Spin-orbit splitting, Fermi surface topology, and charge-density-wave gapping in $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$

Empirical tight-binding calculations on the layer compound $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ have been performed and are found to replicate the basic phenomenology of Fermi surface topology and charge-density-wave gapping as revealed by angle-resolved photoemission spectroscopy (ARPES). The recently discovered piece of Fermi surface having a “dog’s bone” shape is a consequence of the large spin-orbit splitting of $\mathrm{Ta}5d$ levels. The $3\times 3$ reconstruction, simulated here by bond strengthenings and weakenings, gives rise to gapping, predominantly on the $K\left(H\right)$-centered Fermi surface pocket in agreement with ARPES data. The concept of nesting is not used in the analysis.

Figure 1

(Color online) (a) Band structure of unreconstructed $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ both with [green (light gray) curves] and without (black curves) the Ta $5d$ spin-orbit coupling as measured by the spin-orbit parameter $\xi$. (b) and (c) Corresponding Fermi surface cuts in the $\Gamma MK$ plane $(k_z=0)$ and in the $ALH$ plane $(k_z=\pi ∕c)$.

Figure 2

(Color online) Unit cell of the $3\times 3$ reconstruction of $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ [green (light gray) lines] and the seven-atom cluster pattern having inequivalent “a,” “b,” and “c” Ta atoms. The arrows indicate the displacements of the Ta atoms from their original positions.

Figure 3

(Color online) Band structure (left, thin gray curves) and density of states (right) of reconstructed $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ with inclusion of Ta spin-orbit coupling as a function of the bond-length change $ϵ$: (a) $ϵ=0$, (b) $ϵ=0.01$, and (c) $ϵ=0.02$. Spectral weight distributions are shown as gray scale plots with black corresponding to high intensity. Dotted density-of-states curves in (b) and (c) represent the same curve as in (a). Capital letters (bottom axis) denote high-symmetry points of the $1\times 1$ Brillouin zone, whereas small letters (top axis) denote high-symmetry points of the reconstructed Brillouin zone.

Figure 4

(Color online) Spectral weight distributions at the Fermi level (“Fermi surface intensity maps”) for $2H\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ for two different values of $k_z$ as a function of the bond-length change $ϵ$: (a) $ϵ=0$, (b) $ϵ=0.01$, and (c) $ϵ=0.02$. Spectral weight is represented in a grayscale with black corresponding to high intensity. Brillouin zones of the normal and charge-density-wave phase are indicated.