Glass and possible non supersolid origin of TO anomaly

E. Abrahams (Rutgers)

M. Graf, Z. Nussinov, S. Trugman,

AVB (Los Alamos),

1. 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”

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.

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).

dTc ~ 300 mk10 ppm

HUGE effect!

Articles

1 AVB and E. Abrahams, “Effect of impurities on supersolid condensate: a Ginzburg-Landau approach”J.of Superconducticity and Novel Magnetism, 19, cond-mat/0602530Outlines 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/0610743Glass and possible non supersolid origin of torsional oscillator anomalyCausality links dissipation and period.How to get a peak in dissipation and drop in period?

Thermodynamics and oscillator dynamics of glasses application to “supersolids”

1. Hypothesis: normal glass (due to dislocations?) responsible• for most of the features2. 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.

TO anomaly, not supersolid2

( )( ) ~

4 ( ) ( )

I TT

I T T

Oscillation periodIs all that is observed

Change in I(T) leads to NCRI Change in damping (T) also causes change in period . Does not require NCRI to explain the effect.4He Glass: freezout below 100mK

Simple table top analogy

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

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.

Spinning an egg: apply external torque (spin) from time and then let go

d

dt final

ext ( t )

Iefftinitial

t final

d t

tinitial t t final

If the egg were an ideal rigid solid and no spurious effects were present: final angular rotation speed

The torsional oscillator

Nussinov et al., cond-mat/0610743

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.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Rittner and Reppy, PRL 2006.Did you notice BeCu? See Todoshchenko’s pressure gauge glitch, cond-mat/0703743!

[Ioscd2

dt2

d

dt ] ext (t) %g(t, t ;T )( t )d t

(t) d t (t, t )ext ( t ) ( ) ( )ext ( )

1 0 1 ggl ,0

1 [ i Ieff2 ]

ggl g0[1 is] , s(T ) s0eDT0 /(T T0 )

General idea

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).

( ,T )

( ,T )

Balatsky et al., PRB 75, 094201 (2007)Nussinov et al., cond-mat/0610743

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.

s(T ) so exp[kBT

]

(T0 0)

g g0

1 is( 1)

Period and dissipation for simplistic model: activated

dynamics

Q 1 1

Ieff

g0s

1 (0s)2

P 2

0 y

y g0

2Ieff0

1

1 (0s)2

0 Resonant oscillator frequency in low temperature limit

Period:

Dissipation:

Deviations from undistributed activated dynamics:

the real glass

The deviation from the semi-circle ( =1) showThere is a substantial distribution of relaxation timesAs in a real glass. Initial analysis of new data showsThat the To is of the order of 100mK.

Dissipation and period of torsional oscillator

Rittner and Reppy, PRL 97, 165301 (2006)Nussinov et al., cond-mat/0610743, PRB to be publ

Single mode glass model for pressure cell & glass system.

The deviation from the semi-circle ( =1) showThere is a substantial distribution of relaxation timesAs in a real glass. Initial analysis of new data shows

That the To is of the order of 100mK.

Cole Davison plot

1/(1 ( ))

" ~ sin( ), ' ~ cos( ),

" ' an arc

semicircle only for = 1

i s T

s

vs

T>>To, T <<To2

2

2

0

(1 ( ))

0

( ) 0

~

HeI C g

g go i s T

T T

I C go

I

C go

2

2

2

0

(1 ( ))

0

0

~

HeI C g

g go i s T

T T

I C

I

C

Period goes down on cooling

Fitting double oscillator experiments (Kojima et al)

Fitting empty cell:?

Fitting filled cell with the same parameters for both frequencies

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)

C(T ) 15

4

(5 / 2)

(3 / 2)RT

Tc

3/2

SBEC (Tc ) 5R

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):

Balatsky et al., PRB 75, 094201 (2007)

P(E) P0dE

CTS (E,T ) kB(E

kBT)2 eE /(kBT )

(1 eE /(kBT ))2

CTS (T ) dECTS (E,T )P(E)

0

2

6kB

2P0T

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.

Compare with recent data by Chan

Excess specific heat (30 ppm)

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

Clark and Chan, JLTP 138, 853 (2005)Balatsky et al., PRB 75, 094201 (2007)

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)

Excess entropy (30 ppm)?

BEC: S = 5 R = 41.6 J/(K mol) at T=Tc~0.16 K

Excess entropy (760 ppm)?

BEC: S = 5 R = 41.6 J/(K mol) at T=Tc~0.16 K.

Boson peak in glasses

We expect similar fit to workFor 4He solids.

Is there a linear term in specific heat due to glass?

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

3He has larger zero point motion amplitude

Zero point motion amplitude

Pushes 4He asideLess of n_b = more of n_v

Take Is local 3He density is an attractive region for vacancy

Potential that is repulsive for bosons is attractive for vacancies

Not a random mass term

Contrast to SC case and Anderson Theorem ( no Tc enhancement)

Anti Anderson theorem

dTc ~ 300 mk10 ppm

HUGE effect!

Numbers

• Stiffness goes down but by a more modest amount

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.

dTc ~ 300 mk10 ppm

HUGE effect!

Compare to effect of disorderin conventional SC

Huge slopeAnd opposite sign!

3He has highly nontrivial effecton SS state. Not a simple add on!

TESTYOURNCRI

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).

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.

Rim velocity dependence