and the spin polarization p = (N ↑ − N ↓ )/N s can always be given in the direction to the magnetic field. Here N ↑ and N ↓ are the concentrations of electrons having an up spin and a down spin, respectively (N s = N ↑ + N ↓ ). In the present work, we investigate the low temperature conduction in a high mobility Si-MOSFET for vario...

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Scaling and the metal-insulator transition in Si/SiGe quantum wells

Cited by 59 publications

References 17 publications

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

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

Spin Degree of Freedom in a Two-Dimensional Electron Liquid

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