arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1908.10038cond-mat.mes-hall
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二维Dirac材料中声学声子散射的充分考虑

Full consideration of acoustic phonon scatterings in two-dimensional Dirac materials

Khoe Van Nguyen, Yia-Chung Chang

摘要:

通过考虑二维Dirac材料中完全非弹性的声子散射,求解了石墨烯中的面内声子散射问题,得到了大温度范围($T$)和大化学势范围($μ$)下的二维Dirac材料中的声子散射。得到了费米子函数和玻色子函数的严格解析解和对称性。我们说明了掺杂如何改变声学声子散射率的温度依赖性。结果表明,准弹性和Anneumatic方程先前推导出的声学声子散射在石墨烯的非弹性散射方程的限制情况下,这里推导。对于重掺杂的石墨烯,我们发现电阻率的高$T$行为由$ρ(T, μ) \propto T(1 - ζ_aμ^2/3(k_BT)^2)$而不是线性$T$行为更好地描述,并且在低$T$状态中,我们发现了$τ^{-1} \propto (k_BT)^4$,但是与现有的准弹性表达式相比具有不同的前因子(即,$\sim$小3倍)。此外,我们发现了一个简单的分析“半非弹性”表达式的形式$τ^{-1} \propto (k_BT)^4/(1+ c T^3)$匹配几乎完美的完全非弹性的结果,任何温度高达500 K和$μ$高达1 eV。我们简单的分析结果与以前的第一性原理研究和现有的实验数据吻合得很好。此外,我们还得到了声学规范场$β_A = 3βγ_0/4\sqrt{2}$的解析形式。我们的分析为研究二维狄拉克材料异质结构中电子与其他基本激发之间的散射(如石墨烯混合玻色-费米系统中的bogolon介导的电子散射)奠定了基础。

英文摘要:

The in-plane acoustic phonon scattering in graphene is solved by considering fully inelastic acoustic phonon scatterings in two-dimensional (2D) Dirac materials for large range of temperature ($T$) and chemical potential ($μ$). Rigorous analytical solutions and symmetry properties of Fermionic and Bosonic functions are obtained. We illustrate how doping alters the temperature dependence of acoustic phonon scattering rates. It is shown that the quasi-elastic and ansatz equations previously derived for acoustic phonon scatterings in graphene are limiting cases of the inelastic-scattering equations derived here. For heavily-doped graphene, we found that the high-$T$ behavior of resistivity is better described by $ρ(T, μ) \propto T(1 - ζ_aμ^2/3(k_BT)^2)$ rather than a linear $T$ behavior, and in the low $T$ regime we found $τ^{-1} \propto (k_BT)^4$ but with a different prefactor (i.e. $\sim$ 3 times smaller) in comparison with the existing quasi-elastic expressions. Furthermore, we found a simple analytic "semi-inelastic" expression of the form $τ^{-1} \propto (k_BT)^4/(1+ c T^3)$ which matches nearly perfectly with the full inelastic results for any temperature up to 500 K and $μ$ up to 1 eV. Our simple analytic results agree well with previous first-principles studies and available experimental data. Moreover, we obtain an analytical form for the acoustic gauge field $β_A = 3βγ_0/4\sqrt{2}$. Our analyses pave a way for investigating scatterings between electrons and other fundamental excitations with linear dispersion relation in 2D Dirac material-based heterostructures such as bogolon-mediated electron scattering in graphene-based hybrid Bose-Fermi systems.

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