Sequence of Quantum Phase Transitions in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ Cuprates Revealed by In Situ Electrical Doping of One and the Same Sample

Our recently discovered electrical doping technique allows a broad-range variation of carrier concentration without changing the chemical composition. We show that it is possible to induce superconductivity in a nondoped insulating sample and to tune it reversibly all the way to an overdoped metallic state. This way, we can investigate the whole doping diagram of one and the same sample. Our study reveals two distinct critical points. The one at the overdoped side is associated with the onset of the pseudogap and with the metal-to-insulator transition in the $c$-axis transport. The other at optimal doping is associated with the appearance of a “dressed” electron energy. Our study confirms the existence of multiple phase transitions under the superconducting dome in cuprates.

Figure 1

Sketch and SEM images of (a) a zigzag structure and (b) a crystal with six mesa structures on top. (c) Resistive transition $R(T)$. (d) Current density vs voltage for mesa 1 at different doping states from the initial underdoped to the final overdoped state. Note the strong increase of the Josephson critical current density $J_c$. (e) $T_c$ vs the logarithm of $J_c$ (the bottom axis) for $I$-doped zigzag structures and O-doped mesas. The dashed line represents $T_c$ vs doping (the top axis). (f) $dI/dV$ characteristics of mesa 2 at an initial strongly underdoped state (the black line), after $I$ doping (the blue line), and after relaxation at $T\simeq 300\mathrm{K}$ (the red line).

Figure 2

(a) $dI/dV$ vs $V/N$ at different $I$-doping states for mesa 1. (b) Normalized current-voltage characteristics of mesa 1 at different doping states from strongly underdoped to slightly overdoped. Dashed lines are extrapolations of the linear sections at high bias. A finite threshold voltage $\mathrm{\Delta }{V}_{\mathrm{th}}$ appears in the underdoped state. (c) Normalized $R(T)$ curves for $I$-doped zigzag structures around optimal doping. A metal-to-insulator transition occurs at $p=0.19$. (d) Thermal-activation plots for zigzag structures. The slope represents the thermal-activation energy $U_{\mathrm{TA}}$. (e) Doping diagram obtained from low-bias characteristics. Open symbols represent the pseudogap energy, ${\mathrm{\Delta }}_{\mathrm{PG}}=e{V}_{\text{Hump}}/2N$, for $I$-doped (blue) and O-doped (red) mesa structures. Solid blue symbols represent $U_{\mathrm{TA}}$ of $I$-doped zigzag structures. The critical point at $p=0.19$ is associated with the onset of the pseudogap and the metal-to-insulator transition in $c$-axis transport. (f) A doping diagram obtained from high-bias characteristics (threshold voltage). The blue symbols represent $I$-doped zigzag (solid) and mesa (open) structures. Open red symbols represent $\mathrm{\Delta }{V}_{\mathrm{th}}$ for O-doped mesas (data from Ref. [8]). Different types of symbols represent different samples.