Band-Selective Tunneling and Anisotropic Multiband Superconductivity in V₂Ga₅

Multiband superconductors with structural anisotropy offer a fertile ground for exploring unconventional quantum states, yet disentangling their directional pairing characteristics remains a formidable challenge. Here, we present a comprehensive thermodynamic and spectroscopic study of the tetragonal intermetallic superconductor $\text{V}_2\text{Ga}_5$ ($T_{\rm c} \approx 3.5$~K), combining first-principles electronic structure calculations with highly sensitive AC calorimetry and directional low-temperature scanning tunneling spectroscopy. By constructing a self-consistent, anisotropic multiband singlet $s$-wave pairing model within the fully symmetric $A_{1g}$ representation, we successfully reconcile the experimental specific heat and upper critical field anomalies. Crucially, we reveal that the apparent reversal of bulk gap hierarchies in directional tunneling experiments is a direct consequence of band-selective tunneling. This effect is governed by an elegant interplay between localized Fermi velocity 'hot spots' and specific Fermi surface topologies, rather than raw thermodynamic gap magnitudes alone. Our findings provide a clear microscopic picture of direction-dependent, band-selective tunneling in a highly uniaxial anisotropic superconductor, demonstrating how orientation-dependent transport constraints shape the observable signatures of multiband quantum condensates.