Weyl–Wigner description of massless Dirac plasmas: ab initio quantum plasmonics for monolayer graphene

Abstract

We derive, from first principles and using the Weyl–Wigner formalism, a fully quantum kinetic model describing the dynamics in phase space of Dirac electrons in single-layer graphene. In the limit ℏ → 0, we recover the well-known semiclassical Boltzmann equation, widely used in graphene plasmonics. The polarizability function is calculated and, as a benchmark, we retrieve the result based on the random-phase approximation. By keeping all orders in ℏ, we use the newly derived kinetic equation to construct a fluid model for macroscopic variables written in the pseudospin space. As we show, the novel ℏ-dependent terms can be written as corrections to the average current and pressure tensor. Upon linearization of the fluid equations, we obtain a quantum correction to the plasmon dispersion relation, of order ℏ 2, akin to the Bohm term of quantum plasmas. In addition, the average variables provide a way to examine the value of the effective hydrodynamic mass of the carriers. For the latter, we find a relation in which Drude’s mass is multiplied by the square of a velocity-dependent, Lorentz-like factor, with the speed of light replaced by the Fermi velocity, a feature stemming from the quasi-relativistic nature of the Dirac fermions.

Hydrodynamical study of terahertz emission in magnetized graphene field-effect transistors

“…where k F is the Fermi momentum and n is the electron 2D number density. This definition is extensively used in the literature 7,9,10 , and recent developments based on quantum kinetic theory propose corrections to it 26 . Since the electronic fluid is compressible, the effective mass is not a conserved quantity, contrary to customary fluids.…”

Effect of external magnetic field on the instability of THz plasma waves in nanoscale graphene field-effect transistors

“…Therefore, new theoretical frameworks and mathematical techniques must be developed to address this unique aspect of graphene's electronic properties. Here, the Drude mass [36,37] is used as the effective mass…”

Electronic viscous boundary layer in gated graphene

“…Here, p = nm å v is the fluid two-dimensional momentum density , is the pressure stress tensor, and f is the electrical potential. In equations (1), (2), and (3), relativistic corrections, such as those described in [14,19], are absent since the drift velocity of the system under study is much smaller than the Fermi velocity [43]. The twodimensional pressure term in equation (3) can be recast into its hydrostatic and viscous components,…”

“…Advances have also been put forward in the development of hydrodynamic models for Dirac electrons, especially those resulting from semi-classical approaches [10,[14][15][16][17][18], with some more recent works pointing towards fully quantum theories [19]. In any case, a central problem concerns the electron viscosity and the nature of the flow: what is the expected shape of the velocity profile for a specific flow?…”