Hot electron cooling in Dirac semimetal Cd${}_3$As${}_2$ due to polar optical phonons

Abstract

A theory of hot electron cooling power due to polar optical phonons $P_{\mathrm{op}}$ is developed in three-dimensional Dirac semimetal($3$DDS) Cd${}_3$As${}_2$ taking account of hot phonon effect. Hot phonon distribution $N_q$ and $P_{\mathrm{op}}$ are investigated as a function of electron temperature $T_e$, electron density $n_e$, and phonon relaxation time ${\tau }_p$. It is found that $P_{\mathrm{op}}$ increases rapidly (slowly) with $T_e$ at lower (higher) temperature regime. Whereas, $P_{\mathrm{op}}$ is weakly deceasing with increasing $n_e$. The results are compared with those for three-dimensional electron gas ($3$DEG) in Cd${}_3$As${}_2$ semiconductor. Hot phonon effect is found to reduce $P_{\mathrm{op}}$ considerably and it is stronger in 3DDS Cd${}_3$As${}_2$ than in Cd${}_3$As${}_2$ semiconductor. $P_{\mathrm{op}}$ is also compared with the hot electron cooling power due to acoustic phonons $P_{\mathrm{ac}}$. We find that a crossover takes place from $P_{\mathrm{ac}}$ dominated cooling at low $T_e$ to $P_{\mathrm{op}}$ dominated cooling at higher $T_e$. The temperature at which this crossover occurs shifts towards higher values with the increase of $n_e$. Also, hot electron energy relaxation time ${\tau }_e$ is discussed and estimated.

arXiv comment9 pages, 6 figures

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