Direction-Selective Anomalous Quantum Transport from Saddle-like Topological Surface States Coupled to an Electronic Instability in YbSb$_{2}$

We report direction-selective anomalous quantum transport in epitaxial YbSb$_{2}$ thin films associated with an interplay between anisotropic topological surface states and an electronic instability. Quantum oscillations reveal a quasi-two-dimensional orbit with a non-trivial Berry phase and Dirac-like dispersion, observable for current along the $a$-axis but absent along the orthogonal in-plane $c$-axis. Together with first-principles calculations, these observations support its assignment to a saddle-like topological surface state. Its oscillation amplitude exhibits a field-dependent, non-monotonic temperature evolution that departs from conventional Lifshitz-Kosevich behavior. Raman and coherent phonon spectroscopy reveal additional low-temperature modes consistent with a density-wave instability. Their pronounced polarization anisotropy and colossal field-induced Raman enhancement suggest a strongly anisotropic, field-enhanced electronic susceptibility associated with the density-wave modes. Our findings point to dynamical coupling between anisotropic topological surface states and a field-responsive density-wave instability as a route to direction-selective anomalous quantum transport.