Abstract
Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect–phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. We find that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect–phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect–phonon coupling. This allows direct experimental determination of the defect–phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.
Highlights
The generic existence of tunneling two-level systems (TLSs) in disordered and amorphous systems has been postulated more than four decades ago [1, 2] to explain the low temperature universality in amorphous solids [3, 4, 5, 6, 7, 8, 9]
Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively
Since defect-phonon coupling in amorphous solids is expected to be an order of magnitude larger than in disordered crystals [57, 58, 59, 26], our results suggest that the tunneling amplitude of inversion asymmetric TLSs, such as in example C in Fig. 1 of Ref. [55] may be strongly diminished by defect-phonon tunneling, whereas the effect of defect-phonon interaction on the tunneling amplitude of inversion symmetric TLSs such as in examples A and B in Fig. 1 of Ref. [55] is negligible
Summary
The generic existence of tunneling two-level systems (TLSs) in disordered and amorphous systems has been postulated more than four decades ago [1, 2] to explain the low temperature universality in amorphous solids [3, 4, 5, 6, 7, 8, 9]. Strong defect phonon coupling provides an additional mechanism, through its symmetry dependent attenuation of the tunneling amplitude, for the preference of locally inversion symmetric two level systems as the entities constituting the low energy tunneling systems in disordered solids. In contrast to the two-state approximation we find that strong defect-phonon coupling does not suppress tunnelling It reduces the cubic symmetry of the defect effectively to inversion symmetric states, between which tunneling remains nearly unaffected by the interaction. Neglecting face and space diagonal tunnelling completely, the problem factorizes into three twolevel systems (TLS), one for each tunneling direction, [16, 22] with energy splitting ∆k This justifies two-state approximations for thermal and dielectric properties but not for the more complex acoustic response due to the tensor character of the elastic moment [23]. Elastic perturbations induce two types of transitions as indicated by the solid arrows in Fig. 1a, namely between ground and second excited and between first and third excited states, and between the degenerate states of the first excited states and between the degenerate states of the second excited states
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