掺杂石墨烯的Bloch-Grüneisen温度和归一化电阻率的普适标度
Bloch-Grüneisen temperature and universal scaling of normalized resistivity in doped graphene revisited
摘要：
在这项工作中，我们解决了一些有争议的问题上的Bloch-Grüneisen（BG）温度掺杂石墨烯通过分析和数值计算的基础上完全非弹性电声声子（EAP）散射率和各种近似方案。通过半非弹性（SI）近似（它给出的散射率与完全非弹性散射率非常吻合）得到的BG温度的解析结果与通过准弹性（QE）近似和通常采用的$Θ^{LA}_{F} = 2\hbar v_{LA} k_F/k_B$值得到的结果进行了比较。发现当使用电阻率的低温和高温极限满足的交叉点温度时，石墨烯（$Θ^{LA}_{F}$）中通常采用的BG温度比通过QE近似获得的值大约5倍，比通过SI近似获得的值大约2.5倍。基于SI近似的校正的解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$T$行为确定的转变温度非常吻合。我们还介绍了一种方法来确定BG温度，包括全非弹性EAP散射率和电子能量从化学势（$μ$）的偏差，通过找到$\partial ρ(μ,T)/\partial T$的最大值数值。利用$Θ_{BG,1}$的解析表达式，我们可以证明，定义为$R_{1}=ρ(μ,T)/ρ(μ,Θ_{BG,1})$的归一化电阻率作为$(T/Θ_{BG,1})$的函数绘制，与载流子密度无关。将我们的结果应用到以前提取的实验数据中，发现了一个普遍的标度行为，这与以前的研究不同。
英文摘要：
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.
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