Spin polarization and metallic behavior in a silicon two-dimensional electron system

Okamoto, Tohru; Ooya, Mitsuaki; Hosoya, Kunio; Kawaji, Shinji

doi:10.1103/physrevb.69.041202

Cited by 53 publications

(55 citation statements)

References 24 publications

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“…7,8,9 In Figure 3(c), we plot B c as a function of n. We also include the data obtained by Okamoto et al, 21 measured at densities n > 1 × 10 11 cm −2 . Results from two experiments are in good agreement with each other.…”

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confidence: 94%

Two-dimensional metal-insulator transition and in-plane magnetoresistance in a high-mobility strained Si quantum well

et al. 2005

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The apparent metal-insulator transition is observed in a high quality two-dimensional electron system (2DES) in the strained Si quantum well of a Si/Si1−xGex heterostructure with mobility µ = 1.9 × 10 5 cm 2 /Vs at density n = 1.45 × 10 11 cm −2 . The critical density, at which the thermal coefficient of low T resistivity changes sign, is ∼ 0.32 × 10 11 cm −2 , so far the lowest observed in the Si 2D systems. In-plane magnetoresistance study was carried out in the higher density range where the 2DES shows the metallic-like behavior. It is observed that the in-plane magnetoresistance first increases as ∼ B 2 ip and then saturates to a finite value ρ(Bc) for Bip > Bc. The full spin-polarization field Bc decreases monotonically with n but appears to saturate to a finite value as n approaches zero. Furthermore, ρ(Bc)/ρ(0) ∼ 1.8 for all the densities ranging from 0.35 × 10 11 to 1.45 × 10 11 cm −2 and, when plotted versus Bip/Bc, collapses onto a single curve.The two-dimensional (2D) metal-to-insulator transition (MIT) has been of great current interests. 1,2 According to the well-established scaling theory, 3 any amount of disorder in a non-interacting 2D electron system (2DES) will localize the carriers at zero temperature (T ) and zero magnetic (B) field, and the ground state of the 2DES is an insulator, whose conductivity logarithmically goes to zero as T → 0. Recent experimental studies in high quality dilute 2D systems where the electron-electron (e − e) interaction is large, however, have shown the existence of a metallic-like state and an apparent metal-insulator transition. There, the magnitude of the 2DES resistivity (ρ) undergoes a change from decreasing with decreasing T , (dρ/dT > 0), a metallic behavior, to increasing with decreasing T , (dρ/dT < 0), an insulating behavior, at a critical density n c .One of the fundamental questions in this apparent MIT problem is the nature of the metallic state 4 and its response to a pure in-plane magnetic field (B ip ). 5,6,7,8,9,10,11,12,13 It is observed that in conventional clean Si-MOSFET's the in-plane magnetoresistance (MR) of the 2DES, ρ(B ip ), first increases as B 2 ip at low B ip . After a critical B field B c , which has been identified as the full spin polarization B field for the 2DES, 7,8,9 the in-plane MR saturates to a constant value ρ(B c ).14 The enhancement of ρ(B ip ) under high in-plane B field in this 2DES is attributed to the reduction of screening of charged impurities in a Fermi liquid, caused by the loss of spin degeneracy, 15,16,17 and a ratio of ρ(B c )/ρ(0) = 4 or ∼ 1.2 is expected when the background impurity scattering 15 or the remote ionized impurity scattering 17 dominates. Thus, it is surprising that close to the critical density n c , the enhancement can be as large as several orders of magnitude.1,2,5,7,8,10,11 Furthermore, it has been shown that under B ip the metallic state is suppressed, and completely destroyed for n < 1.5n c . A recent study has demonstrated that the disappearance of the positive dρ/dT in large B ip is due t...

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Two-dimensional metal-insulator transition and in-plane magnetoresistance in a high-mobility strained Si quantum well

et al. 2005

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“…These 2D systems are a promising candidate for studying the energy spectrum and transport properties of strongly interacting electrons [21]. Anisotropy of the magnetoresistance opposite to that expected for the finite thickness of the quantum well was reported for SiGe/Si/SiGe quantum wells [22]. However, the cause of this anisotropy remained unclear.…”

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confidence: 99%

Unusual anisotropy of inplane field magnetoresistance in ultra-high mobility SiGe/Si/SiGe quantum wells

Mel'nikov

Dolgopolov

Shashkin

et al. 2017

Journal of Applied Physics

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We find an unusual anisotropy of the inplane field magnetoresistance with higher resistance in the parallel orientation of the field, B , and current, I, in ultra-high mobility SiGe/Si/SiGe quantum wells. The anisotropy depends on the orientation between the inplane field and current relative to the crystallographic axes of the sample and is a consequence of the ridges on the quantum well surface. For the parallel or perpendicular orientations between current and ridges, a method of converting the magnetoresistance measured at I ⊥ B into the one measured at I B is suggested and is shown to yield results that agree with the experiment.

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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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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 polarization and metallic behavior in a silicon two-dimensional electron system

Cited by 53 publications

References 24 publications

Two-dimensional metal-insulator transition and in-plane magnetoresistance in a high-mobility strained Si quantum well

Two-dimensional metal-insulator transition and in-plane magnetoresistance in a high-mobility strained Si quantum well

Unusual anisotropy of inplane field magnetoresistance in ultra-high mobility SiGe/Si/SiGe quantum wells

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

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