Modelling electron-phonon interactions in graphene with curved space hydrodynamics

Abstract

We introduce a different perspective describing electron-phonon interactions in graphene based on curved space hydrodynamics. Interactions of phonons with charge carriers increase the electrical resistivity of the material. Our approach captures the lattice vibrations as curvature changes in the space through which electrons move following hydrodynamic equations. In this picture, inertial corrections to the electronic flow arise naturally effectively producing electron-phonon interactions. The strength of the interaction is controlled by a coupling constant, which is temperature independent. We apply this model to graphene and recover satisfactorily the linear scaling law for the resistivity that is expected at high temperatures. Our findings open up a new perspective of treating electron-phonon interactions in graphene, and also in other materials where electrons can be described by the Fermi liquid theory.

Axisymmetric flows on the torus geometry

“…In recent years there has been a growing interest in studying and understanding hydrodynamic flows on curved surfaces, supported by increasing evidence for their relevance in a wide range of problems in nature and engineering. Examples include phenomena in materials science, such as the motion of electrons in graphene (Giordanelli, Mendoza & Herrmann 2018), interface rheology in foams (Cox, Weaire & Glazier 2004) and the dynamics of confined active matter (Keber et al 2014; Janssen, Kaiser & Löwen 2017; Henkes, Marchetti & Sknepnek 2018; Pearce et al 2019); in biophysics, such as flows on curved biomembranes (Arroyo & Desimone 2009; Henle & Levine 2010; Al-Izzi, Sens & Turner 2018; Fonda et al 2018) or fluid deformable surfaces (Torres-Sánchez, Millán & Arroyo 2019; Voigt 2019); in fusion technology, such as plasma motion under toroidal confinement (Boozer 2005); and in geophysics, such as zonal flows on planets and the Sun (Sasaki, Takehiro & Yamada 2015).…”

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

“…Hydrodynamics on curved manifolds is relevant for a wide range of physical phenomena. Examples range from the motion of electrons in graphene at the micro-scale [21], through thin liquid films [27,51], confined active matter [25,29,32] and bio-membranes [3,26] at the meso-scale, to relativistic flows in astrophysics [41] and at the cosmological scale [18]. However, despite its importance, the study of flows on curved space has received much less attention when compared to corresponding investigations on two-and three-dimensional flat space.…”

Confining massless Dirac particles in two-dimensional curved space

“…as explained in Ref. 46 . The positions of the atoms and consequently h α can be determined by scanning tunneling microscopy and atomic force microscopy.…”