TWO-LEVEL SYSTEMS AND THE MICROSCOPIC STRUCTURE OF AMORPHOUS SOLIDS

Amorphous solids show remarkable universality at temperatures below 1-3 K. Unlike insulating lattices, the specific heat of amorphous solids is linear in temperature, their thermal conductivity is quadratic in temperature, and their internal friction is temperature independent. Furthermore, very different amorphous solids, disordered lattices, amorphous polymers and quasicrystals, show quantitative universality in their values of thermal conductivity and internal friction at low temperatures. In what is named the "standard tunnelling model" (STM), it was suggested that microscopic tunnelling two-level systems (TLSs) which are weakly interacting with the strain give rise to the above phenomena. The STM has proven extremely successful, and TLSs are generally accepted as the dominant degrees of freedom in amorphous solids at low energies, dominating phenomena including 1/f noise, slow relaxation, conductance fluctuations in nano-devices, and decoherence in superconducting qubits, nano-mechanical oscillators, and superconducting micro-resonators. Yet, the reason for quantitative universality, as well as the microscopic nature of TLSs, is not well understood. Based on the microscopic properties of the group of disordered lattices showing universality, we have recently introduced a model which includes two types of TLSs, differing by their local symmetry under inversion, and consequently by their strength of interaction with the strain. All aspects of the model were thoroughly validated for the disordered lattices. In this talk I will discuss the model in view of recent results in superconducting qubits and micro-resonators, its general applicability to amorphous solids, and what we can learn from it about the microscopic structure of amorphous solids.