Evolution of charge correlations in the hole-doped kagome superconductor CsV$_{3-x}$Ti$_x$Sb$_5$

This study reveals that while hole doping via Ti substitution in CsV$_{3-x}$Ti$_x$Sb$_5$ preserves conventional superconductivity across two distinct domes, it fundamentally alters charge correlations by rapidly suppressing competing $2\times 2 \times 2$ and $2\times 2 \times 4$ superstructures in the first dome and eliminating detectable charge order entirely in the second, highlighting key differences from Sn doping on Sb sites.

The Gist

Imagine a microscopic city built on a special kind of playground floor called a kagome lattice. This floor is made of triangles that share corners, creating a pattern full of "geometric frustration"—it's like trying to fit three friends into a two-person swing; they can't all be happy at the same time.

In the city of CsV₃Sb₅, the residents are electrons. Usually, these electrons behave in two interesting ways:

1. The Charge Dance (CDW): They line up in a rigid, repeating pattern, like soldiers marching in formation.
2. The Superconducting Flow: At very low temperatures, they pair up and flow without any friction, like a super-highway with no traffic jams.

In this specific city, scientists have discovered something strange: there are two separate "Superconducting Seasons" (called domes) where the electrons flow perfectly, separated by a time when the "Charge Dance" is very strong.

The Experiment: Changing the Neighborhood

The researchers wanted to see what happens if they swap out some of the city's residents. They replaced some Vanadium (V) atoms with Titanium (Ti) atoms. Think of this as swapping out the local citizens for slightly different neighbors. Because Titanium has a different number of "keys" (electrons) than Vanadium, this is called hole-doping—it's like removing a few people from the party, changing the crowd's energy.

They tested three different levels of this swap:

1. Light Swap (x=0.02): Just a few new neighbors.
2. Medium Swap (x=0.05): A moderate number of new neighbors.
3. Heavy Swap (x=0.15): A lot of new neighbors.

What They Found

1. The "Marching Soldiers" Disappear
In the original city, the electrons marched in two specific patterns: a tight 2×2×2 formation and a stretched 2×2×4 formation.

• Light Swap: Both patterns were still there, but the "stretched" one (2×2×4) started to crumble quickly.
• Medium Swap: The stretched pattern vanished completely. Only the tight formation remained, and it was getting shaky.
• Heavy Swap: Total silence. All the marching patterns disappeared. The electrons stopped dancing in a rigid line entirely.

2. The "Super-Flow" Survives
Here is the surprise: Even though the "Charge Dance" (the marching) disappeared, the Superconducting Flow didn't just vanish; it actually got a second wind!

• The city entered a second "Superconducting Season" (the second dome).
• The researchers used a super-sensitive magnetic camera (a nano-SQUID) to look at the "vortices" (tiny whirlpools of magnetic field) inside the superconductor.
• The Result: The whirlpools looked exactly the same as in the original city. They formed a perfect, standard triangle pattern. This tells us that even though the electrons stopped marching, they are still pairing up in the standard, "normal" way to flow without friction. They aren't doing anything weird or exotic in this second season.

The Big Difference: Who You Swap Matters

The researchers compared this to a previous study where they swapped Antimony (Sb) atoms instead of Vanadium.

• Swapping Sb (The "Soft" Swap): When they swapped the Sb atoms, the "Charge Dance" didn't disappear completely. It turned into a weak, fuzzy, one-dimensional wobble that still lingered in the second superconducting season.
• Swapping V with Ti (The "Hard" Swap): In this new study, swapping the Vanadium atoms (which are right in the middle of the triangle playground) created more disorder. It was like throwing a bunch of random obstacles onto the playground floor. This disorder was so strong that it completely wiped out the "Charge Dance" patterns, leaving no trace of them in the second season.

The Takeaway

Think of the electrons in this material as a crowd at a concert.

• Sometimes they form a rigid, organized mosh pit (the Charge Density Wave).
• Sometimes they form a smooth, flowing dance circle (Superconductivity).

This paper shows that if you change the crowd by swapping out the people in the middle of the dance floor (Vanadium sites), you can completely break up the rigid mosh pit, but the smooth dance circle can still survive and even thrive in a new way. However, if you swap people on the edges (Antimony sites), the mosh pit just turns into a sloppy, lingering mess.

In short: The "personality" of the impurity you add matters just as much as the amount you add. By adding Titanium to the core of the structure, the scientists successfully erased the complex charge patterns, proving that disorder can be a powerful tool to reshape how electrons behave in these quantum materials.

Technical Summary

1. Problem Statement

The kagome metal CsV$_3$Sb$_5$ exhibits a complex electronic phase diagram featuring a charge density wave (CDW) order and a double superconducting (SC) dome structure. While it is known that chemical doping (specifically hole-doping) can tune the interplay between CDW and superconductivity, the specific role of the dopant site and the associated disorder potential remains unclear.

• Context: Previous studies on Sb-site doping (e.g., CsV$_3$Sb$_{5-x}$Sn$_x$) revealed that beyond the suppression of 3D CDW order, incommensurate quasi-1D charge correlations persist, potentially linking the formation of the second SC dome to a crossover in charge correlation character.
• Gap: The evolution of charge correlations upon hole-doping directly on the kagome V-sites (via Ti substitution) was less explored. It was unknown whether the stronger disorder introduced by substituting V (part of the kagome lattice) would suppress these correlations differently compared to Sb-site doping, and how this affects the nature of the superconducting state (specifically regarding fractional vortices or unconventional pairing).

2. Methodology

The authors employed a multi-modal experimental approach on high-quality single crystals of CsV$_{3-x}$Ti$_x$Sb$_5$:

• Crystal Synthesis: Single crystals were grown using a flux-based technique with varying Ti concentrations ($x = 0, 0.02, 0.03, 0.05, 0.07, 0.15, 0.17, 0.22$).
• Bulk Characterization:
  • Magnetization: Magnetic susceptibility ($\chi$) was measured using a Quantum Design MPMS3 to map the electronic phase diagram, identifying CDW ($T_{CDW}$) and superconducting ($T_c$) transition temperatures.
  • Composition Analysis: Energy dispersive spectroscopy (EDS) was used to verify Ti doping levels.
• Synchrotron X-ray Diffraction (XRD):
  • Performed at the Cornell High Energy Synchrotron Source (CHESS) using high-energy X-rays ($\lambda = 0.676$ Å).
  • Focus: Investigated the evolution of superlattice reflections corresponding to CDW orders (specifically $2\times2\times2$ and $2\times2\times4$ reconstructions) across the phase diagram.
  • Samples: Detailed analysis focused on $x=0.02$ (SC1 dome), $x=0.05$ (phase boundary), and $x=0.15$ (SC2 dome).
• Nano SQUID-on-Tip (nSOT) Measurements:
  • Utilized a sharp tip with a superconducting quantum interference device (SQUID) to perform local magnetometry.
  • Goal: Image the vortex lattice structure to determine the nature of the superconducting ground state (conventional vs. unconventional/fractional pairing).

3. Key Results

A. Electronic Phase Diagram

• Double Dome Structure: The phase diagram confirms a double superconducting dome structure.
  • SC1 Dome ($x \approx 0.02 - 0.05$): Coexistence of SC and CDW. Light Ti doping rapidly suppresses $T_{CDW}$ and $T_c$. Notably, the superconducting volume fraction decreases significantly in this region, indicating disorder-induced suppression.
  • SC2 Dome ($x \approx 0.15$): The CDW order is completely suppressed, and the superconducting volume fraction recovers to a full state.

B. Evolution of Charge Correlations (XRD)

• Parent Compound ($x=0$): Exhibits competing $2\times2\times2$ and $2\times2\times4$ CDW supercells.
• Light Doping ($x=0.02$): Both $2\times2\times2$ and $2\times2\times4$ orders persist, though the correlation lengths are reduced compared to the parent. The $2\times2\times2$ state is more robust than the $2\times2\times4$ state.
• Phase Boundary ($x=0.05$): The $2\times2\times4$ reflections vanish, indicating the suppression of the mixed CDW state. Only a weakened $2\times2\times2$ order remains.
• Deep Doping ($x=0.15$, SC2 Dome): Crucial Finding: No charge correlations or superlattice reflections are detected. Unlike the Sb-site doping case (CsV$_3$Sb$_{5-x}$Sn$_x$), there is no evidence of remnant incommensurate quasi-1D charge correlations in the second superconducting dome.

C. Superconducting Ground State (nSOT)

• Vortex Imaging: Magnetic imaging of the vortex lattice in the parent, SC1 ($x=0.02$), and SC2 ($x=0.15$) samples reveals a conventional Abrikosov triangular vortex lattice.
• Pairing Symmetry: The vortices carry a flux of $h/2e$. No fractional vortices (which would indicate $4e$ or $6e$ composite pairing) were observed in the ground state.
• Disorder Effects: At low fields, dislocations in the vortex lattice were observed, attributed to pinning by local disorder, but the underlying lattice symmetry remained conventional.

4. Key Contributions

1. Site-Dependent Disorder: The study establishes that the chemical nature of the dopant is critical. Substituting V (kagome site) with Ti introduces a stronger disorder potential than substituting Sb. This strong disorder completely suppresses charge correlations in the SC2 dome, whereas Sb-site doping leaves behind weak, quasi-1D correlations.
2. Absence of Remnant Order in SC2: Contrary to the Sn-doped system, the Ti-doped system shows a complete suppression of CDW order before entering the second superconducting dome. This suggests that the mechanism driving the second SC dome in Ti-doped samples may not rely on the crossover to quasi-1D charge fluctuations seen in Sn-doped samples.
3. Conventional SC State: The nSOT data provides strong evidence that the superconducting ground state in both SC domes is conventional ($h/2e$ pairing), ruling out theories requiring fractional vortices or composite pairing in the ground state of this specific material system.
4. Suppression Mechanism: The results highlight that the $2\times2\times4$ CDW state is more fragile to hole-doping on the kagome lattice than the $2\times2\times2$ state, and that disorder plays a dominant role in destroying long-range charge order.

5. Significance

This work significantly refines the understanding of the interplay between CDW and superconductivity in kagome metals. By isolating the effect of kagome-site doping, the authors demonstrate that the "residual" charge correlations often cited as a driver for the second superconducting dome are not a universal feature of hole-doped CsV$_3$Sb$_5$ but are highly sensitive to the specific disorder potential introduced by the dopant.

The findings suggest that:

• The double-dome structure can exist even in the absence of remnant charge correlations.
• The "disorder potential" is a tunable parameter that can switch the system between a regime with competing orders (Sn-doped) and a regime with a clean separation of phases (Ti-doped).
• The superconductivity in CsV$_3$Sb$_5$ is likely conventional ($h/2e$) in the ground state, challenging hypotheses of exotic fractional pairing in the bulk ground state, though such states might still exist in fluctuation regimes.

This study provides a critical benchmark for theoretical models attempting to explain the origin of the double SC dome and the anomalous properties of kagome superconductors.