The work, published in Frontiers in Thermal Engineering by Huimin Huang and Qiang Cheng of the State Key Laboratory of Coal Combustion at Huazhong University of Science and Technology, combines first-principles density functional theory calculations with fluctuation-dissipation theory to model two suspended χ3-phase borophene sheets separated by a vacuum gap of 10 nanometers. The researchers applied uniaxial strain ranging from −4 percent compression to +4 percent tension along either the x-axis, which corresponds to the borophene lattice direction a, or the y-axis, perpendicular to it. Their central finding is stark: the direction of strain matters as much as its magnitude. Straining along the x-axis produced a nonlinear response, with the normalized heat transfer coefficient first dipping slightly below unity and then climbing to 1.72 at +4 percent tension. Straining along the y-axis, by contrast, drove a monotonic, switch-like surge, with the coefficient reaching 8.96 at the same tension—roughly a ninefold amplification of near-field heat flow.

The physical mechanism behind this anisotropy lies in borophene’s dielectric function, the quantity that describes how the material’s electrons respond to electromagnetic fields. Borophene is intrinsically anisotropic: its optical response along the lattice direction differs sharply from the perpendicular direction, a property the team confirmed by calculating the complex dielectric function over the frequency range of 0 to 4 electronvolts. Under x-axis compression, the real part of the dielectric function εxx maintains a pronounced resonance peak around 0.8 to 1.0 electronvolts whose intensity grows with increasing compression, while the imaginary part exhibits a stable absorption peak near 1.1 to 1.3 electronvolts that intensifies without shifting position. Compression along the loading direction therefore strengthens the electronic polarization response in that direction, whereas the perpendicular component εyy remains nearly untouched.

Y-axis strain operates through an entirely different channel. Compression along the y-axis leaves the main resonance and absorption structures essentially intact, producing only slight local intensity fluctuations. But large tensile strain along the y-direction—particularly at +3 and +4 percent—triggers a distinct uplift in the low-frequency region of the real dielectric function near zero energy, in both εxx and εyy. This enhanced low-frequency polarization background does not destroy the original resonance modes; instead, it raises the material’s ability to support low-energy evanescent-wave coupling. Because near-field heat transfer between two closely spaced sheets is dominated by the tunneling of evanescent waves at frequencies set by the surface electromagnetic modes, this strain-induced dielectric uplift modifies the resonance condition of those modes and dramatically increases their coupling probability within the dominant heat-transfer frequency window.

The electronic band structure calculations reinforce this picture. The team found that χ3-borophene remains metallic under all investigated strain conditions, with several bands continuously crossing the Fermi level. X-axis strain produces only moderate changes in the electronic structure near the Fermi level, indicating limited reconstruction of low-energy states. Y-axis tensile strain, however, induces pronounced band flattening and denser electronic states near the Fermi level, especially at +4 percent tension. This densification of available states enhances low-energy interband transitions, strengthens the low-frequency dielectric response, and ultimately feeds through to the near-field heat-transfer spectrum via the Fresnel reflection coefficients and the energy transmission coefficient of evanescent waves.

The spectral heat transfer coefficient h(ω) reveals these effects quantitatively. Under single-layer x-axis compression, the main spectral peak—located around ω ≈ 2 × 10^14 radians per second—rises from 4.6 × 10^−16 to 5.5 × 10^−16 joules per radian per kelvin per square meter at −4 percent strain, with the peak position essentially stable. Under single-layer y-axis tension, the response is far more dramatic: the peak value climbs to 9.56 × 10^−15 at +4 percent, roughly an order of magnitude above the corresponding x-direction condition. The team attributes this staged, nonlinear surge to the strain-induced enhancement of the low-frequency dielectric response, which improves the surface electromagnetic response and strengthens evanescent-wave coupling across the dominant frequency range.

When both borophene sheets are strained simultaneously in the same direction—what the authors call bilayer co-directional strain—the modulation effects amplify considerably. Bilayer x-axis tension at +4 percent produces a normalized coefficient of 3.64, with the spectral peak reaching 2.10 × 10^−15, approximately 4.6 times the unstrained value, accompanied by a redshift suggesting strengthened interfacial mode coupling. Bilayer y-axis tension is the standout configuration: the normalized heat transfer coefficient rises from 0.65 under −4 percent compression to 1.31 at +2 percent, then leaps to 28.11 at +3 percent and 125.92 at +4 percent. The spectral peak under this configuration reaches 1.72 × 10^−13, roughly 220 times the unstrained state. The reason both sheets undergo similar y-axis tensile-strain-induced dielectric modulation, so the simultaneous enhancement of the low-frequency dielectric response at the two interfaces improves the matching of surface modes, thereby increasing the evanescent-wave transmission coefficient and producing a much higher spectral peak.

A third configuration—bilayer orthogonal strain, where one sheet is strained along the x-direction and the other along the y-direction at equal magnitude—produces an intermediate outcome. Under compression, the normalized coefficient fluctuates only slightly around unity, with a variation amplitude of approximately 0.08, indicating that strain modulation in orthogonal directions partially cancels out. Under large tensile strain, the coefficient climbs to 4.13 at +3 percent and 20.58 at +4 percent, with the spectral peak reaching 1.83 × 10^−14. The team attributes this enhancement primarily to the y-axis tensile layer, whose strengthened low-frequency dielectric response dominates the coupling within the heat-transfer band. However, because the x-strained layer’s dielectric response and surface-mode dispersion do not fully match those of the y-strained layer, the energy transmission coefficient is enhanced but falls short of the bilayer co-directional y-axis tensile level, demonstrating that the mismatch of strain-modified dielectric responses limits synergistic coupling between the two interfaces.

The strain range investigated here—±4 percent—was deliberately chosen to remain within the elastic deformation regime. Previous first-principles studies have shown that free-standing χ3 borophene possesses good dynamical and mechanical stability, with in-plane Young’s moduli of 180 to 210 newtons per meter along both lattice directions, and prior strain-engineering work suggests deformation up to roughly ±6 percent remains mechanically sustainable. All compressive strain cases converged successfully in geometry optimization without structural collapse or severe out-of-plane instability, lending confidence that the predicted enhancements are physically realizable rather than artifacts of an unstable model.

The implications reach well beyond borophene itself. Near-field radiative heat transfer already underpins emerging technologies including near-field thermophotovoltaics, thermal rectification, localized heat dissipation of nanostructures, and near-field thermal microscopy, and functional devices such as thermal switches, thermal diodes, and thermal transistors have enabled precise heat-flow management at the micro- and nanoscale. Previous strain-engineering efforts in two-dimensional materials—up to 73 percent modulation in black phosphorus and more than 60 percent reduction in thermal conductance in bilayer graphene—demonstrated the principle, but the order-of-magnitude switching behavior predicted here for borophene represents a substantial leap in modulation depth. The authors note that their work provides a theoretical basis for developing efficient thermal management devices based on borophene, and that carefully designing the direction and magnitude of strain enables precise control over near-field heat transport.

Caveats remain. The study is based on an ideal freestanding borophene model; in practical applications, substrates may alter the dielectric response and surface-mode dispersion, while defects, vacancies, and surface contamination may introduce additional scattering or damping. The mechanical and thermal stability of borophene under large tensile strain, as well as the experimental control of strain and nanoscale gaps, must be addressed in future work. Borophene was first synthesized on silver substrates in 2015, and its excellent electronic properties have already driven interest in metal-ion batteries, gas sensing, and micro/nanoelectronics; its outstanding optical properties enable near-field thermal radiation capability that surpasses conventional metals and metal oxides. If strain-tunable borophene devices can be fabricated with the precision the theory demands, the result could be a new class of nanoscale thermal switches in which a few percent of mechanical deformation flips heat flow by two orders of magnitude—a capability that would reshape how engineers manage heat in the smallest devices ever built.

Subject of Research: Strain-tunable near-field radiative heat transfer in borophene sheets

Article Title: Regulation of near-field radiative heat transfer between two-dimensional borophene sheets under uniaxial strain based on first-principles calculations

Article References: Huang, H., & Cheng, Q. (2026). Regulation of near-field radiative heat transfer between two-dimensional borophene sheets under uniaxial strain based on first-principles calculations. Frontiers in Thermal Engineering, 6, Article 1864229. https://doi.org/10.3389/fther.2026.1864229

Image Credits: AI Generated

DOI: 10.3389/fther.2026.1864229

Keywords: borophene, near-field radiative heat transfer, mechanical strain, first-principles calculations, thermal management, two-dimensional materials, Regulation, near-field, radiative, heat, transfer, between