The triangular linear analytic method for two-dimensional spectral functions

Ashraff, J A; Loly, P. D.

doi:10.1088/0022-3719/20/29/017

Cited by 11 publications

(15 citation statements)

References 18 publications

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“…We use 200 × 200 k-mesh and the triangular integration method 52 to generate an accurate electronic density of states. The phonon dispersion and the electron-phonon scattering matrix elements are calculated within density functional perturbation theory 53 , initially on a coarse 10 ×10 q-mesh, and then along with the electronic structure on a coarse 10 ×10 kmesh, are interpolated using the EPW package 54,55 to a dense 300 × 300 k-mesh covering half of the Brillouin zone centered around the Γ point and 300 × 300 q-mesh in the full Brillouin zone using maximally localized Wannier functions 56 for calculating the electronic relaxation time due to electron-phonon interaction, which is given by the Fermi's golden rule 57 as …”

Section: Methodsmentioning

confidence: 99%

“…The summation in Eq. (1) is performed using the triangular method 52 to improve the convergence, and eliminate the need of choosing the Gaussian broadening parameter when doing the summation using Gaussian functions to approximate the delta functions. The calculated electronic relaxation times are then plugged into the standard formulae of the transport properties based on the Boltzmann transport equation 60 .…”

Section: Methodsmentioning

confidence: 99%

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Ab initiostudy of electron-phonon interaction in phosphorene

et al. 2015

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The monolayer of black phosphorous, or "phosphorene", has recently emerged as a new 2D semiconductor with intriguing highly anisotropic transport properties. Existing calculations of its intrinsic phonon-limited electronic transport properties so far rely on the deformation potential approximation, which is in general not directly applicable to anisotropic materials since the deformation along one specific direction can scatter electrons traveling in all directions. We perform a first-principles calculation of the electron-phonon interaction in phosphorene based on density functional perturbation theory and Wannier interpolation.Our calculation reveals that 1) the high anisotropy provides extra phase space for electronphonon scattering, and 2) optical phonons have appreciable contributions. Both effects cannot be captured by the deformation potential calculations. Our simulation predicts carrier mobilities ~170 cm 2 /Vs for both electrons and holes at 300K, and a thermoelectric figure of merit zT of up to 0.14 in p-type impurity-free phosphorene at 500K.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Ab initiostudy of electron-phonon interaction in phosphorene

et al. 2015

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“…where n indexes the triangles, i indexes the vertices, and the branch indices have been suppressed. The triangulation scheme is adapted from the earlier work [37,38]. The equations for the real part as listed in Ref.…”

Section: Appendix: Two-dimensional Green's Function Triangulation Schemementioning

confidence: 99%

“…The equations for the real part as listed in Ref. [38] contain errors and are corrected here. Only the final equations are listed here, whereas the detailed derivation procedure can be found in Refs.…”

Section: Appendix: Two-dimensional Green's Function Triangulation Schemementioning

confidence: 99%

Ab initio phonon scattering by dislocations

et al. 2017

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Heat management in thermoelectric and power devices as well as in random access memories poses a grand challenge and can make the difference between a working and an abandoned device design. Despite the prevalence of dislocations in all these technologies, the modeling of their thermal resistance is based on 50-year-old analytical approximations, whose simplicity was driven by practical limitations rather than physical insight. We introduce an efficient ab initio approach based on Green's functions computed by two-dimensional reciprocal space integration. By combining elasticity theory and density functional theory, we calculate the scattering strength of a 90 • misfit edge dislocation in Si. Because of the breakdown of the Born approximation, earlier literature models fail, even qualitatively. We find that a dislocation density larger than 10 9 cm −2 is necessary to substantially influence thermal conductivity at room temperature and above. We quantify how much of the reduction of thermal conductivity measured in nanograined samples can be explained by realistic dislocation concentrations.

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“…This problem may be overcome using the Triangular Linear Analytic (TLA) method 27,28 . We divide the square Brillouin zone into small squares, and each small square is further subdivided into two right trangles along one of the diagonals.…”

Section: Density Responsementioning

confidence: 99%

Excitonic effects in two-dimensional massless Dirac fermions

et al. 2011

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We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power law behavior at small wavevectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at 2kF , leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.

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The triangular linear analytic method for two-dimensional spectral functions

Cited by 11 publications

References 18 publications

Ab initiostudy of electron-phonon interaction in phosphorene

Ab initiostudy of electron-phonon interaction in phosphorene

Ab initio phonon scattering by dislocations

Excitonic effects in two-dimensional massless Dirac fermions

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