Kondo insulators and in particular their non-cubic representatives have remained poorly understood. Here we report on the development of an anisotropic energy pseudogap in the tetragonal compound CeRu4Sn6 employing optical reflectivity measurements in broad frequency and temperature ranges, and local density approximation plus dynamical mean field theory calculations. The calculations provide evidence for a Kondo insulator-like response within the a − a plane and a more metallic response along the c axis and qualitatively reproduce the experimental observations, helping to identify their origin.Correlated materials with gapped or pseudo-gapped ground states continue to be of great interest. The gap in the electronic density of states (DOS) either opens gradually with decreasing temperature, as the pseudogap of high-temperature superconductors [1], or emerges at a continuous or first order phase transition [2][3][4]. In heavy fermion compounds [5] -systems in which f and conduction electrons strongly interact -a narrow hybridization gap is known to emerge gradually [6][7][8][9]. Generically, the Fermi energy is situated in one of the hybridized bands and a metallic heavy fermion ground state arises. Only for special cases the Fermi energy lies within the gap and the ground state is Kondo insulating. Metallic heavy fermion systems have been intensively investigated over the past decades and are now, at least away from quantum criticality [10], well understood [11] within the framework of Landau Fermi liquid theory. Hence, a very few parameters, most notably the effective mass, allow us to describe thermodynamic and transport properties at the lowest temperatures. In comparison, the physics of Kondo insulators has proven to be much less tractable. This is at least in part due to the fact that the gapped ground state inhibits a characterization via the above properties. Many experimental efforts have therefore focussed on the determination of the gap width from temperature dependencies, which has frequently led to conflicting results, in particular for anisotropic Kondo insulators such as CeNiSn [12]. Here the strongly anisotropic transport and magnetic properties have been interpreted phenomenologically on the basis of a V-shaped DOS [13] or by invoking a hybridization gap with nodes [14][15][16] or extrinsic effects such as impurities, off stoichiometry or strain [17,18]. To advance the field it appears mandatory to model a number of carefully chosen materials ab initio, taking all essential ingredients into account.Here we investigate a new material, CeRu 4 Sn 6 , which due to its tetragonal crystal structure is simpler than the previously studied orthorhombic materials. In a combined experimental and theoretical effort we provide direct spectroscopic evidence for the development of an anisotropic pseudogap: While weak metallicity prevails in the optical conductivity along the c axis, insulatorlike behavior without a Drude peak is observed in the a − a plane. We trace this back to a correlated band structure whic...