Kaganov-Lifshitz-Tanatarov theory for tilted Dirac-cone materials: anisotropic heating from uniform light

Abstract

We point out that in the tilted Dirac cone materials the non-equilibrium (hot) electron relaxation with phonons is anisotropic in the Brillouin zone. It means that there is a preferential heating of the lattice degrees of freedom in the specific directions of the Brillouin zone, in particular, in the direction opposite to the tilt velocity in the model considered by us. This observation will have novel consequences: (1) With pump-probe spectroscopy applied to a given tilted Dirac cone material an anisotropic relaxation would lead to a transient anisotropic heating which can further lead to a transient Seebeck effect as transient thermal gradients would exist in the specific directions of the BZ, and (2) this direction of anisotropic heating can be controlled by controlling the direction of the tilt velocity which can be externally tuned by the application of an external pressure. We foresee novel applications of this effect in ultrafast sensor applications involving transient heating effects. This is equivalent to inducing a transient Seebeck effect by just shinning light on a tilted Dirac cone material!

Figures (6)

• Figure 1: Dirac Cone (no tilt).
• Figure 2: Tilted Dirac cone (Type-I material).
• Figure 3: Definition of the angles.
• Figure 4: Polar plot of $\bar{U}(\phi)$ for various values of scaled tilt velocity $\bar{v}_t=\frac{v_t}{v_F} = 0.2, 0.4, 0.6, 0.8$, as depicted in the figure. We notice that the energy relaxation is anisotropic in the Brillouin zone. It is maximum for the directions of wave vector $\mathbf{k}$ at an angle of $\pi$ with the direction of the tilt velocity. The tilt velocity points towards the positive x-direction (in the figure). $\bar{U}(\phi)$ is minimum when the wave vector $\mathbf{k}$ is along the direction of tilt velocity. For the numerical plot we took: $\mu = 2~eV$, lattice temperature $T= 100~K$, electron temperature $T_e = 400~K$, $v_F = 10^{6}~m/s$, sound speed $c_s = 10^{3}~m/s$.
• Figure 5: 8-Pmmn Borophene: a type-I tilted Dirac cone material.