Nonmonotonic pseudogap in high-$T_c$ cuprates

The mechanism of high-temperature superconductivity has not been resolved for so long because the normal state of cuprates, which exhibits enigmatic pseudogap phenomena, is not yet understood. We performed careful temperature- and momentum-resolved photoemission experiments to show that the depletion of the spectral weight in slightly underdoped cuprate superconductor, usually called the “pseudogap,” exhibits an unexpected nonmonotonic temperature dependence: decreases linearly approaching $T^{\ast }$ at which it reveals a sharp transition but does not vanish and starts to increase gradually again at higher temperature. The low-temperature behavior of the pseudogap is remarkably similar to one of the incommensurate charge ordering gap in the transition-metal dichalcogenides, while the reopening of the gap at room temperature fits the scenario of temperature-driven metal-insulator transition. This observation suggests that two phenomena, the electronic instability to density-wave formation and the entropy-driven metal-to-insulator crossover, may coexist in the normal state of cuprates.

Figure 1

(Color online) Temperature evolution of the ARPES spectra. Panels in color scale, which represent the “ARPES images” (the momentum distribution of the photoemission intensity) taken along the “hot-spot” cross section (see the last panel), demonstrate the evolution of the quasiparticle spectral weight in a wide temperature range of 20–320 K. All spectra are measured at 50 eV excitation energy at which only the antibonding band is visible. The sketch of the Fermi surface (FS) (white solid lines) illustrates the position of the hot spots (large points), which are the points on the FS connected by the $\left(\pi ,\pi \right)$ vector (thin yellow arrow); the dotted line represents the FS shifted by the $\left(\pi ,\pi \right)$ vector; the solid vertical and dashed diagonal double-headed arrows show the position of the hot-spots crossing and nodal crossing, respectively.

Figure 2

(Color online) The temperature map. (a) The temperature map which consists of a number of momentum-integrated EDCs measured at different temperatures at a hot spot. Separate EDCs are shown in panels (b–g): as compared to each other (panels b and e) and to the similar EDCs measured each for the same temperature but along the nodal direction (panels c, d, f, g). The gap is seen as a shift of the LEM. In terms of the color scale of panel a, the LEM corresponds to white color close to the Fermi level. All the hot-spot EDCs are integrated in momentum range of $\pm 0.15{\text{Å}}^{-1}$ around $k_F$.

Figure 3

(Color online) Nonmonotonic gap function. The position of the LEM of the integrated $k_F$ EDCs (averaged for two Fermi crossings) as a function of temperature for an underdoped Tb-BSCCO (left) with $T_c=77\text{K}$ and $T^{\ast }=170\text{K}$ is remarkably similar to the pseudogap in a transition-metal dichalcogenide ${\text{TaSe}}_2$ (right) (Ref. 6) with the transitions to the commensurate and incommensurate CDW phases at $T_{\text{ICC}}=90\text{K}$ and $T_{\text{NIC}}=122\text{K}$, respectively.

Figure 4

(Color online) Momentum anisotropy of the pseudogap. The dependences of the gap on the Fermi surface as a function of angle in Dy-BSCCO in the pseudogap state (left) and in ${\text{TaSe}}_2$ in the incommensurate CDW state (right) are almost identical.