Diffusion of Dirac fermions across a topological merging transition in two dimensions

Adroguer, Pierre; Carpentier, David; Montambaux, Gilles; Orignac, Edmond

doi:10.1103/physrevb.93.125113

Cited by 47 publications

(48 citation statements)

References 38 publications

(61 reference statements)

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“…7, we show our numerical results forμ = 0, 1, 2.5, 5 and 10, evaluated from Eqs. (41) and (42) √ Ω dependence of the clean limit (solid blue curve of Fig. 2).…”

Section: Impurity Scatteringmentioning

confidence: 99%

“…In this case, the material parameters m and v have dropped out as has the scattering rate √ Γ which appears in Eqs. (41) and (42) so that the remaining prefactor unit is simply e 2 /h. There are only small differences between these curves and the corresponding curves for graphene (not shown).…”

Section: Impurity Scatteringmentioning

confidence: 99%

“…They also calculate a diffusion coefficient from the mean square displacement of the charge carriers and find that it is very different for relativistic than for the nonrelativistic dispersion curves. In related work, Adroguer et al 41 use both a Boltzmann formalism and a Kubo formula approach in a random impurity model to treat the optical intraband transitions. They find a resulting residual scattering rate which is not only dependent on energy but is, as well, highly anisotropic.…”

Section: Introductionmentioning

confidence: 99%

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Optical properties of a semi-Dirac material

2019

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Within a Kubo formalism, we calculate the absorptive part of the dynamic longitudinal conductivity σ(Ω) of a 2D semi-Dirac material. In the clean limit, we provide separate analytic formulas for intraband (Drude) and interband contributions for σ(Ω) in both the relativistic and nonrelativistic directions. At finite doping, in the relativistic direction, a sumrule holds between the increase in optical spectral weight in the Drude component and that lost in the interband optical transitions. For the nonrelativistic direction, no such sumrule applies. Results are also presented when an energy gap opens in the energy dispersion. Numerical results due to finite residual scattering are provided and analytic results for the dc limit are derived. Energy dependence and possible anisotropy in the impurity scattering rate is considered. Throughout, we provide comparison of our results for √ σxxσyy with the corresponding results for graphene. A generalization of the 2D Hamiltonian to include powers of higher order than quadratic (nonrelativistic) and linear (relativistic) is considered. We also discuss the modifications introduced when an additional flat band is included via a semi-Dirac version of the α-T3 model, for which an α parameter tunes between the 2D semi-Dirac (graphene-like) limit and the semi-Dirac version of the dice or T3 lattice.

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“…7, we show our numerical results forμ = 0, 1, 2.5, 5 and 10, evaluated from Eqs. (41) and (42) √ Ω dependence of the clean limit (solid blue curve of Fig. 2).…”

Section: Impurity Scatteringmentioning

confidence: 99%

Section: Impurity Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optical properties of a semi-Dirac material

2019

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“…In this paper, we consider both optical and transport properties. Recently Adroguer et al 34 have considered in the diffusive limit some aspects of the transport and optics using both a Boltzmann and a diagrammatic approach with particular emphasis on anisotropy in the residual scattering that has its origin in the semi-Dirac nature of the model. In one direction, the band structure is "relativistic" (energy is linear in momentum), while in the other it is "nonrelativistic" (energy is quadratic in momentum).…”

Section: Introductionmentioning

confidence: 99%

Signatures of merging Dirac points in optics and transport

Ćarbotte

Nicol

2019

Phys. Rev. B

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We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter ∆, there are two distinct Dirac points with linear dispersion, these are connected by a saddle point at higher energy. As ∆ goes to zero, the two Dirac points merge and the resulting dispersion exhibits semi-Dirac behaviour which is quadratic in the x-direction ("nonrelativistic") and linear the y-direction ("relativistic"). In the clean limit for each direction (x, y) the contribution of the intraband and interband optical transitions are both given by universal functions of photon energy Ω and chemical potential µ normalized to the energy gap. We provide analytic formulas for both small and large Ω/2∆ and µ/∆ limits. These define, respectively, Dirac and semi-Dirac-like regions.For Ω/2∆ and µ/∆ of order one, there are deviations from these asymptotic behaviors. Considering optics and also transport, such as dc conductivity, thermal conductivity and the Lorenz number, such deviations provide signatures of the evolution from the Dirac to the semi-Dirac regime as the gap ∆ is varied.

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“…Materials possessing semi-Dirac points are called semi-Dirac semimetals, which provide a platform where massless and massive Dirac fermions coexist. Besides the apparent highly anisotropic transport properties [7] , a number of other interesting properties have been predicted for the semi-Dirac semimetals, such as distinct Landau-level spectrum in a magnetic field [8,9] , non-Fermi liquid [10] , Anderson localization [11] and Bloch-Zener oscillations [12] . It is therefore of great interest to search for materials realizing the semi-Dirac semimetals.…”

Section: Introductionmentioning

confidence: 99%

Semi-Dirac semimetal in silicene oxide

Zhong

Chen

Xie

et al. 2017

Phys. Chem. Chem. Phys.

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Semi-Dirac semimetal is a material exhibiting linear band dispersion in one direction and quadratic band dispersion in the orthogonal direction and, therefore, hosts massless and massive fermions at the same point in the momentum space. While a number of interesting physical properties have been predicted in semi-Dirac semimetals, it has been rare to realize such materials in condensed matters. Based on the fact that some honeycomb materials are easily oxidized or chemically absorb other atoms, here, we theoretically propose an approach of modifying their band structures by covalent addition of group-VI elements and strain engineering. We predict a silicene oxide with chemical formula of Si 2 O to be a candidate of semi-Dirac semimetal. Our approach is backed by the analysis and understanding of the effect of p-orbital frustration on the band structure of the graphene-like materials.2 Dirac Semimetals, as represented by graphene, have been intensively studied in the past decade as a condensed matter platform of massless Dirac fermions [1,2] . The electronic structure of graphene is characterized by two Dirac points, located at K and K', respectively, in the momentum space [3] . In a tight-binding (TB) picture, by tuning the nearest-neighbor hopping energies in a graphene lattice, as illustrated in Figure 1, the two Dirac points can approach each other and merge into one forming the so-called semi-Dirac point, near which the band dispersion exhibits a peculiar feature, i.e., being linear in one direction and quadratic in the orthogonal direction [4][5][6] . Materials possessing semi-Dirac points are called semi-Dirac semimetals, which provide a platform where massless and massive Dirac fermions coexist. Besides the apparent highly anisotropic transport properties [7] , a number of other interesting properties have been predicted for the semi-Dirac semimetals, such as distinct Landau-level spectrum in a magnetic field [8,9] , non-Fermi liquid [10] , Anderson localization [11] and Bloch-Zener oscillations [12] . It is therefore of great interest to search for materials realizing the semi-Dirac semimetals.While the TB picture provides important guidance, the search for semi-Dirac semimetals still relies on non-trivial materials design. A VO 2 /TiO 2 superlattice has been theoretically proposed to hold multiple semi-Dirac points within the first Brillouin zone (BZ) [13] . The formation mechanism of the semi-Dirac points in this material is described by a TB model [14] different from that illustrated in Figure 1. Recently, black phosphorus (BP) has been predicted to exhibit a single semi-Dirac point in the BZ under pressure [15] . An exciting experiment has shown that a giant Stark effect through electron doping on the surface of BP indeed yields a semi-Dirac point [16] , albeit at heavily n-type doped condition with the semi-Dirac point below the Fermi level by about 0.5 eV. A Dirac-to-semi-Dirac transition by merging two Dirac points, as illustrated in Figure 1, still remains 3 to be demonstrated in a solid-...

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Diffusion of Dirac fermions across a topological merging transition in two dimensions

Cited by 47 publications

References 38 publications

Optical properties of a semi-Dirac material

Optical properties of a semi-Dirac material

Signatures of merging Dirac points in optics and transport

Semi-Dirac semimetal in silicene oxide

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