[Paper Review] Electronic transport and dynamical polarization in bilayer silicene-like system

Chen-Huan Wu|arXiv (Cornell University)|Sep 17, 2018

Graphene research and applications48 references3 citations

TL;DR

This paper investigates electronic transport and dynamical polarization in bilayer silicene-like systems under charged impurities and external fields, using a low-energy Dirac model with interlayer hopping and trigonal warping. Key findings show that strong interlayer coupling induces parabolic band dispersion, leading to temperature-dependent mobility anisotropy and screening effects governed by random phase approximation, with phonon scattering dominating at high temperatures via deformation-potential approximation—results applicable to bilayer graphene and MoS₂ as well.

ABSTRACT

We investigate the semiclassical electronic transport properties of the bilayer silicene-like system in the presence of charged impurity. The trigonal warping due to the interlayer hopping, and its effect to the band structure of bilayer silicene is discussed. Besides the trigonal warping, the external field also gives rise to the anisotropic effect of the mobility (at finite temperature) which can be explored by the Boltzmann theory. The dynamical polarization as well as the scattering wave vector-dependent screening within random phase approximation are very important in determining the scattering behavior and the self-consistent transport. We detailly discuss the transport behavior under the short- or long-range potential. The phonon scattering with the acoustic phonon mode which dominant at high temperature is also studied within the density functional theory (DFT). Our results are also valid for the bilayer graphene or bilayer MoS$_{2}$, and other bilayer systems with strong interlayer coupling.

Motivation & Objective

• To understand the impact of interlayer hopping and trigonal warping on the band structure and transport in bilayer silicene-like systems.
• To investigate how charged impurities and external fields affect electron mobility and relaxation rates via Boltzmann transport theory.
• To compute the dynamical polarization function and wave vector-dependent screening within the random phase approximation (RPA).
• To model electron-phonon scattering at finite temperature using Fermi’s golden rule and deformation-potential approximation.
• To extend findings to other bilayer systems such as bilayer graphene and MoS₂ with strong interlayer coupling.

Proposed method

• Develops a low-energy four-band Dirac Hamiltonian incorporating interlayer hopping $ t_\perp = 2 \, \text{eV} $, trigonal warping $ t_w = 0.16 \, \text{eV} $, and spin-orbit coupling $ \lambda_{\text{SOC}\perp} = 0.5 \, \text{meV} $.
• Derives the dynamical polarization function $ \Pi^{\text{bi}}(\mathbf{q}, i\Omega) $ using Matsubara formalism and trace over Green's functions in the RPA framework.
• Applies the Boltzmann transport equation to compute temperature-dependent mobility under long-range and short-range impurity potentials.
• Uses Fermi’s golden rule with deformation-potential approximation to calculate electron-phonon scattering rates at finite temperature.
• Performs DFT-based analysis of acoustic phonon modes and compares electron-phonon coupling in silicene and MoS₂.
• Solves the energy spectrum $ \varepsilon^{\pm} $ from the effective Hamiltonian to determine band dispersion and gap opening.

Experimental results

Research questions

• RQ1 How does interlayer hopping and trigonal warping affect the band structure and Fermi surface topology in bilayer silicene?
• RQ2 What is the role of dynamical polarization and screening in determining transport behavior under long- or short-range impurity potentials?
• RQ3 How does temperature influence electron mobility and relaxation rates due to charged impurities and phonon scattering?
• RQ4 To what extent do the transport properties of bilayer silicene resemble or differ from those of bilayer graphene or MoS₂?
• RQ5 How does the presence of an external electric field modify the carrier density and screening in the system?

Key findings

• The band structure of bilayer silicene exhibits parabolic dispersion due to strong interlayer hopping $ t_\perp = 2 \, \text{eV} $, leading to a significant band gap and modified Fermi surface geometry.
• Dynamical polarization in the RPA framework shows strong wave vector and frequency dependence, with screening effects dominating at long wavelengths and finite temperatures.
• Temperature-dependent mobility is anisotropic due to trigonal warping, with the Boltzmann theory revealing reduced backscattering and enhanced transport in certain directions.
• Electron-phonon scattering at high temperatures is dominated by acoustic phonons, with scattering rates derived via deformation-potential approximation and Fermi’s golden rule.
• The static polarization of bilayer silicene is nearly temperature-independent in the adiabatic limit when a large band gap is present.
• The results are transferable to other bilayer systems such as bilayer graphene and MoS₂, particularly in cases with strong interlayer coupling and similar band structures.