Bloch-Grüneisen temperature and universal scaling of normalized resistivity in doped graphene revisited

Abstract

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 ${\Theta }_F^{LA}=2\hslash v_{LA}{k}_F/k_B$. It is found that the commonly adopted BG temperature in graphene (${\Theta }_F^{LA}$) 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 ($\mu$) numerically by finding the maximum of $\partial \rho (\mu ,T)/\partial T$. Using the analytic expression of ${\Theta }_{BG,1}$ we can prove that the normalized resistivity defined as $R_1=\rho (\mu ,T)/\rho (\mu ,{\Theta }_{BG,1})$ plotted as a function of $(T/{\Theta }_{BG,1})$ 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.

5 pages, 4 figures

References in corpus (13)

• Controlling electron-phonon interactions in graphene at ultra high carrier densities
• Acoustic phonon scattering limited carrier mobility in 2D extrinsic graphene
• Limits on electron quality in suspended graphene due to flexural phonons
• Electron-phonon heat transfer in monolayer and bilayer graphene
• Supercollision cooling in undoped graphene
• Electron-Phonon Interactions and the Intrinsic Electrical Resistivity of Graphene
• Phonon-limited resistivity of graphene by first-principle calculations: electron-phonon interactions, strain-induced gauge field and Boltzmann equation
• Competing Channels for Hot Electron Cooling in Graphene
• Electron-phonon mediated heat flow in disordered graphene
• Chirality-dependent phonon-limited resistivity in multiple layers of graphene
• First-principles study of the electrical and lattice thermal transport in monolayer and bilayer graphene
• Flexural phonon scattering induced by electrostatic gating in graphene
• Bloch-Grüneisen nonlinearity of electron transport in GaAs/AlGaAs heterostructures