Two-gap feature in optimally electron-doped cuprates

The dependence of the Hall conductivity on temperature and magnetic field in optimally doped ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4\pm \delta }$ $(x=0.105)$ thin films demonstrates that both the hole and the electron bands undergo Cooper pairing. The magnetic field suppresses the dominant hole band pairing more effectively, making the subdominant electron band pairing visible. Positively charged Cooper pairs dominate the Hall signal in the mixed state at a weak magnetic field near $T_c$, while at large field the negatively charged Cooper pairs take over. Sign reversals of the Hall conductivity induced by superconducting fluctuation occur in the transition and can be explained by a weakly coupled two-band Ginzburg-Landau-Lawrence-Doniach model.

Figure 1

Temperature dependence of (a) ${\rho }_{xx}$, (b) ${\sigma }_{xx}$, and (c) ${\sigma }_{xy}/B$ for S1 at constant fields between 1 and 9 T, respectively. (d) Field dependence of ${\sigma }_{xy}/B$ at constant temperatures between 7 and 30 K which are extracted from (c). The linear normal parts are highlighted by the red dashed line.

Figure 2

(a) Field dependence of ${\sigma }_{xy}^s/B$ at constant temperatures from 10 to 26 K. The solid curves are drawn to guide the eye. (b) Temperature dependence of ${\sigma }_{xy}^s/B$ at constant fields from 0.5 to 8 T.

Figure 3

(a) Temperature dependence of $R/R\left(300\text{K}\right)$ for all the samples. (b) and (c) Temperature dependence of ${\sigma }_{xy}/B$ at different fields for S2 and S3, respectively. (d) and (e) Field dependence of ${\sigma }_{xy}^s/B$ at different temperatures for S2 and S3, respectively.

Figure 4

$H\text{−}T$ phase diagram without coupling. The $h$ pairing and $e$ pairing represent the areas dominated by hole and electron Cooper pairs, respectively. $H_{c2,i}$ and $T_{c,i}$ correspond to $H_{c2}$ at zero temperature and $T_c$ at zero field. The subscript $i=e$ or $h$ refers to the electron and hole bands. The blue and the green lines represent the temperature dependence of the upper critical fields for the hole and electron band, respectively, which are stimulated by Werthamer-Helfand-Hohenberg (WHH) theory and their cross point is denoted by $[T^{*},H^{*}]$. The area between the solid curve and the gray dashed line is the vortex liquid region. The area scattered with red dots corresponds to the specific vortex liquid region where hole and electron Cooper pairs compete with each other.

Figure 5

(a) Temperature dependence of ${\sigma }_{xx}^s$ at low magnetic fields between 1 and 2.5 T and high temperatures 18–28 K for S1. The solid curves are the fitting results. Dominated by the hole band. (b) Same for large fields 4.5–8 T and low temperatures 6–18 K. Dominated by the electron band. (c) Temperature dependence of ${\sigma }_{xy}^s/B$ at low magnetic fields between 1 and 2.5 T and high temperatures 18–28 K. (d) Same for large fields 4.5–8 T and low temperatures 6–18 K.