Charge order in the Pr substituted YBa$_2$Cu$_3$O$_7$ from high-field Hall effect measurements

High-field Hall effect measurements reveal that Pr-substituted YBa$_2$Cu$_3$O$_7$ exhibits 2D charge order and Fermi surface reconstruction similar to pure YBCO, demonstrating that the carrier concentration in the CuO$_2$ planes, rather than the specific doping mechanism or disorder level, is the primary factor governing electronic orders in these systems.

The Gist

Imagine a high-performance sports car (a superconductor) that can carry electricity with zero resistance, but only if you tune its engine just right. The "engine" in these materials is a grid of copper and oxygen atoms called the CuO2 plane. The "fuel" that makes the car run is a specific number of missing electrons, known as holes.

For decades, scientists have studied a famous model car called YBCO (Yttrium-Ba-Copper-Oxide). They know that if you change the fuel mixture (doping) just right, the car develops a strange "traffic jam" of electrons called charge order. This traffic jam rearranges the road map (the Fermi surface) and changes how the car drives, sometimes even fighting against the car's ability to go super-fast (superconductivity).

Now, the researchers in this paper decided to build a slightly different version of this car. Instead of using Yttrium, they swapped in Praseodymium (Pr). This is like swapping the engine block for a different brand.

Here is what they found, explained simply:

1. The "Wrong" Engine, The "Right" Result

In the original YBCO car, you control the fuel (holes) by adding or removing oxygen from the fuel lines (chains). In the new Pr-YBCO car, the Praseodymium acts like a sponge that soaks up the fuel, reducing the holes in a completely different way.

You would expect that because the fuel is being removed differently, the car's behavior would be totally different. But it wasn't.

The researchers found that despite the different engine and fuel system, the new car behaved almost exactly like the old one. When they measured how electricity flowed under strong magnetic fields (like driving through a heavy storm), they saw the same "traffic jam" (charge order) and the same road-map changes (Fermi surface reconstruction) that they see in the original YBCO.

The Analogy: It's like driving two different cars—one with a V8 engine and one with an electric motor. You'd expect them to handle corners differently. But if you put both on the same track, they both hit the same "sweet spot" where they start to drift in the exact same way. This tells the scientists that the amount of fuel (holes) in the engine room matters more than how you got that fuel there.

2. The Hall Effect: The "Compass"

To see these changes, the scientists used a tool called the Hall effect, which acts like a compass for electrons.

• In a normal metal, the compass points one way (positive).
• In the superconducting "sweet spot," the compass flips and points the other way (negative). This flip is the smoking gun that proves the road map has been rearranged by the charge order.

They found that in the new Pr-YBCO cars, the compass flipped just like in the old YBCO cars, but only when the car was tuned to the right speed (doping level). If they added too much Praseodymium (too much "sponge"), the compass never flipped, and the car just became an insulator (a brick that doesn't conduct electricity).

3. The "Ghost" Traffic Jam

Here is the twist: In the original YBCO, this charge order (the traffic jam) fights hard with superconductivity. It's like the traffic jam is so bad it slows the car down significantly.

In the new Pr-YBCO, the traffic jam exists, but it doesn't seem to fight the superconductivity as hard. The car doesn't slow down as much.

• Why? The paper suggests the "traffic jam" in the new car is much shorter and messier (more disordered) than in the old one. It's like a traffic jam that is only a few cars long instead of a mile long. Because it's so short and messy, it doesn't block the super-fast electrons as effectively.

4. The Big Conclusion

The main takeaway is a lesson in simplicity: The rules of the game are dictated by the players on the field, not the coach.

Even though the Praseodymium car has a different coach (different doping mechanism) and a messier field (more disorder), the players (the electrons in the copper planes) still follow the same rules. As long as the number of players is right, the game (the electronic phase diagram) looks the same.

In summary: The scientists proved that you can change the recipe for making these superconductors, but if you get the number of charge carriers right, the electrons will still organize themselves into the same patterns, creating the same "traffic jams" and road-map changes, regardless of how messy the kitchen is.

Technical Summary

Technical Summary: Charge order in the Pr substituted YBa2Cu3O7 from high-field Hall effect measurements

Problem and Context
The mechanism of doping in the composite system Pr$_x$Y$_{1-x}$Ba$_2$Cu$_3$O$_{7-\delta}$ (Pr-YBCO) differs fundamentally from that of pure YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO). In pure YBCO, hole doping is controlled by oxygen stoichiometry in the CuO chains, whereas in Pr-YBCO, superconductivity is suppressed via Pr cation substitution while oxygen stoichiometry remains largely constant. The Pr substitution introduces distinct effects: orbital hybridization between Pr 4$f$ and O 2$p$ orbitals leads to hole localization, and the magnetic moment of Pr ions causes pair-breaking via spin exchange. Despite these structural and doping disparities, the phase diagram of Pr-YBCO closely resembles that of pure YBCO, featuring antiferromagnetic (AFM) and superconducting (SC) domes. A central question remains whether the ubiquitous 2D charge order (CO) and the associated Fermi surface reconstruction (FSR) observed in underdoped YBCO also exist in Pr-YBCO, and how disorder and distinct doping mechanisms influence these electronic orders.

Methodology
The authors synthesized six twinned Pr-YBCO single crystals with nominal Pr concentrations ($x$) ranging from 0.2 to 0.45, corresponding to superconducting transition temperatures ($T_c$) between 32 K and 70 K. The samples were fully oxygenated ($y=7$) to isolate the effects of Pr substitution. Transport measurements were conducted using pulsed magnetic fields up to 65 T at the LNCMI-EMFL facility in Toulouse. The study focused on magnetoresistance ($\rho_{xx}$) and the Hall coefficient ($R_H$) measurements. To ensure accuracy, measurements were performed with two field polarities at each temperature to allow for symmetrization of magnetoresistance and antisymmetrization of Hall resistance, effectively eliminating $c$-axis contamination. The Hall coefficient was analyzed as a function of temperature and magnetic field across the doping range to detect signatures of Fermi surface reconstruction.

Key Results

1. Hall Effect Sign Reversal: The Hall coefficient $R_H(T)$ exhibits a temperature-dependent sign change in samples with lower Pr content (higher $T_c$, specifically $x=0.2$ and $x=0.35$). At high temperatures, $R_H$ is positive; as temperature decreases, it reaches a maximum, falls sharply, and becomes negative. The temperature at which $R_H = 0$ ($T_0$) decreases as Pr content increases (and $T_c$ decreases). In samples with higher Pr content ($x=0.4$ and $x=0.45$), $R_H$ remains positive across all measured temperatures.
2. Comparison with YBCO: The behavior of $R_H$ in Pr-YBCO mirrors that of pure YBCO. In YBCO, a sign reversal from positive to negative is associated with a Fermi surface reconstruction driven by 2D charge order, creating small electron pockets. The observation of a similar sign reversal in Pr-YBCO suggests the presence of a comparable 2D charge order and FSR.
3. Suppression of Competition: Unlike pure YBCO, where charge order strongly competes with superconductivity (evidenced by a depression in $T_c$ and the upper critical field $H_{c2}$ near optimal doping), Pr-YBCO shows a lack of such competition. The irreversibility field $H_{irr}$ (a proxy for $H_{c2}$) decreases monotonically with increasing Pr content, without the characteristic suppression dip seen in YBCO near $p \approx 0.125$.
4. Disorder Effects: The sign reversal in Pr-YBCO occurs at lower temperatures compared to YBCO for equivalent $T_c$ values. This shift, combined with previous X-ray scattering results indicating a charge order correlation length three times smaller in Pr-YBCO (25–30 Å vs. ~80–100 Å in YBCO), suggests that disorder significantly smears the charge order transition.

Significance and Claims
The paper claims that the primary factor governing electronic orders in these systems is the amount of charge carriers in the CuO$_2$ planes, rather than the specific mechanism of doping (oxygen reduction vs. Pr substitution) or the level of disorder. Despite the distinct doping mechanisms and the additional disorder introduced by Pr, the phase diagrams of Pr-YBCO and YBCO are "decidedly symmetric."

The authors propose that the observed Fermi surface reconstruction in Pr-YBCO stems from 2D charge correlations. The apparent lack of competition between this charge order and superconductivity is attributed to the short correlation length of the charge order and the high level of disorder in the Pr-YBCO system, which effectively smears out well-defined transitions. While the study confirms the presence of 2D charge order signatures via transport, it does not definitively resolve whether Pr-YBCO hosts 3D charge order similar to that induced in YBCO by high magnetic fields or strain, noting that previous X-ray studies have yielded conflicting interpretations regarding 3D order in Pr-YBCO.

In summary, the work demonstrates that 2D charge order and Fermi surface reconstruction are robust features of the cuprate phase diagram, persisting even when the doping mechanism is altered and disorder is significantly increased, provided the carrier concentration in the planes is comparable.