Transcript power point
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
Low temperature universality in disordered solids
Moshe Schechter In collaboration with: Philip Stamp (UBC) Alejandro Gaita-Arino (UBC) Below
T
T U
3
K C v
T
T
1 2
Q
1 / 2
l
10 3 Zeller and Pohl, PRB 4, 2029 (1971) Pohl, Liu, Thompson, RMP 74, 991 (2002)
Low temperature universality in disordered solids
Moshe Schechter In collaboration with: Philip Stamp (UBC) Alejandro Gaita-Arino (UBC) Below
T
T U
3
K C v
T
T
1 1
Q
1 / 2
l
10 3 Freeman and Anderson, PRB 34, 5684 (1971)
Standard tunneling model
2-level systems Below
T
T U
3
K
1 2 0 0
P
( , 0 )
p
0 0
C v
T
0
T
2
Q
const C v
T
T
1 2
Q
2
l
/ 10 3
C
0
p
0
c
2 2 0 .
1
n
c
2 2
Q
1
C
0 / 2 0 1 /
C
0 Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972) Philips, J. Low Temp. Phys. 7, 351 (1972)
Standard tunneling model
2-level systems Below
T
T U
3
K
1 2 0 0
P
( , 0 )
p
0 0
C v
T
0
T
2
Q
const C v
T
T
1 2
Q
2
l
/ 10 3
C
0
p
0
c
2 2 0 .
1
n
c
2 2
Q
1
C
0 / 2 0 1 /
C
0 TLS in aging, 1/f noise, qubit decoherence Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972) Philips, J. Low Temp. Phys. 7, 351 (1972)
Standard tunneling model
2-level systems Below
T
T U
3
K
1 2 0 0
P
( , 0 )
p
0 0
C v
T
0
T
2
Q
1
const C v
T
T
1 2
Q
1 / 2
l
10 3
C
0
p
0
c
2 2 0 .
1
n
c
2 2
Q
1
C
0 / 2 0 1 /
C
0 1. What is tunneling?
C
10
T U
3 4. Magnitude of specific heat, non-integer exponents
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) Lubchenko and Wolynes, Phys. Rev. Lett. 87, 195901 (2001) Sethna and Chow, Phase Tans. 5, 317 (1985); Solf and Klein, PRB 49, 12703 (1994)
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)
CN impurities in KBr:KCl mixed crystals – strain vs. interactions
C
0
p
0
c
2 2 Universal characteristics down to low x.
Tunneling strength linear in x Strain, and not TLS-TLS interactions Watson, PRL 75, 1965 (1995) Topp and Pohl, PRB 66, 064204 (2002)
Amorphous vs. Disordered
Ion implanted crystalline Silicon – amorphisity not important Liu et al., PRL 81, 3171 (1998)
Tau and S TLSs
Change of axis – S excitations 180 flips – tau excitations
X
x
S i z
X
x
x
i z
Weak linear Tau coupling to phonons
H
i
s S i z
w
i z
X
x
Weak linear Tau coupling to phonons
H
i
s S i z
w
i z
X
x
Weak linear Tau coupling to phonons
H
i
s S i z
w
i z
X
x
s
E C
5 eV
w
E
0 .
1 eV
g
w s
E
E C
0 .
01 0 .
03 ~ deviations from inter-atomic distance
DFT calculation of weak and strong coupling constants - Confirm theoretical prediction
w
in agreement with experiment: positive identification of TLSs, prediction for S-TLSs A. Gaita-Arino and M.S., in preparation
Effective TLS interactions
H
i
s
S i z
w
i z
X
x
H S
ij
J ij SS S i z S j z
J ij S
S i z
j z
J ij
i z
j z
J
0
SS
c
2
s
2
R
0 3
J
0 300 K
T
int
gT U
g
2
T G J
0
S
c s
2
w R
0 3
gJ
0 3 10 K
J
0
c
2
w
2
R
0 3
g
2
J
0 100 mK
C
0
p
0
c
2 2 0 .
1
n
c
2 2
P
( , 0 )
p
0 0
p
0 0 .
1
n C s
0 .
1
n s
c
2
s
2 0 .
1
n S
1
J
0
R
0 3
c
s
2 2
C
0 .
1
n
c
2
w
2 0 .
1
s w
0 .
1
g
10 3
n
1
gJ
0
R
0 3
s c
2
w
Dipole gap – strength of the weak
H S
ij
J ij SS S i z S j z
J ij S
S i z
j z
J ij
i z
j z
n
1
gJ
0
R
0 3
E
gJ
0
n s
0 1
J
0
R
0 3
gn
E
J
0
E s i
j J ij SS S j z
j J ij S
j z E
j
i J ij S
S i z
i J ij
i z E S i
j
E S i
E
j
2
J ij S
0 Efros and Shklovskii, J Phys C 8, L49 (1975)
J ij S
c ij S
R
3
ij J
0
S
a
3 0
DOS of S-TLS
n s
(
E
)
n s
(
E
)
j
(
E s
E
j
2
U j
)
n s
(
E
)
P
(
E s
)
C S
C
n s
s
2
n
w
2
P
(
E
) 0 .
1 1
a
0 6
E
0 .
2
E
gJ
0 3 K
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
l
/ 1 - Strain important, not glassiness or amorphous structure - Agreement with experiments:
n
1
gJ
0
R
0 3
T G
1 , mixed crystals
Amorphous Solids
Local order – small deviations from lattice, ~3% in 1 st n.n. distance Disorder contribution to
w
1 /
R
4 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)
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