Glass and possible non supersolid origin of TO anomaly

1
Glass and possible non supersolid origin of TO
anomaly

• E. Abrahams (Rutgers)
• M. Graf, Z. Nussinov, S. Trugman,
• AVB (Los Alamos),

• Thermodynamic considerations
• Counting number of states across a phase
  transition.
• Counting frozen-in states of a glass.
• 2. Torsional oscillator considerations
• Causality links dissipation and period.
• How to get a peak in dissipation and drop in
  period?
• 3. Outlines of the effects of disorder (3He) on
  supersolid

2
Conclusion

• Disorder and Glassiness (due to dislocations?)
  are the key to TO and solid He 4 anomalies seen.
• We developed a glass theory that
• A) allows to FIT the TO anomalies
• B) takes into account the thermodynamic features
  seen so far.
• Anomalous state, often called Supersolid state
  can benefit from lighter atoms if they attract
  vacancies.
• Effect of 3He is not a benign add on. It is HUGE,
  organic and highly unexpected for a phase
  fluctuation driven superstate.

3
experiments

• TO Chan et al., Reppy et al, Shirahama et al,
  Kubota et al
• Specific heat experiments
• Effects of 3He.
• .No direct evidence of superflow, or any flow
  (Beamish).

HUGE effect!
dTc 300 mk 10 ppm
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Articles
1 AVB and E. Abrahams, Effect of impurities on
supersolid condensate a Ginzburg-Landau
approachJ.of Superconducticity and Novel
Magnetism, 19, cond-mat/0602530 Outlines of the
effects of disorder (3He) on supersolid 2.
Thermodynamic considerations, AVB, M. Graf, Z.
Nussinov, and S. A. Trugman, PRB 75, 094201
(2007) cond-mat/0606203 Entropy of solid He4
the possible role of a dislocation glass
Counting number of states across a phase
transition.Counting frozen-in states of a
glass. 3. Z. Nussinov, AVB, M. J. Graf, and S. A
.Trugman On the origin of the decrease in the
torsional oscillator period of solid He4 PRB
(2007) in print cond-mat/0610743 Glass and
possible non supersolid origin of torsional
oscillator anomaly Causality links dissipation
and period.How to get a peak in dissipation and
drop in period?
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Thermodynamics and oscillator dynamics of
glasses application to supersolids

• 1. Hypothesis normal glass (due to
  dislocations?) responsible
• for most of the features
• Torsional oscillator considerations
• Causality links dissipation and period.
• How to get a peak in dissipation and drop in
  period?
• 3. Counting number of states across a phase
  transition.
• Counting frozen-in states of a glass.
• 4. Enormous effect of 3He on glass state.

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TO anomaly, not supersolid
Oscillation period Is all that is observed
Change in damping ?(T) also causes change in
period . Does not require NCRI to explain the
effect. 4He Glass freezout below 100mK
7
Simple table top analogy
Spinning an egg apply external torque (spin)
from time and
then let go
Hard boiled egg (more solid like- analogue of
proposed glass at low T) fast rotation, low
dissipation
Soft boiled egg (more liquid like- analogue of
system far above the glass transition
temperature) low rotational frequency, high
dissipation
If the egg were an ideal rigid solid and no
spurious effects were present final angular
rotation speed
On its own, the change in rotational speed here
can also be interpreted in terms of an effective
missing moment of inertia in the hard boiled egg
relative to that of the soft boiled egg.
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The torsional oscillator
Q What is a torsional oscillator? A Oscillator
coupled system of pressure cell
something. Q What does torsional oscillator
experiment report? A Linear response function of
coupled system.
Rittner and Reppy, PRL 2006. Did you notice BeCu?
See Todoshchenkos pressure gauge glitch,
cond-mat/0703743!
Nussinov et al., cond-mat/0610743
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General idea
Balatsky et al., PRB 75, 094201 (2007) Nussinov
et al., cond-mat/0610743
Any transition of a liquid-like component into a
glass (whether classical or an exotic quantum
superglass) will lead to such an angular
response function. We argued it could be
dislocation induced. In any system, the real and
imaginary parts of the poles of the angular
response function dictate the period
and dissipation. The divergent equilibration
time in the glass will lead to a larger real
part of the poles of and thus a
faster rotation of the oscillator. This occurs
regardless of any possible tiny supersolid
fraction ( see our bounds from the specific heat
measurements). Possible connection to vortex
and/or glass( Anderson, Huse, Philips, et al).
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Simplifying limiting form (activated dynamics
with no distribution of relaxation times)
To avoid the use of too many parameters in any
fit, we focus on the simplest- and unphysical-
limit of a real glass that of vanishing
transition temperature (activated dynamics) with
no distribution of relaxation times.
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Period and dissipation for simplistic model
activated dynamics
Period
Dissipation
Resonant oscillator frequency in low temperature
limit
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Deviations from undistributed activated
dynamicsthe real glass
The deviation from the semi-circle (? 1)
show There is a substantial distribution of
relaxation times As in a real glass. Initial
analysis of new data shows That the To is of the
order of 100mK.
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Dissipation and period of torsional oscillator
Single mode glass model for pressure cell glass
system.
The deviation from the semi-circle (? 1)
show There is a substantial distribution of
relaxation times As in a real glass. Initial
analysis of new data shows That the To is of the
order of 100mK.
Rittner and Reppy, PRL 97, 165301 (2006) Nussinov
et al., cond-mat/0610743, PRB to be publ
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Cole Davison plot
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TgtgtTo, T ltltTo
Period goes down on cooling
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Fitting double oscillator experiments (Kojima et
al)
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Fitting empty cell?
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Fitting filled cell with the same parameters for
both frequencies
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Phase transition and entropy

• Entropy measures number of states.
• States are redistributed near 2nd order phase
  transition, even if there is no singularity in C.
• BEC (Bose-Einstein Condensation) phase transition

Balatsky et al., PRB 75, 094201 (2007)
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Low temperature normal glass

• Two-Level-System (TS) glass model (tunneling)
• Anderson, Halperin, Varma (1972), Phillips
  (1972) .
• TS leads to linear specific heat at low
  temperatures!
• Perfect Debye crystal has cubic specific heat at
  low temperatures.
• TS (e.g., dislocation glass)

A is with 3He, B is set by Debye
temperature
A term is always present (dislocations) but grows
with 3He 4He is a glass even without 3He.
Balatsky et al., PRB 75, 094201 (2007)
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Compare with recent data by Chan
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Excess specific heat (30 ppm)

• System 4He w/30 ppm 3He.
• Debye cubic term at high temperatures, 0.15 K lt
  T lt 0.6 K ?D/50.
• Glass Debye linear cubic term at low
  temperatures, T lt 0.15 K.

Clark and Chan, JLTP 138, 853 (2005) Balatsky et
al., PRB 75, 094201 (2007)
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Excess specific heat (760 ppm)

• System 4He w/760 ppm 3He.
• Linear cubic term in C at lowest temperatures!
• Linear term increases with 3He concentration.

Clark and Chan, JLTP 138, 853 (2005) Balatsky et
al., PRB 75, 094201 (2007)
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Excess entropy (30 ppm)?

BEC DS 5 R 41.6 J/(K mol) at TTc0.16 K
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Excess entropy (760 ppm)?

BEC DS 5 R 41.6 J/(K mol) at TTc0.16 K.
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Boson peak in glasses
We expect similar fit to work For 4He solids.
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Is there a linear term in specific heat due to
glass?
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Effects of 3He impurities on SS

• 3He requires more elbow space in 4He matrix for
  zero point motion
• It is an attractive site for vacancies
• Increases Tc in GL?!
• Illustrated in WF approach

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3He has larger zero point motion amplitude
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Not a random mass term
HUGE effect!
dTc 300 mk 10 ppm
Anti Anderson theorem
Contrast to SC case and Anderson Theorem ( no Tc
enhancement)
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Numbers

• Stiffness goes down but by a more modest amount

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Comparison with experiments

• Tc will go up but not as much as
• what is measured by Chan et al. Effect of 3He is
  to enormoulsy increase TO feature, much more
  then dirt add on to specific heat.
• Problem for any phase fluctuation picture Tc is
  set by ?s. Tc goes up, ?s goes down with 3He.

HUGE effect!
dTc 300 mk 10 ppm
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Compare to effect of disorderin conventional SC
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TEST YOUR NCRI
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What is working and where are problems for a
normal glass?

• working
• fits to specific heat
• Fits to torsional oscillator ( the only ones so
  far)
• Annealing effect in some samples.
• No mass superflow in Beamish expts.
• Huge sensitivity to 3He effects.
• Not working(?)
• Blocking annulus glass state in blocked and non
  blocked expts are different, need better
  characterization. Remains to be seen how
  reproducible it is and if blocking changes
  stiffness dramatically for the same sample
  quality.
• NCRIF as a function of rim velocity.
  Demonstrated to be not a general fact(new Chan
  data, Reppy data).

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Conclusion

• Disorder and Glassiness (due to dislocations?)
  are the key to TO and solid He 4 anomalies seen.
• We developed a glass theory that
• A) allows to FIT the TO anomalies
• B) takes into account the thermodynamic features
  seen so far.
• Anomalous state, often called Supersolid state
  can benefit from lighter atoms if they attract
  vacancies.
• Effect of 3He is not a benign add on. It is HUGE,
  organic and highly unexpected for a phase
  fluctuation driven superstate.

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Rim velocity dependence
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