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The in-plane phonon-drag thermopower $S^g$, diffusion thermopower $S^d$ and the power factor $PF$ are theoretically investigated in twisted bilayer graphene (tBLG) as a function of twist angle $\theta$, temperature $T$ and electron density $n_s$ in the region of low $T$ (1-20 K). As $\theta$ approaches magic angle $\theta_m$, the $S^g$ and $S^d$ are found to be strongly enhanced, which is manifestation of great suppression of Fermi velocity ${\nu_F}^*$ of electrons in moire flat band near $\theta_m$. This enhancement decreases with increasing $\theta$ and $T$. In the Bloch- Gruneisen (BG) regime, it is found that $S^g \sim {\nu_F}^{* -2}$, $T^3$ and ${n_s}^{-1/2}$. As $T$ increases, the exponent $\delta$ in $S^g \sim T^\delta$, changes from 3 to nearly zero and a maximum $S^g$ value of $\sim$ 10 mV/K at $\sim$ 20 K is estimated. $S^g$ is larger (smaller) for smaller $n_s$ in low (high) temperature region. On the other hand, $S^d$, taken to be governed by Mott formula, $\sim {\nu_F}^{* -1}$, $T$ and ${n_s}^{-1/2}$ and $S^d< \sim$ 2 K. The power factor $PF$ is also found to be strongly $\theta$ dependent and very much enhanced. Consequently, possibility of a giant figure of merit is discussed.In tBLG, $\theta$ acts as a strong tuning parameter of both $S^g$ and $S^d$ and $PF$ in addition to $T$ and $n_s$. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.

We have carried out a theoretical investigation of hot electron power loss $P$, involving electron-acoustic phonon interaction, as a function of twist angle $\theta$, electron temperature $T_e$ and electron density $n_s$ in twisted bilayer graphene (tBLG). It is found that as $\theta$ decreases closer to magic angle $\theta_m$, $P$ enhances strongly and $\theta$ acts as an important tunable parameter, apart from $T_e$ and $n_s$. In the range of $T_e$ =1-50 K, this enhancement is $\sim$ 250-450 times the $P$ in monolayer graphene (MLG), which is manifestation of the great suppression of Fermi velocity ${v_F}^*$ of electrons in moir\'e flat band. As $\theta$ increases away from $\theta_m$, the impact of $\theta$ on $P$ decreases, tending to that of MLG at $\theta$ $\sim$ 3$^{\circ}$. In the Bloch-Gr\"uneisen (BG) regime, $P$ $\sim$ ${T_e}^4$, ${n_s}^{-1/2}$ and ${v_F}^{*-2}$. In the higher temperature region ($\sim$10- 50 K), $P$ $\sim$ ${T_e}^{\delta}$, with $\delta \sim$ 2.0, and the behavior is still super linear in $T_e$, unlike the phonon limited linear-in- $T$ ( lattice temperature) resistivity $\rho_p$. $P$ is weakly, decreasing (increasing) with increasing $n_s$ at lower (higher) $T_e$, as found in MLG. The energy relaxation time $\tau_e$ is also discussed as a function of $\theta$ and $T_e$. Expressing the power loss $P = F_e(T_e)- F_e(T)$, in the BG regime, we have obtained a simple and useful relation $F_e(T) \mu_p (T) = (e{v_s}^2$/2) i.e. $Fe(T) = (n_se^2 {v_s}^2/2)\rho_p$, where $\mu_p$ is the acoustic phonon limited mobility and $v_s$ is the acoustic phonon velocity. The $\rho_p$ estimated from this relation using our calculated $F_e(T)$ is nearly agreeing with the $\rho_p$ of Wu et al (Phys. Rev. B 99, 165112 (2019)).

The power loss $P$ of hot Dirac fermions through the coupling to the intrinsic intravalley and intervalley acoustic and optical phonons is analytically investigated in silicene as a function of electron temperature $T_e$ and density $n_s$. At very low $T_e$, the power dissipation is found to follow the Bloch-Gr\"{u}neisen power-law $\propto T_e^4$ and $n_s^{-0.5}$, as in graphene, and for $T_e \lesssim20-30$ K, the power loss is predominantly due to the intravalley acoustic phonon scattering. On the other hand, dispersionless low energy intervalley acoustic phonons begin to dominate the power transfer at temperatures as low as $\sim$$30$ K, and optical phonons dominate at $T_e \gtrsim200$ K, unlike the graphene. The total power loss increases with $T_e$ with a value of $\sim$$10^{10}$ eV/s at $300$ K, which is the same order of magnitude as in graphene. The power loss due to intravalley acoustic phonons increases with $n_s$ at higher $T_e$, whereas due to the intervalley acoustic and optical phonons is found to be independent of $n_s$. Interestingly, the energy relaxation time in silicene is about $4$ times higher than that in graphene. For this reason, silicene may be superior over graphene for its applications in bolometers and calorimeters. Power transfer to the surface optical phonons $P_{\text{SO}}$ is also studied as a function of $T_e$ and $n_s$ for silicene on Al$_2$O$_3$ substrate and it is found to be greater than the intrinsic phonon contribution at higher $T_e$. Substrate engineering is discussed to reduce $P_{\text{SO}}$., Comment: 12 pages, 15 figures

Transport of electrons at high electric fields is investigated in an intrinsic three-dimensional Dirac semimetal cadmium arsenide, considering the scattering of electrons from acoustic and optical phonons. Screening and hot phonon effect are taken in to account. Expressions for the hot electron mobility $\mu$ and power loss $P$ are obtained as a function of electron temperature $T_e$. The dependence of drift velocity $v_d$ on electric field $E$ and electron density $n_e$ has been studied. Hot phonon effect is found to set in the saturation of $v_d$ at relatively low $E$ and significantly degrades its magnitude. The drift velocity is found to saturate at a value $v_{ds} \sim 10^7$ cm/s and it is weakly dependent on $n_e$. A large saturation current density $\sim 10^6$ A/cm$^2$ is predicted.

A theoretical model is presented for the phonon limited mobility of the Dirac-Fermion gas in a three-dimensional (3D) Dirac semimetal Cd$_3$As$_2$ considering scattering from both the acoustic and the optical phonons. Screening effects are taken into account and it is found that they lead to a significant enhancement of the mobility. Simple analytical equations and power laws are obtained in both the Bloch-Gruneisen and equipartition regimes. The dependence of mobility on the temperature $T$ and the electron density $n_e$ is investigated. It is found that optical phonon limited mobility $\mu_{op}$ dominates over the acoustic phonon limited mobility $\mu_{ap}$ in the higher temperature region. There is a crossover of $\mu_{ap}$ and $\mu_{op}$ and the crossover temperature $T_c$ shifts to higher value with increasing $n_e$. Our calculations of the mobility are in good agreement with the recent experimental data. Comparison is also made with the results in the conventional 3D electron gas in a degenerate semiconductor.

We have studied, in bilayer graphene (BLG), the hot electron cooling power $F_{VP} (T, n_s)$ due to acoustic phonons via vector potential (VP) coupling. It is calculated as a function of electron concentration $ns$ and temperature $T$ and compared with $F_{DP} (T, n_s)$ that due to deformation potential coupling. For the $n_s$ around $1\times10^{12} cm^{-2}$, $F_{VP} (T, n_s)$ is much smaller than $F_{DP} (T, n_s)$ . With increase of $n_s$, $F_{DP} (T, n_s)$ decreases faster than $F_{VP} (T, n_s)$ does. A cross over is predicted and dominant contribution of $F_{VP} (T, n_s)$ can be observed at large $n_s$. In the Bloch- Gr\"uneisen (BG) regime $F_{VP} (T, n_s)~ n_s^{-1/2}$ and $F_{DP} (T, n_s)~ n_s^{-3/2}$. Both $F_{VP} (T, n_s)$ and $F_{DP} (T, n_s)$ have the same $T$ dependence with $T^4$ power law in BG regime. Behaviour of $F_{DP} (T, n_s)~ n_s^{-3/2}$ and $T^4$ is in agreement with the experimental results at moderate $n_s$. Besides, in BG regime, we have predicted, for both the VP and DP coupling, a relation between $F(T, n_s)$ and the acoustic phonon limited mobility $\mu_p$, opening a new door to determine $\mu_p$ from the measurements of $F(T, n_s)$., Comment: 6 pages

Expressions for the electron power loss F(T) and mobility {\mu}_p due to acoustic phonon scattering are given in the Bloch-Gr\"uneisen (BG) regime for three- and two- dimensional electron gas in semiconductors and Dirac-fermions. We obtain a simple relation F(T) {\mu}_p = {\eta}ev_s^2, where {\eta} (~1) is a constant, e is the electron charge and v_s is acoustic phonon velocity. It is found to be independent of temperature and electron concentration. This relation is applied to GaAs heterojucntions and graphene, to obtain {\mu}_p from the measured F(T). We propose that, using this relation, the measurements of F(T), in BG regime, which depends exclusively upon acoustic phonons coupling, could serve as a tool to determine the low temperature {\mu}_p, which is otherwise difficult to measure due to the contributions from disorders, Comment: 4 pages and 1 table

The phonon-drag thermopower is studied in monolayer graphene on a piezoelectric substrate. The phonon-drag contribution S^g_PA from the extrinsic potential of piezoelectric surface acoustic (PA) phonons of a piezoelectric substrate (GaAs) is calculated as a function of temperature T and electron concentration n_s. At very low temperature, S^g_PA is found to be much greater than S^g_DA of the intrinsic deformation potential of acoustic (DA) phonons of the graphene. There is a crossover of S^g_PA and S^g_DA at around ~5 K. In graphene samples of about >10 um size, we predict S_g ~20 uV at 10 K, which is much greater than the diffusion component of the thermopower and can be experimentally observed. In the Bloch-Gruneisen (BG) regime T and n_s dependence are, respectively, given by the power laws S^g_PA (S^g_DA) ~ T^2(T^3) and S^g_PA, S^g_DA ~ n_s^(-1/2). The T (n_s) dependence is the manifestation of the two-dimensional phonons (Dirac phase of the electrons). The effect of the screening is discussed. Analogous to Herring's law (S_g mu_p ~T^-1), we predict a new relation S_g mu_p ~n_s^0, where mu_p is the phonon-limited mobility. We suggest that n_s dependent measurements will play a more significant role in identifying the Dirac phase and the effect of screening., Comment: 8 pages, 6 figures. v2 has minor corrections to Eq. 5 and to expression for F^0_PABG in section E

A theory of low-temperature phonon-drag magnetothermopower $S_{xx}^g$ is presented in graphene in a quantizing magnetic field. $S_{xx}^g$ is found to exhibit quantum oscillations as a function of magnetic field $B$ and electron concentration $n_e$. Amplitude of the oscillations is found to increase (decrease) with increasing $B$ ($n_e$). The behavior of $S_{xx}^g$ is also investigated as a function of temperature. A large value of $S_{xx}^g $($\sim$ few hundreds of $\mu $V/K) is predicted. Numerical values of $S_{xx}^g $ are compared with the measured magnetothermopower $S_{xx}$ and the diffusion component $S_{xx}^d$ from the modified Girvin-Jonson theory., Comment: 8 pages, 4 figures. To appear in Journal of Physics: Condens. Matter

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.

We study hot-electron cooling by acoustic and optical phonons in monolayer MoS$_2$. The cooling power $P$ ($P_e = P/n$) is investigated as a function of electron temperature $T_e$ (0-500 $\mathrm{K}$) and carrier density $n$ ($10^{10}$-$10^{13}$ $\mathrm{cm}^{-2}$) taking into account all relevant electron-phonon (el-ph) couplings. We find that the cross over from acoustic phonon dominated cooling at low $T_e$ to optical phonon dominated cooling at higher $T_e$ takes place at $T_e \sim 50$-$75$ $\mathrm{K}$. The unscreened deformation potential (DP) coupling to the TA phonon is shown to dominate $P$ due to acoustic phonon scattering over the entire temperature and density range considered. The cooling power due to screened DP coupling to the LA phonon and screened piezoelectric (PE) coupling to the TA and LA phonons is orders of magnitude lower. In the Bloch-Gr\"uneisen (BG) regime, $P\sim T_e^4$ ($T_e^6$) and $P\sim n^{-1/2}$ ($P_e\sim n^{-3/2}$) are predicted for unscreened (screened) el-ph interaction. The cooling power due to optical phonons is dominated by zero-order DP couplings and the Fr\"ohlich interaction, and is found to be significantly reduced by the hot-phonon effect when the phonon relaxation time due to phonon-phonon scattering is large compared to the relaxation time due to el-ph scattering. The $T_e$ and $n$ dependence of the hot-phonon distribution function is also studied. Our results for monolayer MoS$_2$ are compared with those in conventional two-dimensional electron gases (2DEGs) as well as monolayer and bilayer graphene., Comment: 14 pages, 10 figures, published version