Influence of parallel magnetic fields on a single-layer two-dimensional electron system with a hopping mechanism of conductivity

Shlimak, I.; Khondaker, Saiful I.; Pepper, M.; Ritchie, D. A.

doi:10.1103/physrevb.61.7253

Cited by 27 publications

(36 citation statements)

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“…The temperature dependence of the resistivity in zero field was attributed to Efros-Shklovskii variable range hopping with α = 1 2 down to ≈ 0.3 K by Mertes et al [11] and Jarozynski et al [13] and over a broader range to lower temperatures by Mason et al [22]. The zero-field resistivity was found to obey the same form in a single two-dimensional layer of δ-doped GaAs/Al x Ga 1−x As [25]. By contrast, Arrhenius-type activated behavior (α = 1) was claimed for silicon in zero field by Shashkin et al [12].…”

Section: Fig 1: Nonlinear Current-voltage (I-v) Characteristics In Zeromentioning

confidence: 86%

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Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Sarachik

2017

Phys. Rev. B

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The resistivities of the dilute, strongly-interacting 2D 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 ρ(T ) = ρ0exp[(TES/T ) 1/2 ], with TES and 1/ρ0 mapping onto each other if one applies a shift of the critical density nc reported earlier.With and withoug magnetic field, the parameters TES and 1/ρ0 = σ0 exhibit scaling consistent with critical behavior approaching a metal-insulator transition.PACS numbers: 71.30.+h, 72.20.Ee, 64.60.FTwo-dimensional (2D) electron systems realized in semiconductor heterostructures and on the surface of doped semiconductor devices such as silicon MOSFETs have been intensively studied for more than half a century [1]. Significant advances in fabrication techniques in recent years have yielded samples with greatly increased electron mobility thereby allowing access to lower electron densities, a regime where the energy of interactions between the electrons is dominant and substantially larger than their kinetic energy. Rather than exhibiting a resistivity that increases logarithmically toward infinity as the temperature is reduced [2] as expected within the theory of localization [3], the resistivity of these stronglyinteracting dilute 2D electron systems displays metalliclike behavior at low temperatures and insulating behavior as the electron density is reduced below a materialdependent critical electron density n c (see references [4-6] for reviews). The apparent metal-insulator transition and metallic phase observed in high-mobility, strongly interacting 2D electron systems is widely regarded as one of the most important unresolved problems in condensed matter physics.Exceptionally large magnetoresistances have been reported in response to in-plane magnetic field in the vicinity of the critical electron density, n c . For electron densities n s > n c on the just-metallic side of the transition, increasing the parallel magnetic field causes the resistivity to increase by several orders of magnitude at low temperatures and reach saturation at a density-dependent field B sat ; for B > B sat the temperature dependence of the resistivity is that of an insulator. Measurements have confirmed that the saturation of the sample resistivity corresponds to full spin polarization [7,8]. Since the parallel magnetic field does not couple to the orbital motion of electrons in sufficiently thin 2D systems, this suggests an important role for the electron spins.The magnetoresistance has been thoroughly investigated on the metallic side of the transition, while considerably less information has been gathered in the insulating phase. In order to better understand the effect of spin, we embarked on a detailed comparison of the resistivity of the insulating state arrived at by: (1) reducing the electron density below the critical density n c in ...

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Section: Fig 1: Nonlinear Current-voltage (I-v) Characteristics In Zeromentioning

confidence: 86%

“…For a single two-dimensional layer of δ-doped GaAs/Al x Ga (1−x) As in parallel fields of 8 T and 6 T, Shlimak et al reported an exponent of 0.8 [25].…”

Section: Fig 1: Nonlinear Current-voltage (I-v) Characteristics In Zeromentioning

confidence: 99%

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Sarachik

2017

Phys. Rev. B

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“…The strong positive MR persists deep in the insulating state and is exhibited by systems which were perfectly insulating at H ¼ 0 [4]. The temperature dependence of the MR is close to the Arrhenius law even if for H ¼ 0 the system exhibits a variable range hopping of Efros-Shklovskii type (such a behavior was observed for Si MOS-FETS [4] and n-type GaAs heterostructures [15]). As we have discussed earlier, the activated behavior of MR in the hopping regime can be a signature of the hopping over the states of the UHB.…”

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A Possible Role of the D ^– Band in Hopping Conductivity and Metal–Insulator Transition in 2D Structures

Козуб

2002

phys. stat. sol. (b)

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It is demonstrated that the upper Hubbard band (UHB) can play an important role in the hopping conductivity; 2D geometry and vicinity of the metal-insulator transition emphasize this role. A simple model for the recently observed metal-insulator transition is suggested. The model starts from the insulating limit and implies a principal role of the UHB. It gives a qualitative explanation for most of the features of the transition. The quantitative analysis of MR in the strongly insulating limit leads to values of g-factors in good agreement with the known values.The hopping transport over states within the upper Hubbard band (involving doubly occupied (D À ) localized states) has been considered already in early years of studies of the hopping conductivity [1]. Although the presence of this channel was never disputed, during recent years the hopping was typically considered as related to the "standard" impurity band [2]. It was mainly due to the fact that the theoretical estimate of the binding energy of the doubly occupied state appeared to be too small in comparison to the Bohr energy and the activation to the D À states apparently cannot be discriminated from the activation to the conductance band. This paper is aimed at demonstrating that actually the possibilities to observe a contribution of the upper Hubbard band (UHB) are much better than it has been generally believed. The most favorable situation seems to correspond to the 2D structures. Moreover, we believe that it is a contribution of the D À states which can throw light on the problem of the recently observed metalinsulator transition (MIT) in 2D ([3], see also the review paper [4]). We will describe a simple model starting from the insulating limit which allows to explain the main features of this phenomenon.We start from the nearest neighbor hopping where the contribution of the UHB is associated with the so-called e 2 conductivity. While the temperature dependence of the conductivity does not allow to make a clear conclusion concerning the role of the UHB, the magnetoresistance gives such an opportunity. Indeed, it can be shown that the spin correlations in the D À state lead to an increase of the effective Hubbard energy U (and, correspondingly, of the activation energy e 2 $ U) by the addition [5]As seen, at low temperatures the magnetic field leads to the "universal" addition m B gH which includes the only material parameter --the g-factor. Basing on these considerations, we have reconsidered the existing data on the magnetoresistance for the nearest neighbor hopping in recent papers [5,6]. The surprisingly good agreement between the g-factor values extracted from the experimental data and the corresponding handbook values leads us to the conclusion that in many cases the magnetoresistance is related to phys. stat. sol. (b) 230,

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“…Measurements were made on two silicon MOSFET's of mobility approximately 20 000 V/cm 2 at 4.2 K using a gate to control electron densities between 0.64ϫ10 11 cm Ϫ2 and 3.60ϫ10 11 cm Ϫ2 . Contact resistances were minimized by using a split-gate geometry that allows a higher electron density in the vicinity of the contacts than in the 2D system under investigation.…”

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confidence: 99%

“…We now briefly consider the behavior of the resistance in high fields for electron densities above 1.35ϫ10 11 …”

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Temperature dependence of the resistivity of a dilute two-dimensional electron system in high parallel magnetic field

et al. 2001

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We report measurements of the resistance of silicon metal-oxide-semiconductor field-effect transistors as a function of temperature in high parallel magnetic fields where the two-dimensional system of electrons has been shown to be fully spin polarized. In a field of 10.8 T, insulating behavior is found for densities up to n s Ϸ1.35ϫ1011 cm Ϫ2 Ϸ1.5n c ; above this density the resistance is a very weak function of temperature, varying less than 10% between 0.25 and 1.90 K. At low densities →ϱ more rapidly as the temperature is reduced than in zero field and the magnetoresistance ⌬/ diverges as T→0. A great deal of interest is currently focused on the behavior of dilute strongly interacting two-dimensional ͑2D͒ systems of electrons and holes. The resistance of these materials displays strongly insulating behavior below some critical density, n c , above which metallic temperature dependence is observed, suggesting that there is a metal-insulator transition and an unexpected metallic phase in two dimensions.1 One of the most interesting properties of these dilute 2D systems is their enormous positive magnetoresistance in response to magnetic fields applied parallel to the plane of the electrons. As the field is raised the resistivity increases dramatically by several orders of magnitude, the total change depending on density and temperature, and then saturates to a new fieldindependent plateau value above a density-dependent field H sat . [2][3][4][5][6] From an analysis of the positions of Shubnikov-de Haas oscillations in tilted magnetic fields, Okamoto et al. 7 have argued that the magnetic field above which the resistivity saturates is the field required to fully polarize the electron spins. A more direct demonstration of the onset of complete spin alignment for H ʈ ϷH sat has recently been provided by small-angle Shubnikov-de Haas measurements of Vitkalov et al. 8 Thus, the value of the resistance appears to be determined by the degree of spin polarization of the 2D electron system.The temperature dependence of the resistance of dilute 2D systems has been measured in the absence of a magnetic field in a number of different materials. In this paper, we report measurements of the temperature dependence of the resistivity of high-mobility silicon MOSFET's in a high magnetic field of 10.8 T applied parallel to the plane of the electrons.Measurements were made on two silicon MOSFET's of mobility approximately 20 000 V/cm 2 at 4.2 K using a gate to control electron densities between 0.64ϫ10 11 cm Ϫ2 and 3.60ϫ10 11 cm Ϫ2 . Contact resistances were minimized by using a split-gate geometry that allows a higher electron density in the vicinity of the contacts than in the 2D system under investigation. dc four-probe methods were used, and excitation currents were kept to a minimum to avoid heating of the electrons and insure that measurements were taken in the linear I-V regime. Data were taken in a 3 He Oxford Heliox system for temperatures between 0.25 and 1.90 K in magnetic fields to 10.8 T. A rotator was used to...

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Influence of parallel magnetic fields on a single-layer two-dimensional electron system with a hopping mechanism of conductivity

Cited by 27 publications

References 22 publications

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

A Possible Role of the D ^– Band in Hopping Conductivity and Metal–Insulator Transition in 2D Structures

Temperature dependence of the resistivity of a dilute two-dimensional electron system in high parallel magnetic field

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Influence of parallel magnetic fields on a single-layer two-dimensional electron system with a hopping mechanism of conductivity

Cited by 27 publications

References 22 publications

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

A Possible Role of the D – Band in Hopping Conductivity and Metal–Insulator Transition in 2D Structures

Temperature dependence of the resistivity of a dilute two-dimensional electron system in high parallel magnetic field

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A Possible Role of the D ^– Band in Hopping Conductivity and Metal–Insulator Transition in 2D Structures