Atomic Tunneling Systems in Solids
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1 Atomic Tunneling Systems in Solids real crystals Christian Enss Kirchhoff-Institut of Physics Heidelberg University glasses
2 Tunneling of Atoms in Solids
3
4 KCl:Li Specific Heat specific heat roughly a factor of 10 higher at 0.5 K J.P. Harrison, Phys. Rev. 171, 1037 (1968)
5 Li-Tunneling Systems in KCl-Crystals Li + substitutes K + ionic radius: Li + 8 off-center positions in <111> direction K + Cl - (100)-plane
6 Quantum States of <111> Systems edge tunneling face diagonal tunneling room diagonal tunneling
7 Tunneling Systems with Cubic Symmetry <111> <100> <110> KCl:Li, KBr:CN KCl:OH, LiF:OH NaBr:F
8 Li-Tunneling Systems in KCl-Crystals Li + substitutes K + ionic radius: Li + 8 off-center positions in <111> direction tunnel splitting: K + Cl - (100)-plane with X. Wang, F. Bridges, Phys. Rev. B46, 5122 (1992)
9 Isotope effect Schottky-Anomaly number density J.P. Harrison, Phys. Rev. 171, 1037 (1968)
10 KCl:CN concentration dependence P.P. Peressini, J.P. Harrison, R.O. Pohl, Phys. Rev. 182, 939 (1969)
11 Thermal Conductivity NaF: OH - KCl:Li T.F. McNelly, Ph.D. thesis (Cornell University 1974) P.P. Peressini, J.P. Harrison, R.O. Pohl, Phys. Rev. 180, 926 (1969)
12 C. Enss, M. Gaukler, S. Hunklinger, M. Tornow, R. Weis, A. W ürger, Phys. Rev. B 53, (1996) Dielectric Susceptibility
13 Dielectric Susceptibity: High Concentrations C. Enss, M. Gaukler, S. Hunklinger, M. Tornow, R. Weis, A. Würger, Phys. Rev. B 53, (1996)
14 Interacting Tunneling Systems
15 Transition to Incoherent Tunneling defects in crystals: at high concentrations cross over to incoherent tunneling consequences: reduced resonant contribution new phononless relaxation channel incoherent tunneling in glasses at very low temperatures? A. Würger, R. Weis, M. Gaukler, C. Enss, Europhys. Lett. 33, 533 (1996)
16 Thermally Activated Pairs S. Ludwig, C. Enss, J. Low Temp. Phys. 137, 371 (2004)
17 Tunneling of Li Pairs
18 Coherent Properties coherent regime two-pulse polarization echoes: 1 GHz microwave cavity Rabi frequency 1 GHz 50 mk
19 Echo Theoretical Background I coherent regime: two level approximation: applied field: Schrödinger equation: mit ansatz: Rabi frequency:
20 Phase Jump Rotary Echoes coherent regime: applied field: occupation number difference periodic change of polarisation with
21 Phase Jump Rotary Echoes (KBr) 1-x (KCN) x (KBr) 0.95 (KCN) 0.05 many oscillations well defined W R fit: fixed values of E, p Lorentz distribution of D 0 width 10% G. Baier, M.v. Schickfus, C. Enss, Europhys. Lett. 8, 487 (1989)
22 Coherent Pair Tunneling Rabi-Frequency of NN2 pairs of different isotopes R. Weis, C. Enss, A. Würger, F. Lüty, Ann. Phys. 6, 263 (1956) only NN2 pairs contribute
23 Atomic Tunneling Systems in Amorphous Solids glasses
24 Structure of Crystalline and Amorphous Materials C B A Crystal Glass
25 Atomic Tunneling Systems in Glasses
26 Specific Heat broad distribution of low-energy excitations J.C. Lasjaunias, et al., Solid State Commun. 17, 1045 (1975)
27 Atomic Tunneling Systems in Glasses W.A. Phillips, J. Low. Temp. Phys. 7, 351 (1972) P.W. Anderson et al., Philos. Mag. 25, 1 (1972) energy splitting tunnel splitting distribution function elastic, dielectric und thermal properities
28 Thermal Properties in the Tunneling Modell Specific heat: Thermal Conductivity:
29 R. C. Zeller and R. O. Pohl. Phys. Rev. B 4, 2029 (1971) Specific Heat
30 Heat Release of Amorphous Solids M. Schwark, et al., J. Low Temp. Phys. 58, 171 (1985)
31 Thermal Conductivity strong coupling to phonons systems are localized R. C. Zeller and R. O. Pohl. Phys. Rev. B 4, 2029 (1971)
32 Thermal Conductivity strong coupling to phonons systems are localized H.-Y. Hao, et al., Rev. Sci. Instrum. 75, 2718 (2004)
33 Universality R. B. Stephens, Phys. Rev. B 8, 2896 (1973)
34 Elastic and Dielectric Properties resonant processes relaxational processes modulation of D T < 1 K one-phonon relaxation à wide distribution even for fixed E
35 Dielectric Susceptibility in the STM Resonant Part E 0 p E2 2 0 Relaxational Part E 2 E sech 2 2k B T 1 1+! E 0 p E2 2 0
36 Dielectric Constant and Dielectric Loss Dielectric constant: δε Dielectric loss: tan δ
37 Sound Velocity and Internal Friction
38 Elastic Measurements with Mechanical Oscillators SEM picture 1 µm silver film good thermalization laser-cut glass neck 2 cm torsion bending torsion
39 Sound Velocity discrepancy at low temperatures J. Classen, T. Burkert, C. Enss, S. Hunklinger Phys. Rev. Lett. 84, 2176 (2000)
40 Internal Friction T < 30 mk J. Classen, T. Burkert, C. Enss, S. Hunklinger Phys. Rev. Lett. 84, 2176 (2000) additional relaxation channel
41 Coherent Properties coherent regime two-pulse polarization echoes: 1 GHz microwave cavity Rabi frequency 1 GHz 50 mk
42 Echo Theoretical Background I coherent regime: two level approximation: applied field: Schrödinger equation: mit ansatz: Rabi frequency:
43 Echo Theoretical Background II polarisation vector: Bloch equations: t 1 energy relaxation T < 1 K one phonon prozess...? t 2 phase coherence time t 1 processes spectral diffusion spin diffusion...?
44 Two Pulse Echo polarization vector rotating frame
45 Echo Decay time window 1200 µs sensitivity: five orders of magnitude
46 Temperature Dependence
47 Spectral Diffusion short time limit (no flip limit): Gaussian decay long time limit (multiple flip limit): exponential decay
48 Temperature Dependence short time limit (no flip limit): long time limit (multiple flip limit): Theoretical papers: P. Hu, S.R. Hartmann, PRB 9, 1 (1974) J.L. Black, B.I. Halperin, PRB 16, 2879 (1976) P. Hu, L.R. Walker, PRB 18, 1300 (1978) R. Maynard, R. Rammal, R. Suchail, J. Phys. Paris Lett. 41, L-291 (1980) B.D. Laikhtman, PRB 31, 400 (1985) Yu.M. Galperin, V.L. Gurevich, D.A. Parshin, PRB 37, (1988)
49 Temperature Dependence A. L. Burin, J. M. Leveritt III, G. Ruyters, C. Schötz, M. Bazrafshan, P. Faßl, M. von Schickfus, A. Fleischmann, C. Enss, Europhys. Lett. 104, (2013)
50 Phase Jump Rotary Echoes coherent regime: applied field: occupation number difference periodic change of polarisation with
51 Phase Jump Rotary Echoes BK7: (SiO2, B2O3, NaO, CaO,... ) 1 GHz few oscillations broad distribution of W R Fit: tunneling model distribution uniform distribution fixed dipole moment C. Enss, R. Weis, S. Ludwig, S. Hunklinger, Czech. J. Phys. 46, 3287 (1996)
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