Hot electron cooling in three-dimensional Dirac fermion systems at low temperature: effect of screening

TL;DR

This study investigates how screening affects hot electron cooling via acoustic phonons in 3D Dirac fermion systems at low temperatures, revealing significant suppression and characteristic dependencies on temperature and electron concentration.

Contribution

It provides a detailed analysis of screening effects on hot electron cooling rates in 3D Dirac semimetals, highlighting new temperature and concentration dependencies and proposing experimental signatures.

Findings

Screening significantly suppresses cooling rate below 0.5 K.

Cooling rate depends on T_e as T_e^9 in screened case.

Maximum of P/T_e^4 is nearly constant across n_e.

Abstract

Hot electron cooling rate P, due to acoustic phonons, is investigated in three-dimensional Dirac fermion systems at low temperature taking account of screening of electron-acoustic phonon interaction. P is studied as a function of electron temperature T_e and electron concentration n_e. Screening is found to suppress P very significantly for about T_e < 0.5 K and its effect reduces considerably for about T_e > 1K in Cd_3As_2 . In Bloch-Gruniesen (BG) regime, for screened (unscreened) case T_e dependence is P ~ T_e^ 9 (T_e^ 5) and ne dependence gives P ~ n_e ^-5/3(n_e^-1/3). The T_e dependence is characteristics of 3D phonons and n_e dependence is characteristics of 3D Dirac fermions. In BG regime, screening effect is found to enhance for larger n_e. Screening is found to reduce the range of validity of BG regime temperature. Plot of P / T_e^ 4 vs T_e shows a maximum at temperature T_e m which shifts to higher values for larger n_e. Interesting observation is that maximum of P / T_e^4 is nearly same for different n_e and T_em / n_e^ 1/3 appears to be nearly constant. More importantly, we propose, the n_e dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase.