论文标题
重新研究掺杂石墨烯中归一化电阻率的Bloch-Grüneisen温度和通用缩放率
Bloch-Grüneisen temperature and universal scaling of normalized resistivity in doped graphene revisited
论文作者
论文摘要
在这项工作中，我们基于完全无弹性电子声音 - 散射率和各种近似方案，通过分析和数值计算解决了掺杂石墨烯中Bloch-Grüneisen（BG）温度的一些有争议的问题。通过半弹性（SI）近似获得的BG温度的分析结果（与全弹性散射速率非常吻合的散射速率）与Quasi弹性（QE）近似获得的分析率与$θ^{la} _ {la} _ {f} = 2 \ hbar v__________ {la} k f与$θ^{la} _ {la} _ {la} _ {la} _ {la} _ {la} _} kf进行了比较。发现石墨烯中普遍采用的BG温度（$θ^{la} _ {f} $）比QE近似值获得的值大约5倍，而在使用交叉点温度下，在低温和高温限制的抵抗力限制的情况下，使用SI近似值大约2.5倍。基于SI近似的校正分析关系与通过拟合石墨烯电阻率的可用实验数据的低和高$ T $行为确定的过渡温度非常吻合。我们还引入了一种方法来确定BG温度，包括全弹性EAP散射速率和电子能量与化学电位（$μ$）的偏差数值，方法是找到最大$ \ partialρ（μ，t）/\ partial t $。使用$θ_{bg，1} $的分析表达式，我们可以证明，归一化的电阻率定义为$ r_ {1} =ρ（μ，t）/ρ（μ，θ_{bg，1}）$绘制为$（t/θ_{bg，1}）$的函数。将我们的结果应用于先前提取的实验数据显示出普遍的缩放行为，这与以前的研究不同。
In this work, we resolved some controversial issues on the Bloch-Grüneisen (BG) temperature in doped graphene via analytical and numerical calculations based on full inelastic electron-acoustic-phonon (EAP) scattering rate and various approximation schemes. Analytic results for BG temperature obtained by semi-inelastic (SI) approximation (which gives scattering rates in excellent agreement with the full inelastic scattering rates) are compared with those obtained by quasi-elastic (QE) approximation and the commonly adopted value of $Θ^{LA}_{F} = 2\hbar v_{LA} k_F/k_B$. It is found that the commonly adopted BG temperature in graphene ($Θ^{LA}_{F}$) is about 5 times larger than the value obtained by the QE approximation and about 2.5 times larger than that by the SI approximation, when using the crossing-point temperature where low-temperature and high-temperature limits of the resistivity meet. The corrected analytic relation based on SI approximation agrees extremely well with the transition temperatures determined by fitting the the low- and high-$T$ behavior of available experimental data of graphene's resistivity. We also introduce a way to determine the BG temperature including the full inelastic EAP scattering rate and the deviation of electron energy from the chemical potential ($μ$) numerically by finding the maximum of $\partial ρ(μ,T)/\partial T$. Using the analytic expression of $Θ_{BG,1}$ we can prove that the normalized resistivity defined as $R_{1}=ρ(μ,T)/ρ(μ,Θ_{BG,1})$ plotted as a function of $(T/Θ_{BG,1})$ is independent of the carrier density. Applying our results to previous experimental data extracted shows a universal scaling behavior, which is different from previous studies.
