Bragg-Williams order competes with superconductivity

This study demonstrates that Bragg-Williams order acts as an independent competing order parameter that suppresses superconductivity in In2/3PSe3, where the disordered phase exhibits a significantly higher critical temperature (11 K) than the ordered phase (7 K) due to enhanced electron-phonon interactions.

The Gist

Imagine a crowded dance floor where the music (temperature) dictates how the dancers (atoms) move. Usually, when the music stops or slows down, the dancers naturally fall into a neat, organized line. But sometimes, if you cool them down just right, they get stuck in a messy, random shuffle.

This paper is about a specific material, In₂/₃PSe₃ (a sandwich of Indium, Phosphorus, and Selenium), and how the "dance floor arrangement" of its atoms changes its ability to conduct electricity without resistance—a phenomenon called superconductivity.

Here is the story of their discovery, broken down simply:

1. The Missing Dancers (Vacancies)

In this material, the Indium atoms are supposed to fill every spot on the dance floor. But because of how the chemistry works, about one-third of the spots are empty. These empty spots are called vacancies.

Think of these vacancies like empty seats in a theater.

• The Ordered Phase (O-phase): If you cool the material down slowly, the empty seats arrange themselves in a perfect, repeating pattern. It's like a checkerboard where every other seat is empty. The scientists call this Bragg-Williams Order (BWO). It's highly organized.
• The Disordered Phase (D-phase): If you heat the material up and then "quench" it (cool it down extremely fast, like plunging it into ice water), the empty seats get frozen in random spots. The pattern is broken. The seats are messy and chaotic.

2. The Big Surprise: Messiness is Better

Usually, in the world of physics, we think that order is good and messiness is bad. You'd expect the neat, organized crystal to be the "better" one.

The researchers tested both versions by squeezing them with immense pressure (like a giant hydraulic press) to see when they would become superconductors (materials that conduct electricity with zero resistance).

• The Organized Version: It needed a lot of pressure to start superconducting, and even then, it only worked at a relatively chilly 7 Kelvin (about -266°C).
• The Messy Version: Surprisingly, the random, disordered version started superconducting at a lower pressure and reached a much warmer 11 Kelvin (about -262°C).

The Takeaway: In this specific case, chaos helped the superconductivity. The more random the empty seats were, the better the material performed.

3. Why Does This Happen? (The Stiff vs. Soft Mattress)

To understand why, imagine the atoms are connected by springs (bonds).

• In the Organized Version: Because the empty seats are perfectly lined up, the springs connecting the atoms get very stiff and tight. It's like sleeping on a rock-hard mattress. The atoms can't wiggle or vibrate easily.
• In the Messy Version: Because the empty seats are scattered randomly, the springs are looser. The "mattress" is softer. The atoms can wiggle and vibrate more freely.

Superconductivity in this material relies on these vibrations (phonons) to help electrons pair up and flow without resistance.

• Stiff springs (Ordered): The vibrations are too rigid. The electrons can't pair up easily. Superconductivity is weak.
• Soft springs (Disordered): The vibrations are loose and lively. The electrons pair up easily. Superconductivity is strong.

4. Why This Matters

For decades, scientists have known that "charge" (adding extra electrons) and "spin" (magnetism) can fight against superconductivity. This paper introduces a new player: Structural Order.

The authors show that the arrangement of empty spots itself is a powerful force that competes with superconductivity. They proved that you don't need to change the chemical recipe or add new elements; you just need to change the "thermal history" (how fast you cool it down) to toggle between a "good" superconductor and a "bad" one.

Summary

The paper claims that in this specific material, order is the enemy of superconductivity. By scrambling the pattern of missing atoms, the material becomes "softer," allowing electrons to flow freely at higher temperatures. This suggests that controlling how atoms arrange themselves (or disarrange themselves) is a new, powerful knob scientists can turn to engineer better superconductors.

Technical Summary

1. Problem Statement

The relationship between structural order and superconductivity is a central theme in condensed matter physics. While the competition between superconductivity and electronic/magnetic orders (such as Charge Density Waves or Spin Density Waves) is well-documented, the specific role of Bragg-Williams Order (BWO)—a classical structural order parameter describing site occupancy in alloys—remains ambiguous.

• The Challenge: In most known systems (e.g., $YBa_2Cu_3O_{7-x}$ or $K_xFe_{2-y}Se_2$), altering atomic ordering inevitably changes the chemical composition (e.g., oxygen or iron content), thereby introducing charge doping. This makes it impossible to isolate the effect of structural order from the effects of carrier concentration.
• The Goal: To identify a system where BWO can be tuned independently of carrier concentration to determine if pure structural ordering competes with or enhances superconductivity.

2. Methodology

The authors utilized the $In_{2/3}PSe_3$ system as a unique platform to decouple structural order from electronic doping.

• Material Design: They selected a trivalent metal (In$^{3+}$) in a divalent framework ($MPSe_3$), which naturally creates a 1/3 vacancy concentration to maintain charge balance. This allows for two distinct phases with identical stoichiometry but different vacancy configurations:
  • Ordered Phase (O-phase, $\eta=1$): Vacancies are arranged in a long-range periodic pattern (triclinic, space group $P\bar{1}$).
  • Disordered Phase (D-phase, $\eta=0$): Vacancies are randomly distributed (rhombohedral, space group $R\bar{3}$).
• Synthesis & Tuning: Single crystals were grown via chemical vapor transport. The O-phase and D-phase were reversibly switched using thermal treatment (annealing and quenching) without altering the chemical composition.
• Characterization Techniques:
  • Structural: Aberration-corrected Scanning Transmission Electron Microscopy (STEM/HAADF) and Selected Area Electron Diffraction (SAED) to visualize vacancy ordering.
  • High-Pressure Transport: Electrical resistance measurements under hydrostatic pressure (up to ~70 GPa) to induce superconductivity.
  • High-Pressure Diffraction: Synchrotron X-ray diffraction to monitor structural phase transitions and lattice compression.
  • Electronic Properties: Hall effect measurements to extract carrier concentrations.
  • Lattice Dynamics: Raman spectroscopy to probe phonon modes and electron-phonon coupling.
• Theoretical Framework:
  • Phenomenological: Ginzburg-Landau theory introducing a repulsive coupling term between the superconducting order parameter ($\Delta$) and the BWO parameter ($\eta$).
  • Microscopic: BCS-McMillan theory linking the electron-phonon coupling constant ($\lambda$) to phonon frequencies, which are modulated by vacancy ordering.

3. Key Contributions

• Isolation of BWO: The study successfully established a system where the degree of structural order ($\eta$) is tuned purely by thermal history, keeping carrier concentration and stoichiometry constant.
• Discovery of Competing Orders: It provides the first clear experimental evidence that pure Bragg-Williams order acts as an independent order parameter that directly competes with superconductivity, distinct from magnetic or electronic instabilities.
• Mechanism Elucidation: The authors demonstrated that the competition arises from lattice dynamics. Specifically, long-range vacancy ordering stiffens the lattice (increases phonon frequencies), which suppresses electron-phonon coupling and lowers the critical temperature ($T_c$).

4. Key Results

• Superconductivity Transition:
  • Both phases become superconducting under high pressure.
  • D-phase (Disordered, $\eta=0$): Exhibits a significantly higher critical temperature, reaching $T_c \approx 11$ K at ~37 GPa.
  • O-phase (Ordered, $\eta=1$): Exhibits a lower critical temperature, saturating at $T_c \approx 7$ K even at much higher pressures (~70 GPa).
• Carrier Concentration Independence: Hall measurements confirmed that at equivalent pressures (e.g., 30 GPa), the carrier concentrations in both phases are comparable, yet the $T_c$ difference is massive. This rules out carrier doping as the cause of the $T_c$ variation.
• Structural Stability: High-pressure XRD showed no structural phase transitions between the O and D phases upon compression; the difference in $T_c$ is solely due to the initial vacancy configuration.
• Phonon Softening: Raman spectroscopy revealed that the disordered D-phase has "softer" lattice modes (lower frequency) compared to the ordered O-phase. The ordered phase exhibits more vibrational peaks due to reduced symmetry ($P\bar{1}$), but the overall lattice stiffness is higher.
• Theoretical Validation:
  • The Ginzburg-Landau analysis showed that the coupling term $\gamma|\Delta|^2|\eta|^2$ is positive (repulsive), mathematically proving that increasing order ($\eta$) suppresses $T_c$.
  • Microscopic analysis confirmed that vacancy ordering increases the mean-square phonon frequency ($\omega^2$), thereby reducing the electron-phonon coupling constant $\lambda$ (since $\lambda \propto 1/\omega^2$), leading to a lower $T_c$.

5. Significance

• New Paradigm for Competing Orders: This work extends the concept of competing orders beyond the traditional electronic (charge/spin) degrees of freedom to structural degrees of freedom. It proves that structural order parameters can be primary competitors to superconductivity.
• Engineering Quantum Materials: The study identifies BWO as a "versatile knob" for tuning quantum materials. By controlling thermal history, researchers can engineer the degree of disorder to optimize superconducting properties without changing chemical composition.
• Fundamental Physics: It resolves the ambiguity regarding the role of structural order in superconductors, demonstrating that in the absence of magnetic elements and carrier doping, disorder (specifically the loss of Bragg-Williams order) can enhance superconductivity by softening the lattice and strengthening electron-phonon coupling.

In summary, the paper establishes that in $In_{2/3}PSe_3$, the transition from an ordered vacancy state to a disordered state significantly enhances superconductivity ($7$K$\to$ $11$ K) by softening the lattice and enhancing electron-phonon interactions, providing a rare and clean example of Bragg-Williams order competing directly with superconductivity.