🔬 condensed matter

Strain-tunable van Hove singularity and superconducting dome in monolayer kagome metal CsTi $_3$ Bi $_5$

This study demonstrates that biaxial tensile strain effectively tunes the van Hove singularity to the Fermi level in monolayer CsTi $_3$ Bi $_5$ , resulting in a dome-shaped superconducting transition temperature that peaks at 3.6 K under 2% strain.

Original authors: Run Lv, Wenqian Tu, Dingfu Shao, Yuping Sun, Wenjian Lu

Published 2026-10-26

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CC BY 4.0

Original authors: Run Lv, Wenqian Tu, Dingfu Shao, Yuping Sun, Wenjian Lu

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, researchers often look for patterns in how atoms arrange themselves to understand why certain materials conduct electricity or become superconductors. One such pattern is the kagome lattice, a geometric arrangement of atoms that resembles a woven basket or a starry sky, known for creating unique and sometimes unpredictable electronic behaviors. In these materials, electrons can get trapped in specific energy states, creating what scientists call a "van Hove singularity," a point where the number of available energy states spikes dramatically. When this spike aligns perfectly with the energy level where electrons naturally flow, it can trigger exotic phenomena, including superconductivity, a state where electricity flows with zero resistance. While scientists have long studied these effects in bulk materials, understanding how they behave in a single, atom-thin layer has been difficult, especially when unwanted structural changes interfere with the results.

A team of researchers has now turned their attention to a newly discovered material called CsTi3Bi5, a one-atom-thin sheet containing titanium and bismuth arranged in this kagome pattern. Unlike similar materials that suffer from structural instabilities, this new compound offers a clean, stable platform to study the pure electronic properties of the kagome lattice. The researchers wanted to know if they could control the material's behavior without adding impurities or changing its chemical makeup. To do this, they used powerful computer simulations to apply a gentle, invisible stretching force to the material, effectively pulling the atoms apart in a controlled way to see how the internal electronic landscape would shift.

The simulations revealed that this stretching, known as tensile strain, acts like a precise tuning knob for the material's electronic structure. As the researchers gradually stretched the single layer of atoms, they observed a specific energy feature, the van Hove singularity, moving steadily downward until it aligned perfectly with the flow of electrons. This alignment is crucial because it creates the ideal conditions for electrons to pair up and move without resistance. However, the relationship between stretching and superconductivity was not a simple straight line. The researchers found that the temperature at which the material becomes superconducting rose as the strain increased, reaching a peak performance at a stretch of exactly 2 percent. At this optimal point, the material could conduct electricity without resistance at a temperature of 3.6 Kelvin, which is significantly higher than the 1.85 Kelvin observed in the unstrained, bulk version of the material.

If the researchers continued to stretch the material beyond this sweet spot, the superconducting ability began to fade, dropping to 1.2 Kelvin at a 6 percent stretch. This creates a dome-shaped curve where the best performance sits at a specific, moderate level of tension. The study also showed that this improvement was driven by how the atoms vibrated and interacted with the electrons. The stretching caused the atoms to shift in a way that strengthened the connection between the vibrating lattice and the moving electrons, but only up to a point. Beyond the optimal 2 percent stretch, the vibrations changed in a way that weakened this connection, causing the superconducting temperature to fall.

Looking deeper into the microscopic details, the researchers discovered that the superconducting gap—the energy required to break the electron pairs—was not uniform across the material. Instead, it varied depending on which specific atoms and orbitals the electrons were occupying. The electrons associated with the titanium atoms showed a stronger, more robust pairing energy, while those linked to the bismuth atoms showed a slightly weaker effect. This uneven distribution suggests that the superconductivity in this material is a complex interplay between different types of atomic orbitals, rather than a single, uniform behavior.

These findings demonstrate that mechanical strain is a powerful and clean tool for manipulating the properties of two-dimensional kagome metals. By simply stretching the material, scientists can tune the electronic structure to enhance superconductivity without introducing the disorder that often comes with chemical doping. The study confirms that the van Hove singularity can be moved to the perfect energy level through physical deformation, and that this movement directly influences the material's ability to conduct electricity without loss. While the results come from computer simulations rather than physical experiments, they provide a clear roadmap for future research, suggesting that carefully controlling the shape of these atom-thin sheets could unlock new ways to engineer superconductors for future technologies.

Technical Summary: Strain-tunable van Hove singularity and superconducting dome in monolayer kagome metal CsTi3Bi5

Problem and Motivation
The kagome lattice is renowned for its geometric frustration and unique electronic properties, often hosting exotic quantum orders such as charge density waves (CDW) and superconductivity. While the vanadium-based family $AV_3Sb_5$ ( $A$ =K, Rb, Cs) has been extensively studied, its superconductivity is frequently intertwined with CDW order and structural instabilities. The recently discovered titanium-based kagome metal, $CsTi_3Bi_5$ , offers a distinct platform as it exhibits superconductivity without accompanying CDW order. However, its intrinsic electronic structure features a van Hove singularity (VHS) located just above the Fermi level. Previous attempts to tune this VHS to the Fermi level via chemical doping introduce disorder, obscuring the intrinsic physics. Consequently, there is a need for a clean, continuous tuning mechanism to probe the relationship between the electronic structure, the VHS, and superconductivity in the two-dimensional limit of this material.

Methodology
This study employs first-principles calculations based on density functional theory (DFT) using the Quantum ESPRESSO package. The authors model a monolayer slab of $CsTi_3Bi_5$ with a 20 Å vacuum layer to simulate the two-dimensional limit. The calculations utilize ultrasoft pseudopotentials, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for exchange-correlation, and Grimme's DFT-D3 method to account for van der Waals interactions.

To investigate strain effects, biaxial mechanical strain ( $\varepsilon$ ) is applied to the in-plane lattice parameters ( $a$ and $b$ ), ranging from compressive ( $-4\%$ ) to tensile ( $+6\%$ ). While the in-plane lattice constants are fixed according to the applied strain, the out-of-plane coordinates of the apical Bi and Cs atoms are fully relaxed to minimize total energy. The electron-phonon coupling (EPC) strength ( $\lambda$ ) and superconducting transition temperatures ( $T_C$ ) are calculated using the EPW code. The superconducting gaps are determined via the anisotropic Migdal-Eliashberg theory, with the Coulomb pseudopotential set to $\mu^* = 0.1$ .

Key Contributions and Results

Strain-Induced Structural and Electronic Tuning:
The study demonstrates that applying tensile strain causes the apical Bi atoms to move closer to the kagome plane, an effect analogous to hydrostatic pressure in the bulk crystal. This structural change leads to a monotonic shift in the electronic band structure. Specifically, the prominent van Hove singularity (VHS) located at the M point, which originates from Ti- $3d_{xy,x^2-y^2}$ orbitals, shifts toward lower energy as tensile strain increases. At a tensile strain of $\varepsilon = +6\%$ , the VHS is tuned precisely to the Fermi level. Conversely, compressive strain shifts the VHS to higher energies, further away from the Fermi level.
Dome-Shaped Superconducting Transition Temperature:
The superconducting transition temperature ( $T_C$ ) exhibits a non-monotonic, dome-shaped dependence on strain. Calculations using the Allen-Dynes modified McMillan equation show that $T_C$ increases from 0.3 K at $\varepsilon = -4\%$ to a maximum of 3.6 K at an optimal tensile strain of $\varepsilon = +2\%$ . Beyond this optimal point, $T_C$ decreases to 1.2 K at $\varepsilon = +6\%$ .
- This enhancement is driven by the total EPC strength ( $\lambda$ ), which increases from 0.37 at $-4\%$ to a peak of 0.62 at $+2\%$ , before dropping to 0.46 at $+6\%$ .
- The increase in $\lambda$ is attributed to the softening of specific phonon modes: the out-of-plane vibrations of apical Bi atoms and the in-plane vibrations of Ti atoms.
- Notably, the maximum $T_C$ occurs at $\varepsilon = +2\%$ , whereas the VHS aligns with the Fermi level only at $\varepsilon = +6\%$ . This indicates that the enhancement of superconductivity is not solely determined by the VHS-Fermi level alignment but is also critically dependent on the strain-induced modulation of the electron-phonon coupling strength.
Anisotropic and Orbital-Dependent Superconducting Gap:
Using the anisotropic Migdal-Eliashberg theory, the study calculates the momentum-resolved superconducting gap ( $\Delta_{nk}$ ) at the optimal strain ( $\varepsilon = +2\%$ ). The gap is fully open with an average magnitude of 0.35 meV. The distribution is highly anisotropic and orbital-dependent:
- The central Fermi surface pocket, dominated by planar Bi- $6p_z$ orbitals, exhibits the smallest gap ( $\sim 0.32$ meV).
- The hexagonal Fermi surfaces ( $\beta$ and $\gamma$ ), primarily composed of Ti- $3d_{xz,yz}$ and Ti- $3d_{xy,x^2-y^2}$ orbitals, show larger gap values ranging from 0.35 to 0.42 meV.
- The calculated $T_C$ derived from the temperature dependence of the gap ( $\sim 3.2$ K) is consistent with the McMillan equation estimate.

Significance
The paper establishes biaxial strain as an effective, disorder-free, and continuous tuning knob for manipulating the electronic structure and superconductivity of monolayer $CsTi_3Bi_5$ . By demonstrating that tensile strain can monotonically tune the VHS to the Fermi level and significantly enhance $T_C$ (from 0.3 K to 3.6 K), the work provides a detailed understanding of intrinsic kagome superconductivity in the two-dimensional limit. The results suggest that the pairing mechanism in titanium-based kagome superconductors shares common origins with their vanadium-based counterparts, as evidenced by similar orbital-dependent gap distributions. This study offers a theoretical framework for exploring how lattice geometry controls electron pairing in 2D kagome metals without the complications of chemical disorder.

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