Lattice thermal conductivity of MgB2: Scattering physics and design strategies for quantum-enabling superconducting systems

Thermal transport in superconducting materials is a crucial parameter that strongly influences the reliability and performance of cryogenic platforms employed in quantum spaces and superconducting technologies. Here, we use a modified Callaway-type phonon transport model that accounts for interacting scattering mechanisms with frequency-dependent phonon linewidths to study the lattice thermal conductivity of magnesium diboride (MgB 2 ). The present formulation—as opposed to conventional formulations based on Matthiessen's rule—allows a unified treatment of boundary, dislocation, point-defect, normal phonon, Umklapp, and interference scattering processes. This work examines the lattice thermal conductivity and phonon-mediated heat transfer in MgB 2 . Although MgB 2 is an established superconductor, this research does not simulate superconductivity from an electronic perspective; rather, it addresses thermal issues related to superconductivity and quantum devices at cryogenic temperatures. Numerical simulations were conducted across the superconducting and normal temperature regimes and compared with experimentally reported thermal-conductivity data for single-crystalline MgB 2 . Remarkably, it successfully captures the nuclear response to thermally populated phonons in both cases across a broad range of temperatures, with a distinct characteristic temperature dependence of thermal conductivity: a low-temperature increase, a peak near the superconducting transition region, and high-temperature suppression via anharmonic phonon interactions. This bodes well, as analysis of the relaxation spectra identifies temperature-dependent transport regimes in which distinct scattering processes limit phonon transport. The cryogenic regime is dominated by boundary and defect scattering; impurity scattering becomes important at intermediate temperatures, and phonon-phonon Umklapp scattering dominates at high temperatures. The results provide quantitative structure-scattering-property relationships between microstructure parameters — grain size, defect density, and lattice disorder — and thermal transport behavior. The results are highly practical for designing application-specific thermal conductivity of superconductor materials and reveal MgB 2 as a model, easily tunable platform for cryogenic electronics and quantum-enabled superconducting systems.