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Competing lattice structures induced by Sn substitution in CsV $_3$ Sb $_5$

By combining $^{121}$ Sb NQR measurements and density functional theory calculations, this study reveals that Sn substitution in CsV $_3$ Sb $_5$ induces local structural distortions and drives a complex interplay between these impurity effects and competing lattice instabilities, ultimately stabilizing nearly degenerate V-trimer structures in the fully doped limit.

Original authors: Anshu Kataria, Ilija K. Nikolov, Armando Consiglio, Giuseppe Allodi, Ginevra Corsale, Andrea Capa Salinas, Stephen D. Wilson, Domenico Di Sante, Vesna F. Mitrović, Samuele Sanna, Pietro Bonfà

Published 2026-09-04

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CC BY 4.0

Original authors: Anshu Kataria, Ilija K. Nikolov, Armando Consiglio, Giuseppe Allodi, Ginevra Corsale, Andrea Capa Salinas, Stephen D. Wilson, Domenico Di Sante, Vesna F. Mitrović, Samuele Sanna, Pietro Bonfà

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of materials science, some crystals are like crowded dance floors where electrons move in complex, coordinated patterns. Among these, a family of metals known as kagome lattices has recently captured the imagination of researchers. The name comes from a Japanese basket-weaving pattern, a shape that repeats across the material's atomic structure, creating a unique environment for electrons. In these materials, the electrons can organize themselves into waves of charge, a state called a charge density wave, or they can flow without resistance, becoming superconductors. The behavior of these electrons is incredibly sensitive to the shape of the atomic grid they inhabit. If the grid shifts even slightly, the entire electronic personality of the material can change. Understanding how to control these shifts is crucial for unlocking new technologies, but the rules governing how the atomic structure and the electron behavior influence each other remain partially hidden.

A team of scientists set out to uncover these rules by studying a specific kagome metal called CsV3Sb5. They wanted to see what happens when they subtly alter the material's recipe by swapping some of its atoms. Specifically, they replaced a portion of the antimony atoms with tin atoms. This chemical substitution acts like a tuning fork, changing the electronic landscape and the way the atoms sit relative to one another. While previous studies showed that adding tin changes the material's electrical properties, the microscopic mechanism driving these changes was unclear. Did the tin atoms simply act as passive placeholders, or did they actively distort the local atomic neighborhood, forcing the entire structure to rearrange itself in unexpected ways?

To answer this, the researchers combined two powerful approaches: a highly sensitive experimental technique and advanced computer simulations. They used a method called nuclear quadrupole resonance, which acts like a microscopic ear listening to the vibrations of atomic nuclei. By measuring how the nuclei of antimony atoms respond to their local electric environment, the team could detect tiny distortions in the crystal lattice that are too small to be seen by standard X-ray cameras. They tested samples with varying amounts of tin, from a tiny sprinkle to a heavy dose where half the antimony was replaced.

The results revealed a story of local disruption and global competition. Even at very low levels of tin doping, the researchers detected new signals in their measurements. These signals appeared as satellite peaks, distinct from the main signal of the pure material. The team found that these new signals were caused by the tin atoms pushing against their neighbors, creating a localized distortion in the atomic grid. This distortion was not a fleeting event; it persisted across the entire range of doping tested, remaining visible even at room temperature. The data suggested that the tin atoms were not just sitting quietly in the lattice but were actively reshaping the charge environment around them, creating a unique local signature that the computer models confirmed.

The story became even more complex when the researchers looked at the extreme case where every available antimony site was replaced by tin. In this fully substituted state, the computer simulations predicted that the material's stability would shift dramatically. The atomic grid, which usually settles into one specific pattern, became unstable and began to favor two different structures that were nearly equal in energy. One structure featured small clusters of three vanadium atoms grouped together, while the other was a version of that same structure but shifted slightly in height relative to the layers above and below it. The simulations suggested that the material could easily flip between these two nearly identical states, a behavior that would fundamentally alter how the electrons move through the crystal.

These findings paint a picture of a material where the introduction of a foreign atom does more than just change the number of electrons; it actively competes with the material's natural tendency to form specific patterns. The tin atoms create local distortions that ripple through the structure, and at high concentrations, they force the entire lattice to choose between two different, competing shapes. This interplay between the local push of the impurity and the global struggle between different structural phases provides a deeper understanding of how chemical changes can be used to tune the properties of these exotic metals. The work does not claim to have solved the entire puzzle of kagome physics, but it offers a clear, microscopic view of how a simple chemical swap can trigger a complex dance of structural instability, guiding future efforts to engineer materials with tailored electronic behaviors.

Technical Summary: Competing Lattice Structures Induced by Sn Substitution in CsV $_3$ Sb $_5$

Problem Statement
The electronic phase diagram of vanadium-based kagome metals, specifically CsV $_3$ Sb $_5$ , is governed by a complex interplay between local structural distortions and electronic instabilities, manifesting as charge density waves (CDW), superconductivity, and nematic order. While chemical substitution (e.g., Sn for Sb) is known to suppress long-range CDW order and induce a double-dome superconducting feature, the microscopic mechanism driving these changes remains unclear. Specifically, it is not fully understood how Sn substitution alters the local charge environment, induces structural distortions, or competes with the intrinsic lattice instabilities (Star of David vs. Tri-Hexagonal patterns) of the pristine material.

Methodology
The study employs a combined experimental and theoretical approach to investigate the atomic-scale effects of Sn substitution in CsV $_3$ Sb $_{5-x}$ Sn $_x$ :

Experimental: Zero-field $^{121}$ Sb Nuclear Quadrupole Resonance (NQR) measurements were performed on high-quality powder samples across a doping range of $x = 0$ to $x = 0.65$ at both room temperature (RT) and low temperatures (5 K). NQR was utilized to directly probe the electric field gradient (EFG) at nuclear sites, providing sensitivity to local charge distributions and structural distortions inaccessible to bulk diffraction.
Theoretical: Density Functional Theory (DFT) calculations were conducted using the Quantum ESPRESSO package with PBE functionals and van der Waals corrections (rVV10). The study modeled Sn substitution at the in-plane Sb $_1$ site using supercells to calculate EFGs and resonance frequencies. Additionally, phonon dispersion calculations were performed for the fully substituted limit ( $x=1$ , CsV $_3$ Sb $_4$ Sn) to assess dynamical stability and identify ground-state structural phases.

Key Results

Local Structural Distortions at Low Doping: At low Sn concentrations ( $x \leq 0.12$ ), the NQR spectra exhibit distinct satellite peaks surrounding the central Sb $_2$ resonance. These peaks are attributed to Sb $_2$ nuclei experiencing modified EFGs due to Sn impurities at neighboring Sb $_1$ sites. The spectral weight of these satellites follows a binomial distribution consistent with random Sn occupancy at the Sb $_1$ site, where the number of Sn nearest neighbors determines the local environment.
Persistence of Impurity Signatures: Unlike the long-range CDW order, which is suppressed at higher doping levels, these impurity-induced satellite peaks persist across the entire investigated doping range ( $x$ up to 0.65) and remain observable up to room temperature. This suggests that the local lattice distortion caused by the steric effect of Sn substitution is robust and survives the CDW transition.
Microscopic Origin: DFT simulations of the low-doping regime confirm that Sn substitution at the Sb $_1$ site induces local charge redistribution, splitting the Sb $_2$ sites into inequivalent environments. The calculated resonance frequencies qualitatively match the experimental satellite peaks, validating the assignment of these features to local impurity-induced distortions.
Competing Lattice Structures at Full Doping: For the idealized fully substituted case ( $x=1$ $x = 1$ , CsV $_3$ $_{3}$ Sb $_4$ $_{4}$ Sn), phonon dispersion calculations reveal a distinct dynamical instability. The pristine Tri-Hexagonal (TrH) and Star of David (SoD) instabilities are replaced by a new instability characterized by the formation of vanadium trimers (V-trimers).
- Two nearly energy-degenerate equilibrium structures are identified: a $\Gamma$ -phase structure and an $A$ -phase structure.
- Both structures feature V-trimerization but differ by a $\pi$ -phase shift between adjacent layers along the $c$ -axis.
- The $A$ -phase (staggered V-trimers) is found to be the lowest-energy structure, with an energy gain of $\approx 3$ meV/atom relative to the hexagonal lattice, and is significantly more stable than the TrH/SoD patterns observed in the pristine compound.

Significance and Claims
The paper claims that Sn substitution in CsV $_3$ Sb $_5$ drives a complex interplay between local, impurity-induced lattice distortions and competing structural instabilities. The primary significance of the work lies in:

Microscopic Mechanism: Establishing that the "satellite" features in NQR spectra are direct signatures of local structural distortions induced by Sn, which persist even when long-range CDW order is suppressed.
Modified Energy Landscape: Demonstrating that at high doping levels, the energy landscape of the kagome lattice is fundamentally altered. The system transitions from competing TrH/SoD patterns to a regime dominated by V-trimerization with competing $\pi$ -shifted stacking orders.
Tuning Parameter: Providing evidence that chemical substitution acts as a crucial tuning parameter that can decouple local structural responses from global electronic instabilities, offering a microscopic basis for understanding the rich phase diagrams of doped kagome systems.

The authors conclude that these findings highlight how seemingly small perturbations, such as chemical substitution, can act as critical tuning parameters between multiple nearly degenerate electronic and structural states in kagome metals.

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