Low temperature universality in disordered solids

1. Low temperature universality in disordered solids Moshe Schechter In collaboration with: Philip Stamp (UBC) Alejandro Gaita-Arino (UBC) MS and Stamp, arXiv:0910.1283 Gaita-Arino and MS, in preparation

2. Low temperature universality in disordered solids Moshe Schechter In collaboration with: Philip Stamp (UBC) Alejandro Gaita-Arino (UBC) Below Zeller and Pohl, PRB 4, 2029 (1971) Pohl, Liu, Thompson, RMP 74, 991 (2002)

3. Low temperature universality in disordered solids Moshe Schechter In collaboration with: Philip Stamp (UBC) Alejandro Gaita-Arino (UBC) Below Freeman and Anderson, PRB 34, 5684 (1971)

4. Standard tunneling model 2-level systems Below Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972) Philips, J. Low Temp. Phys. 7, 351 (1972)

5. Standard tunneling model 2-level systems Below TLS in aging, 1/f noise, qubit decoherence Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972) Philips, J. Low Temp. Phys. 7, 351 (1972)

6. Standard tunneling model 2-level systems Below 1. What is tunneling? 2. Why is universal and small? 3. What dictates the energy scale of ? 4. Magnitude of specific heat, non-integer exponents

7. Theoretical models • Soft phonons • Large scale behavior of renormalized interactions • Renormalized dipolar TLS-TLS interactions • Frozen domains at the glass transition • Ad-hoc models for specific systems (KBr:CN) Parshin, Phys. Re. B 49, 9400 (1994) Leggett, Physica B: Cond. Matt. 169, 332 (1991) Burin, J. Low. Temp. Phys. 100, 309 (1995) Lubchenkoand Wolynes, Phys. Rev. Lett. 87, 195901 (2001) Sethna and Chow, Phase Tans. 5, 317 (1985); Solf and Klein, PRB 49, 12703 (1994)

8. Disordered lattices – KBr:CN 20% < x < 70% : Universal characteristics 70% CN – ferroelectric phase – glassiness not important De Yoreo, Knaak, Meissner, Pohl, PRB 34, 8828 (1986)

9. CN impurities in KBr:KCl mixed crystals – strain vs. interactions Universal characteristics down to low x. Tunneling strength linear in x Watson, PRL 75, 1965 (1995) Topp and Pohl, PRB 66, 064204 (2002) Strain, and not TLS-TLS interactions

10. Amorphous vs. Disordered Ion implanted crystalline Silicon – amorphisity not important Liu et al., PRL 81, 3171 (1998)

11. Tau and S TLSs Change of axis – S excitations 180 flips – tau excitations

12. Weak linear Tau coupling to phonons

13. Weak linear Tau coupling to phonons

14. Weak linear Tau coupling to phonons ~ deviations from inter-atomic distance

15. DFT calculation of weak and strong coupling constants - Confirm theoretical prediction - in agreement with experiment: positive identification of TLSs, prediction for S-TLSs A. Gaita-Arino and M.S., in preparation

16. Effective TLS interactions

17. Dipole gap – strength of the weak Efros and Shklovskii, J Phys C 8, L49 (1975)

18. DOS of S-TLS

19. Summary - At low energy tau TLSs dictate physics - Universality and smallness of tunneling strength - Tunneling states: inversion pairs. Intrinsically 2-level systems - Accounts for energy scale of ~3K - Below 3K – effectively noninteracting TLS! - Above 3K – crossover to - Strain important, not glassiness or amorphous structure , mixed crystals - Agreement with experiments:

20. Amorphous Solids Local order – small deviations from lattice, ~3% in 1st n.n. distance Disorder contribution to and random Utmost experimental / numerical test: finding that low T TLSs are inversion pairs easier experimental test: Existence of S TLSs, with strong phonon interaction and gapped DOS (phonon echo)

21. Conclusion • Existence of inversion pairs give rise to the universality and smallness of the tunneling strength • Explains well the various experimental results • Future work: • Experimental and numerical verification in disordered solids • Calculation of the specific heat and thermal conductivity • Extension to amorphous solids • TLS in 1/f noise and qubit decoherence • Relation to glass transition • Molecular resonances