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Determine the thermodynamic nature of the specific-heat transition in CNT@ZSM-5

Determine whether the specific-heat anomaly at approximately 233–236 K in boron-doped ultrathin carbon nanotube networks embedded in ZSM-5 zeolite (CNT@ZSM-5) represents a BCS mean-field second-order phase transition with a finite jump in specific heat or a fluctuation-dominated lambda transition characteristic of 3D-XY universality, by resolving the transition shape under zero and finite magnetic fields.

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Background

The authors measure C/T for CNT@ZSM-5 and observe a small anomaly at 233–236 K whose shape broadens under magnetic field, reminiscent of fluctuation-dominated transitions in cuprates. However, the available resolution and the broad feature prevent a definitive identification of the transition type.

Clarifying whether the anomaly is a mean-field BCS jump or a lambda-type transition would establish the role of phase fluctuations and dimensionality in this 3D network of ultrathin CNTs, directly informing the superconducting phase diagram and critical behavior of the material.

References

The width of this feature does not allow us to determine whether it represents the typical BCS mean-field type phase transition, characterized by a jump in specific heat, or the diverging lambda transition typical of cuprate superconductors, where 3D-XY phase fluctuations dominate the transition shape [36,37].

— High temperature superconductivity with giant pressure effect in 3D networks of boron doped ultra-thin carbon nanotubes in the pores of ZSM-5 zeolite (2509.19255 - Wang et al., 23 Sep 2025) in Main — Specific heat section (Fig. 2c)