Embed Size (px)
Citation preview
Low temperature Low temperature universality in disordered universality in disordered
solidssolids
In collaboration with: Philip Stamp (UBC)Alejandro Gaita-Arino (UBC)
Moshe Schechter
Gaita-Arino and MS, in preparation
MS and Stamp, arXiv:0910.1283
Low temperature Low temperature universality in disordered universality in disordered
solidssolids
In collaboration with: Philip Stamp (UBC)Alejandro Gaita-Arino (UBC)
Moshe Schechter
TCv 1
T 2
102/ 31 lQ
KTT U 3Below
Zeller and Pohl, PRB 4, 2029 (1971)
Pohl, Liu, Thompson, RMP 74, 991 (2002)
Low temperature Low temperature universality in disordered universality in disordered
solidssolids
In collaboration with: Philip Stamp (UBC)Alejandro Gaita-Arino (UBC)
Moshe Schechter
TCv 1
T 1
102/ 31 lQ
KTT U 3Below
Freeman and Anderson, PRB 34, 5684 (1971)
Standard tunneling modelStandard tunneling model
0
00 ),(
p
P
Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972)
Philips, J. Low Temp. Phys. 7, 351 (1972)
0
0
2
1
2-level systems
TCv 1
T 2
10/2 3 lQ
Below
TCv
T 20
constQ
KTT U 3
2/01 CQ
00 /1 C2
2
2
2
0 1.0
0 c
n
c
pC
Standard tunneling modelStandard tunneling model
0
00 ),(
p
P
Anderson, Halperin, Varma, Phil. Mag. 25, 1 (1972)
Philips, J. Low Temp. Phys. 7, 351 (1972)
0
0
2
1
2-level systems
TCv 1
T 2
10/2 3 lQ
Below
TCv
T 20
constQ
KTT U 3
2/01 CQ
00 /1 C2
2
2
2
0 1.0
0 c
n
c
pC
TLS in aging, 1/f noise, qubit decoherence
Standard tunneling modelStandard tunneling model
0
00 ),(
p
P
2
2
2
2
0 1.0
0 c
n
c
pC
0
0
2
1
2-level systems
TCv 1
T 2
102/ 31 lQ
Below
TCv
T 20
constQ 1
KTT U 3
2/01 CQ
00 /1 C
1. What is tunneling?
2. Why is universal and small?
3. What dictates the energy scale of ?
30 10
CKTU 3
4. Magnitude of specific heat, non-integer exponents
Theoretical modelsTheoretical models
Soft phononsSoft phonons Large scale behavior of renormalized interactionsLarge scale behavior of renormalized interactions Renormalized dipolar TLS-TLS interactionsRenormalized dipolar TLS-TLS interactions Frozen domains at the glass transitionFrozen 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, 195901 (2001)
Sethna and Chow, Phase Tans. 5, 317 (1985); Solf and Klein, PRB 49, 12703 (1994)
Parshin, Phys. Re. B 49, 9400 (1994)
Disordered lattices – KBr:CNDisordered 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 CN impurities in KBr:KCl mixed crystals – strain vs. crystals – strain vs.
interactionsinteractions
Universal characteristics down to low x.
Tunneling strength linear in x
Strain, and not TLS-TLS interactionsTopp and Pohl, PRB 66, 064204 (2002)
Watson, PRL 75, 1965 (1995)
2
2
0
0 c
pC
Amorphous vs. DisorderedAmorphous vs. Disordered
Ion implanted crystalline Silicon – amorphisity not important
Liu et al., PRL 81, 3171 (1998)
Tau and S TLSsTau and S TLSs
180 flips – tau excitations
Change of axis – S excitationsziSx
X
zixx
X
Weak linear Tau coupling to Weak linear Tau coupling to phononsphonons
x
XSH
i
ziw
zis
Weak linear Tau coupling to Weak linear Tau coupling to phononsphonons
x
XSH
i
ziw
zis
Weak linear Tau coupling to Weak linear Tau coupling to phononsphonons
x
XSH
i
ziw
zis
03.001.0
Cs
w
E
Eg
eV5 Cs E
eV1.0 Ew
~ deviations from inter-atomic distance
DFT calculation of weak and DFT calculation of weak and strong coupling constantsstrong 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
w
Effective TLS interactionsEffective TLS interactions
x
XSH
i
ziw
zis
ij
zj
ziij
zj
zi
Sij
zj
zi
SSijS JSJSSJH
K300030
2
2
0 JRc
J sSS
K10303
020 gJRc
J wsS
mK1000
230
2
2
0 JgRc
J w
GU TggTT 2int
2
2
2
2
0 1.00 c
n
c
pC
npp
P 1.0),( 00
00
1.01.0
2
2
c
ns
ssC
2
2
300
1
sS
c
RJn
ws
c
RgJn
2
300
1
32
2
101.01.01.0 g
c
n
s
wwC
Dipole gap – strength of the Dipole gap – strength of the weakweak
300
1
RgJn
gnRJns
300
0 1
0gJE
0JE
ij
zj
ziij
zj
zi
Sij
zj
zi
SSijS JSJSSJH
zj
j
Sij
zj
j
SSij
is JSJE
02
Sij
jiSS JEEE
ji
zi
iij
zi
i
Sij
j JSJE
Efros and Shklovskii, J Phys C 8, L49 (1975)
DOS of S-TLSDOS of S-TLS
)()()2()()( ssj
jsss EPEnUEEEnEnj
30
3
0
aR
JcJ
ij
SSijS
ij
1.0)(22 EPnnCC wssS K32.061 00 gJEEa
SummarySummary
- Universality and smallness of tunneling strength
- Tunneling states: inversion pairs. Intrinsically 2-level systems
- Below 3K – effectively noninteracting TLS!
1300
1 GTRgJn- Agreement with experiments: , mixed crystals
- Strain important, not glassiness or amorphous structure
- Accounts for energy scale of ~3K
- Above 3K – crossover to 1/ l
- At low energy tau TLSs dictate physics
Amorphous SolidsAmorphous Solids
Local order – small deviations from lattice, ~3% in 1st n.n. distance
Disorder contribution to 4/1 Rw and 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
ConclusionConclusion
Existence of inversion pairs give rise to the Existence of inversion pairs give rise to the universality and smallness of the tunneling universality and smallness of the tunneling strengthstrength
Explains well the various experimental resultsExplains well the various experimental results Future work: Future work:
Experimental and numerical verification in disordered Experimental and numerical verification in disordered solidssolids
Calculation of the specific heat and thermal conductivityCalculation 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 transitionRelation to glass transition Molecular resonancesMolecular resonances
