First-principles and tight-binding analysis of thermoelectricity in irradiated WSe$_2$

Abstract

Electronic and thermoelectric transport in zigzag monolayer WSe$_2$ nanoribbons are studied under monochromatic irradiation. The electronic structure is described within a six-orbital tight-binding framework constructed from the relevant tungsten and selenium orbitals, with atomic spin-orbit coupling included explicitly. Periodic driving is incorporated via the Peierls substitution, and in the high-frequency limit the system is mapped onto an effective static Floquet Hamiltonian with polarization-dependent renormalized hoppings. Coherent transport is evaluated using wave-function matching within the Landauer-Büttiker formalism. The lattice thermal conductivity is obtained independently from density functional perturbation theory combined with an iterative solution of the phonon Boltzmann transport equation. Light-induced hopping renormalization reshapes the band dispersion and transmission spectrum near the Fermi level, modifying the Landauer transport integrals that determine electrical and thermal conductances and the Seebeck coefficient. Together with spin-orbit-driven band splitting and reduced lattice thermal conductivity from enhanced anharmonic scattering, this leads to a thermoelectric figure of merit $ZT$ exceeding unity over a broad temperature range.

Figures (10)

• Figure 1: Schematic lattice structure of a monolayer WSe$_2$ device connected to two semi-infinite electrodes (gray), maintained at temperatures $T+\frac{\Delta T}{2}$ and $T-\frac{\Delta T}{2}$, where $\Delta T$ denotes an infinitesimal temperature bias. Blue (purple) circles represent W (Se) atoms. The vectors ${\bf a}_i$ (green arrows) denote nearest-neighbor intra-sublattice hopping (W-W and Se-Se), while ${\bf r}_i$ (red arrows) indicate nearest-neighbor inter-sublattice hopping (W-Se). The black wave illustrates incident light irradiation perpendicular to the monolayer surface.
• Figure 2: (a) Side view and (b) top view of the optimized crystal structure of monolayer WSe$_2$, illustrating the trigonal prismatic coordination of W and Se atoms. (c) The corresponding hexagonal Brillouin zone with high-symmetry points and the standard $\Gamma$-M-K-$\Gamma$ path used for electronic structure calculations. (d) Electronic band structures of monolayer WSe$_2$ calculated without spin-orbit coupling (WOSOC, blue lines) and with spin-orbit coupling (WSOC, red lines). Here the SOC-induced band splitting energies at high-symmetry points are highlighted. (e) Total electronic density of states (DOS) computed with and without SOC, where the red arrows highlight prominent DOS peaks induced by SOC near the band edges.
• Figure 3: Transmission probability $\mathcal{T}(E)$ of a zigzag monolayer WSe$_2$ nanoribbon as a function of energy in the (a) absence and (b) presence of light. The light parameters are A$_x = 1$, A$_y= 2$, and $\theta=\pi/4$.
• Figure 4: Behaviour of thermoelectric quantities as functions of the Fermi energy at room temperature ($T=300$ K). Panels (a)-(c) show the results without irradiation, while panels (d)-(f) correspond to the system under light irradiation. The electrical conductance $G$ (a, d), Seebeck coefficient $S$ (b,e), and electronic thermal conductance $\kappa_e$ (c, f) are calculated within the linear-response regime using Eq. (\ref{['eq:Ln']}). All structural and light parameters are the same as those used in Fig. \ref{['fig:transm']}.
• Figure 5: (a) Phonon dispersion of the system calculated without spin-orbit coupling (WOSOC, blue lines) and with spin-orbit coupling (WSOC, red lines) along the high-symmetry $\Gamma$-M-K-$\Gamma$ path. The black rectangular box highlights the SOC-induced avoided crossing between acoustic phonon branches, while the inset provides a magnified view of this region to clearly illustrate the avoided crossing. Phonon softening at the K and $\Gamma$ points is highlighted by magenta arrows. (b) Phonon group velocity as a function of frequency for the WSOC case, and (c) the corresponding group velocity for the WOSOC case, resolved into ZA, TA, LA, and optical modes.