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To understand the essential properties of Dirac crystals, such as theirthermal conductivity, we require models that consider the interaction betweenDirac electrons and dispersive acoustic phonons. The exceptionally high thermalconductivity in 2D Dirac crystals is attributed to near-ideal phonon quantumgases, while undesired limitations arise from electron-phonon (e-ph)interactions which have been shown to limit the thermal conductivity up toseveral microns away. The e-ph thermal conductivity is directly linked to thephonon scattering rate. Conventional calculations overlook phonons withshort-dispersive wavelengths, rendering them inadequate for analyzing 2D Diraccrystals. The phonon scattering rate is typically calculated up to thefirst-order magnitude, considering 3-particle interactions involving the decayof an electron and phonon (EP-E*) to create a new electron. However, processesinvolving the decay of an electron and the creation of a new electron andphonon (E-E*P*) are neglected. In this study, we present an accurate expressionfor the phonon scattering rate and e-ph thermal conductivity in 2D Diraccrystals, accounting for short-dispersive wavelength phonons. We demonstratethe significance of the E-E*P* process even at room temperature in calculatingthe phonon scattering rate and e-ph thermal conductivity, particularly forfirst-order e-ph interactions. Furthermore, we emphasize the importance ofincorporating second-order e-ph interactions, specifically the EP-E*P*interaction involving the decay of an electron and phonon and the creation of anew electron-phonon pair, to accurately determine the phonon scattering rateand e-ph thermal conductivity at high temperatures and low Fermi energies. This4-particle interaction process plays a crucial role in characterizing theseproperties effectively.

Higher-order electron-phonon interactions and their effect on the thermal properties of 2D Dirac crystals