Atomic Tunneling Systems in Solids
Transcript of Atomic Tunneling Systems in Solids
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Atomic Tunneling Systems in Solids
real crystals
glassesChristian EnssKirchhoff-Institut of PhysicsHeidelberg University
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Tunneling of Atoms in Solids
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KCl:Li Specific Heat
specific heat roughly a
factor of 10 higher at 0.5 K
J.P. Harrison, Phys. Rev. 171, 1037 (1968)
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K+ Cl-
Li-Tunneling Systems in KCl-Crystals
Li+ substitutes K+
ionic radius:
8 off-center positionsin <<111111>> direction
(100)-plane
Li+
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Quantum States of <111> Systems
|111
|111
|111
|111
|111
|111
|111
|111
edge tunnelingface diagonal tunneling
room diagonal tunneling
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Tunneling Systems with Cubic Symmetry
<111> <100> <110>
KCl:Li, KBr:CN KCl:OH, LiF:OH NaBr:F
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K+ Cl-
Li-Tunneling Systems in KCl-Crystals
Li+ substitutes K+
ionic radius:
8 off-center positionsin <<111111>> direction
(100)-plane
Li+
tunnel splitting:
with
X. Wang, F. Bridges, Phys. Rev. B46, 5122 (1992)
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Isotope effect
Schottky-Anomaly
number density
J.P. Harrison, Phys. Rev. 171, 1037 (1968)
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KCl:CN
concentration dependence
P.P. Peressini, J.P. Harrison, R.O. Pohl, Phys. Rev. 182, 939 (1969)
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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)
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Dielectric Susceptibility
C. Enss, M. Gaukler, S. Hunklinger, M. Tornow, R. Weis, A. Wurger, Phys. Rev. B 53, 12094 (1996)
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Dielectric Susceptibity: High Concentrations
C. Enss, M. Gaukler, S. Hunklinger, M. Tornow, R. Weis, A. Würger, Phys. Rev. B 53, 12094 (1996)
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Interacting Tunneling Systems
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Transition to Incoherent Tunneling
defects in crystals: at high concentrations cross over to incoherent tunneling
consequences: reduced resonant contributionnew phononless relaxation channel
incoherent tunneling in glasses at very low temperatures?
A. Würger, R. Weis, M. Gaukler, C. Enss, Europhys. Lett. 33, 533 (1996)
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Thermally Activated Pairs
S. Ludwig, C. Enss, J. Low Temp. Phys. 137, 371 (2004)
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Tunneling of Li Pairs
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Coherent Properties
two-pulse polarization echoes:
microwave cavity
1 GHz
coherent regime
Rabi frequency1 GHz 50 mK
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Echo ―Theoretical Background I
coherent regime:
two level approximation:
applied field:
Schrödinger equation:
ansatz:
Rabi frequency:
mit
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Phase Jump Rotary Echoes
coherent regime:
applied field:
occupation number difference
periodic change of polarisation
with
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Phase Jump Rotary Echoes
(KBr)1-x(KCN)x
many oscillations well defined WR
fit: fixed values of E, pLorentz distribution of D0 width 10%
(KBr)0.95(KCN)0.05
G. Baier, M.v. Schickfus, C. Enss, Europhys. Lett. 8, 487 (1989)
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Coherent Pair Tunneling
only NN2 pairs contribute
Rabi-Frequency of NN2 pairs of different isotopes
R. Weis, C. Enss, A. Würger, F. Lüty, Ann. Phys. 6, 263 (1956)
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Atomic Tunneling Systems in Amorphous Solids
glasses
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Structure of Crystalline and Amorphous Materials
C
B
A
Crystal Glass
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Atomic Tunneling Systems in Glasses
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Specific Heat
broad distribution oflow-energy excitations
J.C. Lasjaunias, et al., Solid State Commun. 17, 1045 (1975)
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Atomic Tunneling Systems in Glasses
energy splitting
distribution function
tunnel splitting
elastic, dielectric und thermalproperities
W.A. Phillips, J. Low. Temp. Phys. 7, 351 (1972)P.W. Anderson et al., Philos. Mag. 25, 1 (1972)
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Thermal Properties in the Tunneling Modell
Specific heat:
Thermal Conductivity:
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Specific Heat
R. C. Zeller and R. O. Pohl. Phys. Rev. B 4, 2029 (1971)
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Heat Release of Amorphous Solids
M. Schwark, et al., J. Low Temp. Phys. 58,171 (1985)
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Thermal Conductivity
strong coupling to phonons
systems are localized
R. C. Zeller and R. O. Pohl. Phys. Rev. B 4, 2029 (1971)
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Thermal Conductivity
strong coupling to phonons
systems are localized
H.-Y. Hao, et al., Rev. Sci. Instrum. 75, 2718 (2004)
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Universality
R. B. Stephens, Phys. Rev. B 8, 2896 (1973)
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Elastic and Dielectric Properties
resonant processes
relaxational processes
modulation of D
T << 1 K one-phonon relaxation à wide distribution even for fixed E
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Dielectric Susceptibility in the STM
E
0
pE2 −2
0
E
0
pE2 −2
0
✓1− 2
0
E2
◆sech2
✓E
2kB
T
◆1
1 + !2⌧21
Relaxational Part
Resonant Part
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Dielectric constant: δε
Dielectric loss: tan δ
Dielectric Constant and Dielectric Loss
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Sound Velocity and Internal Friction
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2 cm
torsion bending torsion
1 µm silver film
SEM picture
good thermalization
laser-cut glassneck
Elastic Measurements with Mechanical Oscillators
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Sound Velocity
discrepancy at low temperatures
J. Classen, T. Burkert, C. Enss, S. HunklingerPhys. Rev. Lett. 84, 2176 (2000)
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Internal Friction
T < 30 mK
additional relaxation channelJ. Classen, T. Burkert, C. Enss, S. HunklingerPhys. Rev. Lett. 84, 2176 (2000)
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Coherent Properties
two-pulse polarization echoes:
microwave cavity
1 GHz
coherent regime
Rabi frequency1 GHz 50 mK
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Echo ―Theoretical Background I
coherent regime:
two level approximation:
applied field:
Schrödinger equation:
ansatz:
Rabi frequency:
mit
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Echo ―Theoretical Background II
Bloch equations:
t1 energy relaxation
t2 phase coherence time t1 processesspectral diffusionspin diffusion
T < 1 K one phonon prozess
..... ?
..... ?
polarisation vector:
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Two Pulse Echo
polarization vector
rotating frame
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Echo Decay
time window 1200 µs
sensitivity: five orders of magnitude
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Temperature Dependence
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Spectral Diffusion
short time limit (no flip limit):
Gaussian decay
long time limit (multiple flip limit):
exponential decay
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Temperature Dependence
short time limit (no flip limit):
long time limit (multiple flip limit):
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, 10339 (1988)
Theoretical papers:
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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, 57006 (2013)
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Phase Jump Rotary Echoes
coherent regime:
applied field:
occupation number difference
periodic change of polarisation
with
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Phase Jump Rotary Echoes
BK7: (SiO2, B2O3, NaO, CaO, ... )
1 GHz
few oscillations broad distribution of WR
Fit: tunneling model distributionuniform distributionfixed dipole moment
C. Enss, R. Weis, S. Ludwig, S. Hunklinger,Czech. J. Phys. 46, 3287 (1996)