Nonhomogeneity of the density of states of tunneling two-level systems at low energies

Amorphous solids, and many disordered lattices, exhibit a remarkable qualitative and quantitative universality in their acoustic properties at temperature less than or similar to 3 K. This phenomenon is attributed to the existence of tunneling two-level systems (TTLSs), characterized by a homogeneous density of states (DOS) at energies much lower than the disorder energy (approximate to 0.1 eV). Here we calculate numerically, from first principles, the DOS of KBr:CN glass, the archetypal disordered lattice showing universality. In contrast to the standard tunneling model, we find that the DOS diminishes abruptly at approximate to 3 K, and that tunneling states differ essentially by their symmetry under inversion. This structure of the TTLSs dictates the low temperature below which universality is observed, and the quantitative universality of the acoustic properties in glasses. Consequences to the properties of glasses at intermediate temperatures, as well as to the microscopic structure of amorphous solids, are discussed.