Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

Coelho, Rodrigo C. V.; Mendoza, M.; Doria, Mauro M.; Herrmann, Hans J.

doi:10.1103/physrevb.96.184307

Cited by 20 publications

(20 citation statements)

References 68 publications

(109 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the FD distribution, we use z = 1, which is appropriate, for instance, to model the Dirac fluid on graphene close to the charge neutrality point (µ = 0) [41,40]. So the weight function becomes…”

Section: Expansionmentioning

confidence: 99%

“…In Ref. [41], the first model based on a fifth order expansion of the FD distribution was used to study the Kelvin-Helmholtz instability on graphene. Since this is a viscous fluid dynamical effect, a fully dissipative method is desirable to achieve better accuracy of the results.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we build two-dimensional RLBMs with full dissipation using the MJ and BE distributions and compare them with the model for the FD distribution described in Ref. [41]. To do so, we expand the EDFs up to fifth order and develop new Gaussian quadratures able to calculate tensors up to fifth order and that preserve the spatial resolution.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fully dissipative relativistic lattice Boltzmann method in two dimensions

et al. 2018

Self Cite

View full text Add to dashboard Cite

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-Jüttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot.

show abstract

Section: Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fully dissipative relativistic lattice Boltzmann method in two dimensions

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, several authors have attempted to adapt RLBM schemes to the study of (2 + 1)dimensional relativistic hydrodynamics, motivated by the interest for the study of pseudo-relativistic systems such as the electrons flow in graphene. A series of theoretical works have taken into consideration the possibility of observing Rayleigh-Bénard instability [49,50], Kelvin-Helmholtz instability [51], current whirlpools [52], as well as preturbulent regimes [53,54] in a electronic fluid.…”

Section: Introductionmentioning

confidence: 99%

Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

View full text Add to dashboard Cite

We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, k B T mc 2 , and the non-relativistic one, k B T mc 2 . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1, 2, 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic (k B T ∼ mc 2 ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

show abstract

“…The hamiltonian of the Drude-Sommerfeld framework provides the thermally accessible energy levels E that are accessed through the residual scattering near to the Fermi level. The residual scattering can be formally included through the non-equilibrium Boltzmann-BGK equation 44,45 . The occupation number of an electronic state |χ , H|χ = E|χ , is f 0 ( k) = 1/ {exp [β(E − µ)] + 1}, β ≡ 1/k B T , for a temperature T and µ is the chemical potential.…”

Section: Topological Properties Of the Drude-sommerfeld Modelmentioning

confidence: 99%

The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model

Doria

2019

Eur. Phys. J. B

Self Cite

View full text Add to dashboard Cite

A Drude-Sommerfeld topological model (DSTM) is proposed to describe Weyl fermions under residual collisions. They are nearly free and dressed by their own weak magnetic field that breaks the reflection and time symmetries around a layer. This weak magnetic field brings topological stability to the states through a non-trivial Chern-Simons number which is here calculated in the limit of a Dirac linear spectrum. The Weyl fermions display an energy gap and much above this gap the spectrum becomes Dirac linear. They are obtained from a Schroedinger like hamiltonian for particles with spin and magnetic energy which are momentum confined to a layer 1 . The electrical and the thermal conductivities of the Weyl fermions as well as the corresponding Wiedemman-Franz law are derived in the framework of a constant relaxation time. The Lorenz number coefficient acquires asymptotic value 6.5552 times the bulk value of π 2 /3. The relaxation time is shown to be renormalized by the inverse of the square of the gap, and so, leads to a ballistic regime in the linear Dirac spectrum limit.

show abstract

Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

Cited by 20 publications

References 68 publications

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Relativistic lattice Boltzmann methods: Theory and applications

The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model

Contact Info

Product

Resources

About