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

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

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

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

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

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

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

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

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

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

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

Weak linear Tau coupling to phonons

~ deviations from inter-atomic distance

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

Effective TLS interactions

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

DOS of S-TLS

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

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

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