Temperature dependence of the gaps of high-temperature superconductors in the Fermi-arc region

It is shown how in a high-temperature superconductor, the length of the Fermi arc can be obtained from the doping dependence of the pseudogap and the superconducting gap. In the momentum region spanned by the Fermi arc, the pseudogap temperature dependence follows that of the superconducting gap. The close interconnection of the two gaps suggests that they are both an essential part of the high-temperature superconductivity.

Figure 1

(a) Phase diagram of a HTSC. The pseudogaps for an UD sample and an OD sample, with the same transition temperature $T_c$, are indicated, (b) The angular dependence of the superconducting and the two pseudogap energies from the top part of the figure. The Fermi-arc lengths $\left(45°-\varphi \right)$ are constructed for both cases.

Figure 2

Same as in Fig. 1; however, it was adopted to the experimental conditions of Ref. 18 for a slightly underdoped sample (UD92) with $x=0.14$.

Figure 3

Doping dependence of the Fermi-arc angle, as calculated from Fig. 1b, for a HTSC sample with a maximum $T_c$ of 95 K. The curve is obtained by setting equal the value of the superconducting energy $E_{sc}\left(x\right)$ for a particular doping $x$ and the value of $E_{pg}\left(x\right)\text{cos}\left(2\varphi \right)$ for this sample, thus obtaining the angle $\varphi$, at which the Fermi arc occurs.

Figure 4

Pseudogap energies $\left({\Delta }_{pg}=E_{pg}/2\right)$ and temperatures at which they disappear for a number of Bi2212 samples, from Refs. 18, 19.