Temperature-dependent Fermi surface of $2H{\text{-TaSe}}_2$ driven by competing density wave order fluctuations

Temperature evolution of the $2H{\text{-TaSe}}_2$ Fermi surface (FS) is studied by high-resolution angle-resolved photoemission spectroscopy. High-accuracy determination of the FS geometry was possible after measuring electron momenta and velocities along all high-symmetry directions as a function of temperature with subsequent fitting to a tight-binding model. The estimated incommensurability parameter of the nesting vector agrees with that of the incommensurate charge modulations. We observe detectable nonmonotonic temperature dependence of the FS shape, which we show to be consistent with the analogous behavior of the pseudogap. These changes in the electronic structure could stem from the competition of commensurate and incommensurate charge density wave order fluctuations and could explain the puzzling reopening of the pseudogap observed in the normal state of the transition metal dichalcogenides.

Figure 1

Normal-state Fermi surface of $2H{\text{-TaSe}}_2$ at 276 K (darker regions correspond to higher photoemission intensity). The contours represent the tight-binding fit to the experimental data. This figure serves as a legend for Fig. 3, defining the positions in $\mathbf{k}$ space where Fermi momenta and velocities along the high-symmetry directions have been measured as a function of temperature. The momentum scales are presented in relative lattice units (r.l.u.).

Figure 2

Model of the spectral function with linear dispersion and constant scattering rate in the vicinity of the Fermi level $E_F$ without the PG (left) and with a finite PG (right). The black and white colors correspond to the zero and maximal spectral weight, respectively. The curves at the bottom of both panels show the corresponding momentum distribution curves at the Fermi level ($E_F$ MDC) and the MDF. One can see that in the absence of the PG the peak position in the $E_F$ MDC coincides with the position of the step in the MDF, uniquely defining the value of the Fermi momentum $k_F$. In the presence of the PG, these values differ by approximately $\Delta /v_F$, which makes the definition of the Fermi momentum, and therefore the FS itself, ambiguous.

Figure 3

(Color online) Temperature dependence of Fermi momenta and velocities along high-symmetry directions. For the legend of designations, see Fig. 1. Here $k_i$ and $v_i$ denote Fermi momenta and velocities, respectively, while $d_{ij}$ denotes the distance between points $i$ and $j$ in momentum space. The vertical dotted lines mark the temperatures of the commensurate and incommensurate CDW transitions. The dashed lines are drawn as guides for the eyes. Note that the $\Gamma$ barrel does not change perceptibly in the normal state, whereas both $K$- and $M$-centered barrels show detectable changes even above $T_{\text{ICDW}}$, which are often reversed at $T_{\text{ICDW}}$, becoming nonmonotonic.

Figure 4

(Color online) Nesting properties of the room-temperature Fermi surface of $2H{\text{-TaSe}}_2$. (a) Color map of the Lindhard function in the static limit $\left(\omega =0\right)$ calculated at 300 K as a function of $k_x$ and $k_y$. White areas correspond to the dominant nesting vectors. (b) Profile of the Lindhard function along high-symmetry directions. The arrow marks the position of the nesting vector.

Figure 5

The effective area of the $K$-centered barrel as a function of temperature with ($◇$) and without (•) the pseudogap correction.