Quantum-Hall plateau−plateau transition in top-gated epitaxial graphene grown on SiC (0001)

Shen, Tian; Neal, Adam T.; Bolen, Michael; Gu, Jiangjiang; Engel, L. W.; Capano, Michael A.; Ye, Peide D.

doi:10.1063/1.3675464

Cited by 18 publications

(20 citation statements)

References 35 publications

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“…(11)- (13) are not determined by the graph-theoretic data for the corresponding digraph (even in the simplest case of the critical point in the isotropic system). Therefore, it seems that an explicit calculation of S(p) for a given picture p is a much more challenging problem than that for |F (p)|.…”

Section: Discussionmentioning

confidence: 99%

“…A famous example is the integer quantum Hall (IQH) plateau transition observed in two-dimensional (2D) semiconductor devices subject to strong magnetic fields. The nature of the critical state at and the critical phenomena near the IQH transition are at the focus of intense experimental [8][9][10][11][12][13] and theoretical research. [14][15][16][17][18][19][20][21][22][23] In spite of much effort over several decades, an analytical treatment of most of the critical conducting states in disordered electronic systems, including in particular that of the mentioned IQH transition, has been elusive (although some proposals [14][15][16] have been put forward, but see Refs.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Hall transitions: An exact theory based on conformal restriction

2012

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We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, and for other two-dimensional disordered systems, based on the theory of "conformal restriction". This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the "stochastic geometry" of fractal curves and other stochastic geometrical fractal objects in two-dimensional space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model for the transition. We show that the disorder-averaged PCCs are characterized by a classical probability distribution for certain geometric objects in the plane (which we call pictures), occurring with positive statistical weights, that satisfy the crucial so-called restriction property with respect to changes in the shape of the sample with absorbing boundaries; physically, these are boundaries connected to ideal leads. At the transition point, these geometrical objects (pictures) become fractals. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of "conformal restriction measures" to relate the disorder-averaged PCCs to correlation functions of (Virasoro) primary operators in a conformal field theory (of central charge c = 0). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in two spatial dimensions, including for example the spin quantum Hall effect, the thermal metal phase in symmetry class D, and classical diffusion in two dimensions in a perpendicular magnetic field. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Hall transitions: An exact theory based on conformal restriction

2012

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“…6,7 Both techniques recently achieved at wafer scale mobility and uniformity levels comparable to those of exfoliated graphene. 8,9 As a major drawback, graphene produced by CVD must be transferred onto an insulating substrate for its use in electronics applications. On the contrary, the SiC substrate is insulating, and this in principle offers a clear technological advantage over other methods.…”

Section: Introductionmentioning

confidence: 99%

Bilayer-induced asymmetric quantum Hall effect in epitaxial graphene

Iagallo

Tanabe

Roddaro

et al. 2015

Semicond. Sci. Technol.

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The transport properties of epitaxial graphene on SiC(0001) at quantizing magnetic fields are investigated. Devices patterned perpendicularly to SiC terraces clearly exhibit bilayer inclusions distributed along the substrate step edges. We show that the transport properties in the quantum Hall regime are heavily affected by the presence of bilayer inclusions, and observe a significant departure from the conventional quantum Hall characteristics. A quantitative model involving enhanced inter-channel scattering mediated by the presence of bilayer inclusions is presented that successfully explains the observed symmetry properties.

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“…Specifically, the relativistic quantization of graphene's electronic spectrum results in distinct characteristics, including the presence of a Landau level (LL) at zero energy and chiral QHE. [8][9][10][11][12] In the quantum Hall (QH) regime, the plateau-plateau transition and the scaling behavior have been studied using Hall bar [13][14][15][16][17][18] and Corbino geometry, 19 providing important information about the carrier localization in graphene. A scaling exponent for typical Anderson-type transition κ ≅ 0.42 has been reported in graphene, 13,14 while some studies showed reduced value of κ .…”

mentioning

confidence: 99%

“…[8][9][10][11][12] In the quantum Hall (QH) regime, the plateau-plateau transition and the scaling behavior have been studied using Hall bar [13][14][15][16][17][18] and Corbino geometry, 19 providing important information about the carrier localization in graphene. A scaling exponent for typical Anderson-type transition κ ≅ 0.42 has been reported in graphene, 13,14 while some studies showed reduced value of κ . [15][16][17][18][19] In a graphene Hall bar, the slope of the Hall conductivity at the transition region, d / , exhibits scaling behavior with κ = 0.41 for the first and second LLs, while that of the zeroth LL is temperature (T) independent.…”

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confidence: 99%

Observation of quantum Hall plateau-plateau transition and scaling behavior of the zeroth Landau level in graphenep−n−pjunctions

et al. 2016

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We report distinctive magnetotransport properties of a graphene p-n-p junction prepared by controlled diffusion of metallic contacts. In most cases, materials deposited on a graphene surface introduce substantial carrier scattering, which greatly reduces the high mobility of intrinsic graphene. However, we show that an oxide layer only weakly perturbs the carrier transport, which enables fabrication of a high-quality graphene p-n-p junction through a one-step and resist-free method. The measured conductance-gate voltage ( − ) curves can be well described by a metal contact model, which confirms the charge density depinning due to the oxide layer. The graphene p-n-p junction samples exhibit pronounced quantum Hall effect, a well-defined transition point of the zeroth Landau level (LL), and scaling behavior. The scaling exponent obtained from the evolution of the zeroth LL width as a function of temperature exhibits a relatively low value of κ = 0.21 ± 0.01.Moreover, we calculate the energy level for the LLs based on the distribution of plateauplateau transition points, further validating the assignment of the LL index of the QH plateau-plateau transition. KeywordsGraphene p-n-p junction, quantum Hall effect, plateau-plateau transition, scaling behavior, while that of the zeroth LL is temperature (T) independent. 13 In a Corbino geometry, FWHM Δν of the zeroth LL is T dependent and shows scaling behavior with κ = 0.16, which is attributed to an inhomogeneous charge carrier distribution. 19 However, until now, a well-defined QH plateau-plateau transition point of the zeroth LL of graphene has not been directly observed, obscuring a detailed understanding of the scaling behavior of this unique LL. Moreover, the variation of the T exponent in previous reports suggests the need for further investigation of the scaling behavior of the zeroth LL using different methods for the device structures.In this report, we fabricate a high-quality graphene p-n-p junction, achieved via controlled diffusion of metallic contacts, to explore the QH plateau-plateau transition and 4 scaling behavior of graphene. Interestingly, we observe a well-defined transition point corresponding to the zeroth LL, revealing the scaling behavior and a reduced T exponent.There are additional advantages of utilizing a graphene p-n-p junction to explore the transition region of the QHE. First, the presence of the transition between an integer QH plateau and a QH plateau with a fractional value enables direct access to the transition of the zeroth LL. Second, in a graphene p-n-p geometry, the intrinsic graphene is adjoined by the doped graphene from both sides. The doped graphene regions can be viewed as an ideal contact, facilitating the investigation of the transition region of the intrinsic graphene.Moreover, we derive the value of energy level for the observed LLs, which agrees with the theoretical values, further validating the assignment of the LL index of the QH plateauplateau transition.A detailed device fabrication process can be found i...

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Quantum-Hall plateau−plateau transition in top-gated epitaxial graphene grown on SiC (0001)

Cited by 18 publications

References 35 publications

Quantum Hall transitions: An exact theory based on conformal restriction

Quantum Hall transitions: An exact theory based on conformal restriction

Bilayer-induced asymmetric quantum Hall effect in epitaxial graphene

Observation of quantum Hall plateau-plateau transition and scaling behavior of the zeroth Landau level in graphenep−n−pjunctions

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