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 mk 10 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/ Outlines of the effects of disorder (3He) on “supersolid” 2. Thermodynamic considerations, AVB, M. Graf, Z. Nussinov, and S. A. Trugman, PRB 75, (2007); cond-mat/ “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/ 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?

Thermodynamics and oscillator dynamics of glasses application to “supersolids” 1. Hypothesis: normal glass (due to dislocations?) responsible for most of the features 2.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 supersolid Oscillation period Is 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 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/ 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 Did you notice BeCu? See Todoshchenko’s pressure gauge glitch, cond-mat/ !

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

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.

Period and dissipation for simplistic model: activated dynamics Resonant oscillator frequency in low temperature limit Period: Dissipation:

Deviations from undistributed activated dynamics: the 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.

Dissipation and period of torsional oscillator Rittner and Reppy, PRL 97, (2006) Nussinov et al., cond-mat/ , PRB to be publ 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.

Cole Davison plot

T>>To, T <<To 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 2 nd order phase transition, even if there is no singularity in C. BEC (Bose-Einstein Condensation) phase transition Balatsky et al., PRB 75, (2007)

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, (2007) 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: 4 He w/30 ppm 3 He. 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, (2007)

Excess specific heat (760 ppm) System: 4 He w/760 ppm 3 He. Linear + cubic term in C at lowest temperatures! Linear term increases with 3 He concentration. Clark and Chan, JLTP 138, 853 (2005) Balatsky et al., PRB 75, (2007)

Excess entropy (30 ppm)? BEC:  S = 5 R = 41.6 J/(K mol) at T=T c ~0.16 K

Excess entropy (760 ppm)? BEC:  S = 5 R = 41.6 J/(K mol) at T=T c ~0.16 K.

Boson peak in glasses We expect similar fit to work For 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 aside Less 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 mk 10 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 mk 10 ppm HUGE effect!

Compare to effect of disorder in conventional SC Huge slope And opposite sign! 3He has highly nontrivial effect on SS state. Not a simple add on!

TEST YOUR NCRI

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