Weak-Field Hall Effect in Graphene with Long-Range Scatterers

Noro, Masaki; Ando, Tsuneya

doi:10.7566/jpsj.85.014708

Cited by 14 publications

(8 citation statements)

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“…where l is the magnetic length given by l = √ ch/(eB). Correspondingly, the Green's function is modified intô (25) to the second order in B. We should note that the translational invariance is recovered after taking the average over impurity configurations.…”

Section: Weak-field Magnetoconductivitymentioning

confidence: 99%

“…The weak-field Hall conductivity has already been calculated using this scheme in various systems, including graphene, [17][18][19][20][21][22][23][24][25] molecular conductors, 26,27 and giant Rashba systems, [28][29][30] where transport quantities exhibit intriguing behaviors at a band-crossing point. 7,14,[31][32][33][34][35][36][37][38] It has been shown, further, that a divergence problem can appear, which can cause serious problems in particular in the case of scatterers with long-range potential.…”

Section: Introductionmentioning

confidence: 99%

“…(a) The table showing the values of F(26) and F(25) required for the calculation of the magnetoconductivity. The number in the column denoted as 'Subscript' shows the position of Q− and '0' corresponds to the case that no Q− is included.For example, F0 ≡ F++++++, F2 ≡ F+−++++, F25 ≡ F+−++−+, etc.…”

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confidence: 99%

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Formula of Weak-Field Magnetoresistance in Graphene

Ando

2019

J. Phys. Soc. Jpn.

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The formula of weak-field magnetoconductivity ∆σ(B) proportional to B 2 , with B the strength of a magnetic field, is derived for systems corresponding to monolayer and bilayer graphenes. It is represented by Feynman diagrams given by three hexagons. In order to see qualitative features of the magnetoconductivity, it is calculated for monolayer graphene in a constant broadening approximation, in which a single imaginary self-energy is introduced. The results show that −∆σ(B) is exactly the same as the counter term due to the Hall current in the energy region away from zero energy, leading to the vanishing magnetoresistance in the Hall bar geometry. In the vicinity of zero energy, −∆σ(B) exhibits a prominent double-peak structure similar to that of the counter term. However, its absolute value becomes slightly smaller than the counter term, giving negative magnetoresistance having double-dip structure.

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Section: Weak-field Magnetoconductivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Formula of Weak-Field Magnetoresistance in Graphene

Ando

2019

J. Phys. Soc. Jpn.

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“…. We notice that the recently discussed unusual behavior of R H at vanishing electron-doping concentration in graphene [32,33], where θ tan H tends to zero while σ xx saturates to the minimum conductivity, shares the common origin in mathematics.…”

Section: When E F Locates Below the Bcpmentioning

confidence: 53%

Semiclassical magnetotransport in strongly spin–orbit coupled Rashba two-dimensional electron systems

Xiao

2016

J. Phys.: Condens. Matter

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Semiclassical magnetoelectric and magnetothermoelectric transport in strongly spin-orbit coupled Rashba two-dimensional electron systems is investigated. In the presence of a perpendicular classically weak magnetic field and short-range impurity scattering, we solve the linearized Boltzmann equation self-consistently. Using the solution, it is found that when Fermi energy E F locates below the band crossing point (BCP), the Hall coefficient is a nonmonotonic function of electron density n e and not inversely proportional to n e. While the magnetoresistance (MR) and Nernst coefficient vanish when E F locates above the BCP, non-zero MR and enhanced Nernst coefficient emerge when E F decreases below the BCP. Both of them are nonmonotonic functions of E F below the BCP. The different semiclassical magnetotransport behaviors between the two sides of the BCP can be helpful to experimental identifications of the band valley regime and topological change of Fermi surface in considered systems.

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“…We discretize k and numerically solve the self-consistency equation and Bethe-Salpeter-type equations iteratively in a manner discussed previously. 11,13,14,22,32,[46][47][48][49][50] The actual value of cutoff ε c is irrelevant as long as it is sufficiently larger than typical energy scale γ 1 because states with higher energy do not contribute to physical quantities for scatterers with potential range larger than the lattice constant.…”

Section: B Self-consistent Born Approximationmentioning

confidence: 99%

Theory of Weak-Field Magnetoresistance in Bilayer Graphene

Ando

2019

J. Phys. Soc. Jpn.

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The magnetoconductivity, which is the correction to the diagonal conductivity proportional to the second power of magnetic-field strength, is calculated in bilayer graphene in the presence of scatterers with long-range potential such as a Gaussian potential and screened Coulomb potential in a self-consistent Born approximation. The magnetoresistivity in a usual Hall bar geometry exhibits prominent double-peak structure in the vicinity of zero energy and remains very small in other regions because of the cancellation with a counter term due to the Hall effect. In a constant broadening approximation, on the other hand, the magnetoresistivity becomes negative and has a sharp double-dip structure. These features are quite similar to those in monolayer graphene.

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Weak-Field Hall Effect in Graphene with Long-Range Scatterers

Cited by 14 publications

References 94 publications

Formula of Weak-Field Magnetoresistance in Graphene

Formula of Weak-Field Magnetoresistance in Graphene

Semiclassical magnetotransport in strongly spin–orbit coupled Rashba two-dimensional electron systems

Theory of Weak-Field Magnetoresistance in Bilayer Graphene

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