Evidence for a quantum phase transition in electron-doped ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ from thermopower measurements

The evidence for a quantum phase transition under the superconducting dome in the high-$T_c$ cuprates has been controversial. We report low-temperature normal state thermopower $\left(S\right)$ measurements in electron-doped ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ as a function of doping ($x$ from 0.11 to 0.19). We find that at $2\mathrm{K}$ both $S$ and $S∕T$ increase dramatically from $x=0.11$ to 0.16 and then saturate in the overdoped region. This behavior has a remarkable similarity to previous Hall effect results in ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$. Our results are further evidence for an antiferromagnetic to paramagnetic quantum phase transition in electron-doped cuprates near $x=0.16$.

Figure 1

(Color online) Thermopower $S$ versus temperature $(T<100\mathrm{K})$ at zero field for all the superconducting PCCO films. Inset is the thermopower $S$ of $x=0.16$ film at zero field `(solid blue circle) and ${\mu }_{0}H=9\mathrm{T}$ (open circle) as a function of temperature. Solid line is the temperature dependence of the Hall coefficient for the same film.

Figure 2

(Color online) The normal state thermopower $S$ $({\mu }_{0}H=9\mathrm{T}>{\mu }_0{H}_{c2})$ of all the doped films versus temperature. Inset shows the low-temperature $(T<15\mathrm{K})$ data.

Figure 3

(Color online) (a) $S∕T$ versus temperature ($T<40\mathrm{K}$ and ${\mu }_{0}H=9\mathrm{T}$) for all the films. (b) $S∕T$ ($T=2\mathrm{K}$ and ${\mu }_{0}H=9\mathrm{T}$) as a function of doping $x$.

Figure 4

Normalized $\alpha =S∕T$ and $\sigma \left(T\right)$ for $x=0.11$ versus temperature for $T⩽40\mathrm{K}$. Inset shows the temperature dependence of in-plane resistivity $\rho \left(T\right)$ for the same film.

Figure 5

Doping dependence of $q\left(2\mathrm{K}\right)$ and $q^{\prime }\left(2\mathrm{K}\right)$ of PCCO films [$q$ and $q^{\prime }$ are defined by Eqs. (2, 3) in the text].