C C Can supersolidity be Can supersolidity be lidit lidit b b - - PowerPoint PPT Presentation

C lidit b C lidit b Can supersolidity be Can supersolidity be suppressed in stiffened suppressed in stiffened suppressed in stiffened suppressed in stiffened solid solid 4He? He? solid solid He? He?

Eunseong Eunseong Eunseong Eunseong Kim Kim Kim Kim Center for Center for Center for Center for Supersolid Supersolid Supersolid Supersolid & Quantum & Quantum matter matter Research Research & Quantum & Quantum matter matter Research Research KAIST, Republic of KAIST, Republic of Korea Korea KAIST, Republic of KAIST, Republic of Korea Korea

 Shear

Shear Modulus

• dulus Anomaly

Anomaly

 Shear

Shear Modulus Modulus Anomaly Anomaly

 Simultaneous Measurements :

Simultaneous Measurements : NCRI& NCRI& Shear hear Modulus Modulus NCRI& NCRI& Shear Shear Modulus Modulus

• What is common?

hat is common?

• What is different?

hat is different?

 Summary

Summary

 Summary

Summary

• J. Day, and J. Beamish, Nature 450, 853 (2007).
• J. Day, and J. Beamish, Nature 450, 853 (2007).

2 15

2 d D I A fV    2 A fV 

• A. Granato, K. Lucke, J. of Appl. Phys. 27,

27, 583 (1956).

With most dislocations strongly pinned by impurities strongly pinned by impurities at low temperatures, the shear modulus is close to that of a perfect crystal.

• The detachment of impurities by thermal evaporation

reduces μ by a fraction proportional to ΛL2 at high

2

C L    

μ y p p g temperatures.



• Drive dependence
• Frequency dependence
• 3He concentration

dependence

Y A ki J C G d H

• Y. Aoki, J. C. Graves, and H.

Kojima, PRL 99, 99, (2007)

Two phenomena should be closely related !

Reduction in the resonant period can be understood by stiffening of can be understood by stiffening of solid helium ?

Shear modulus stiffening possibly mimic the Shear modulus stiffening possibly mimic the NCRI.

    ln 5 ~10 ln d f ppm d         ln ln df d f f d          

However, the estimated value is too small. Elastic stiffening alone cannot explain the NCRI. Clark et al., PRB (2008) ( )

NCRI occurs only in a NCRI occurs only in a stiffened Bose solid. stiffened Bose solid. NCRI occurs only in a NCRI occurs only in a stiffened Bose solid. stiffened Bose solid.

• J. T. West, O. Syshchenko, J. Beamish, M. H. W. Chan, Nat Phys 5, 598 (2009)

Effect in Fermi solid Effect in Fermi solid Effect in Fermi solid Effect in Fermi solid 3He ? He ? He ? He ?

Shear modulus is crystal structure dependent. NCRI is quantum statistics dependent. p

How NCRI and How NCRI and shear modulus are shear modulus are How NCRI and How NCRI and shear modulus are shear modulus are l d l d? l d l d? re relate ated? d? re relate ated? d?

Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows quantum statistics dependence quantum statistics dependence quantum statistics dependence quantum statistics dependence

 The

The appearance ppearance of

• f NCRI

NCRI seems eems to

 The

The appearance appearance of

• f NCRI

NCRI seems seems to to require the require the stiffening of solid helium. stiffening of solid helium. It It i b tt tt t b t b th h

 It

It is s bett tter er to measure

• measure both

th p phenomena enomena simultaneously simultaneously

 Torsional Oscillator

• Resonant Freq: 911 Hz

q

• Q factor: 6 x 105
• Annular channel

Diameter:16 mm  Diameter:16 mm  width: 400 μm

 PZT shear transducer

• Area : 1 cm x 1 cm
• Area : 1 cm x 1 cm
• gap : 400 μm
• d15 at low temperature

1.5x 10-10 m/V

• frequency range:
• 10 Hz ~ 40 kHz

10 Hz 40 kHz

l

 Sample preparation

• 10 samples with Blocked

capillary method capillary method

• Pressure of samples: 30 ~

49 bar

 Same thermodynamic

path path

 Same 3He concentration  Compatible S/V ratio  Compatible S/V ratio

Tem perature dependence Tem perature dependence

1.0

]

3.0x10

• 6

 NCRI and the shear

NCRI and the shear modulus increase were modulus increase were

0.5

hase [deg]

1 0x10

• 6

2.0x10

• 6

Q

• 1

modulus increase were modulus increase were

• bserved in a similar
• bserved in a similar

temperature range. temperature range.

0.0

ph

0.0 1.0x10

temperature range. temperature range.

40 50 Shear modulus NCRI 1.5

]

10 20 30 0 0 0.5 1.0

/0 [%]

NCRIF [%

0.02 0.1 10

T [K]

• 0.5

0.0



%]

0.2 0.5

T [K]

Tem perature dependence Tem perature dependence

1.0

]

3.0x10

• 6

Temperature Temperature dependence in dependence in shear modulus increase can be shear modulus increase can be

0.5

hase [deg]

1 0x10

• 6

2.0x10

• 6

Q

• 1

understood by understood by 3He impurity He impurity pinning of dislocation network pinning of dislocation network ( ith b d f ti ti ( ith b d f ti ti

0.0

ph

0.0 1.0x10

(with broad range of activation (with broad range of activation energies) energies). .

40 50 Shear modulus NCRI 1.5

]

Indeed, c Indeed, characteristic haracteristic te temperature mperature of NCRI traces the

• f NCRI traces the

10 20 30 0 0 0.5 1.0

/0 [%]

NCRIF [%

p pinning temperature of pinning temperature of 3He on He on dislocation lines dislocation lines. .

0.02 0.1 10

T [K]

• 0.5

0.0



%]

NCRI probably appears in a tiff d lid!

T [K]

stiffened solid!

f

 No

No correlation between the magnitude o correlation between the magnitude of NCRI NCRI No No correlation between the magnitude o correlation between the magnitude of NCRI NCRI and shear modulus change and shear modulus change and shear modulus change and shear modulus change

 Critical Stress

Critical Stress Critical Stress Critical Stress Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened solid helium. solid helium. solid helium. solid helium.

 Relaxation

Relaxation Relaxation Relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation

Average NCRIF ~ 2%, SM increase ~ 25.7%

 

SM increase 25.7%

• ver 10 samples

ln ln df d f f d          

0.10 0.15 0.20

F [%]

Ei f l i

• 0.05

0.00 0.05

ced NCRI 0.053%

• Eigen frequency analysis

Empty cell : 908.88 Hz

• 60 -40 -20

20 40 60 80 100

• 0.15
• 0.10

25.7% mimic SM increase [%]

Empty cell : 908.88 Hz Solid Helium (SM=1.5x107 Pa) : 907.06 Hz

SM increase [%]

No linear relation between NCRI and No linear relation between NCRI and SM increase SM increase

The magnitude of The magnitude of The magnitude of The magnitude of NCRI seems to have a NCRI seems to have a NCRI seems to have a NCRI seems to have a correlation correlation rather rather correlation correlation rather rather with with with with the absolute the absolute the absolute the absolute l f l f h l f l f h va value o ue of s shear ear va value o ue of s shear ear modulus modulus modulus modulus at at low low at at low low h temperatures t temperatures than an temperatures t temperatures than an the shear modulus the shear modulus the shear modulus the shear modulus l increase at increase at low

• w

increase at increase at low

• w

temperatures. temperatures. temperatures. temperatures.

Interference I Interference I

NO interference from hi high drive am h drive amplitude in litude in g p g p PZT PZT. The softening of solid h li i h helium in the center channel does not affect NCRI NCRI Normal stress on solid h li i th t

PZT shear transducer

Softened solid

helium in the center channel induced by the large torsional

Wh th d ti i th i d

large torsional

• scillation do reduce the

shear modulus.

When the reduction in the period is due to SM increase of 25%. Th i d hift i t d t b

Solid Helium Torsional Oscillator

The period shift is expected to be reduced to 1.2%

Drive dependence NCRI and shear modulus change with Drive dependence g drive sweep

Critical stress of shear modulus

0.37 Pa

c

 

shear modulus

Drive dependence

Different low temperature excitation Different low temperature excitation

Drive dependence

destroys NCRI in a destroys NCRI in a stiffened solid helium stiffened solid helium

Critical stress of shear modulus

0.37 Pa

c

 

shear modulus Critical stress of

0.002 Pa

c

 

NCRI Stress for solid helium is calculated from the S rim velocity of the oscillators. (σ=ρtωv/2)

Different low temperature excitation Different low temperature excitation destroys NCRI in a destroys NCRI in a stiffened solid helium stiffened solid helium

Critical stress for NCRI is always 2 Critical stress for NCRI is always 2 orders of

• rders of

it it d ll th th t f h d l magn magnit itude sma e small ller er th than an th that o

• f s

shear mo ear modulus us

Interference II Interference II

High drive amplitude in TO  Any change in the y g resonant period? N l lid Normal stress on solid helium in the center channel induced by the channel induced by the large torsional oscillations reduce the shear modulus.

PZT shear transducer

Softened solid

Solid Helium Torsional Oscillator

Interference II Interference II

One can estimated the One can estimated the One can estimated the One can estimated the induced stress on solid induced stress on solid induced stress on solid induced stress on solid helium in helium in the center the center helium in helium in the center the center channel channel by the he large large channel channel by the he large large channel channel by by the the large large channel channel by by the the large large amplitude of amplitude of amplitude of amplitude of torsional torsional torsional torsional motion. motion. motion. motion. The maximum shear The maximum shear The maximum shear The maximum shear stress stress induced induced by a stress stress induced induced by a stress stress induced induced by by a stress stress induced induced by by a normal stress is normal stress is about about normal stress is normal stress is about about σ ~ ~ σ ~ ~ ρtωv ρtωv/8. 8. /8. 8. ρ / Again Again critical ritical stress stress for for NCRI CRI is always lways 2 orders

• rders of
• f

Again Again, , critical critical stress stress for for NCRI NCRI is is always always 2 orders

• rders of
• f

magnitude smaller than that of magnitude smaller than that of shear modulus shear modulus

Relaxation by a Tem perature change

NCRI shows slower relaxation than NCRI shows slower relaxation than h d l h d l

1.9x10

• 6

0 30

Relaxation by a Tem perature change

shear modulus. shear modulus.

1.8x10

• 6

1.8x10

• 6

1.9x10

• 6
• 1

0.15 0.20 0.25 0.30

phase(she

1 6x10

• 6

1.7x10

• 6

1.7x10

• 6

1.8x10

40 -> 50 mK TO Q

• 1

phase(SM)

Q

• 0.05

0.00 0.05 0.10

ear modulus) 2000 4000 6000 8000

1.6x10

phase(SM)

Time (sec)

• 0.10

[

• ]

1 2 1 22

NCRI and shear modulus change by

1.0 1.1 1.2 40 -> 50 mK NCRI shear modulus

F [%]

1.20 1.21 1.22 shear mod

NCRI and shear modulus change by the abrupt temperature increase from 40 mK to 50 mK.

0.8 0.9 1.0

NCRI

1.18 1.19 ulus ( /0 ) 2000 4000 6000 8000

Time (sec)

1.17

Davidson Davidson-

• Cole plot of the

Cole plot of the torsional torsional oscillator and SM

• scillator and SM

t measurement measurement

 Shear

Shear modulus

• dulus and

and NCRI CRI are re measured measured Shear Shear modulus

• dulus and

and NCRI CRI are re measured measured

 Shear

Shear modulus modulus and and NCRI NCRI are are measured measured Shear Shear modulus modulus and and NCRI NCRI are are measured measured simultaneously. simultaneously. simultaneously. simultaneously.

 NCRI and SM in solid helium are closely related

NCRI and SM in solid helium are closely related NCRI and SM in solid helium are closely related NCRI and SM in solid helium are closely related but not exactly same but not exactly same effect. effect. but not exactly same but not exactly same effect. effect.

 NCRI has lower critical stress than the SM increase.

NCRI has lower critical stress than the SM increase. NCRI has lower critical stress than the SM increase. NCRI has lower critical stress than the SM increase.

 NCRI shows slower relaxation at low temperatures.

NCRI shows slower relaxation at low temperatures. NCRI shows slower relaxation at low temperatures. NCRI shows slower relaxation at low temperatures.

 Another low temperature excitation in NCRI

Another low temperature excitation in NCRI Another low temperature excitation in NCRI Another low temperature excitation in NCRI should should exist. exist. should should exist. exist.

D.Y. Kim S. Kwon H. Choi