1959-17 workshop on supersolid...
TRANSCRIPT
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1959-17
Workshop on Supersolid 2008
A. Kuklov
18 - 22 August 2008
CUNY, USA
Dislocations and Supersolidity in solid He-4
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Dislocations and Supersolidity in 4He
Anatoly Kuklov (CUNY,CSI)
supersolid 2008, ICTP, Trieste
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Massimo Boninsegni (Univ of Alberta)Lode Pollet (ETH)Nikolay Prokof’ev (UMASS )Gunes Soyler (UMASS)Boris Svistunov (UMASS)Matthias Troyer (ETH)
First principles QMC Dislocation roughening
Darya Aleinikava (CUNY,CSI)Eugene Dedits (CUNY,CSI)David Schmeltzer (CUNY,CCNY)
Thanks to: NSF and CUNY grants
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• Motivation: search for superfluid network of defects • History: Studies of dislocations in He4
• Types of dislocations and their superfluid properties• Core splitting and self-pinning• Mechanical strain and vacancy gap • Approximate phase diagram
• Quantum roughening • Long-range forces between kinks • Kosterlitz-Thouless, RG and MC arguments against quantum
roughening• J. Day & J. Beamish experiment
• Summary
Outline
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in metals: dislocation densities~106-1014 cm-2
Superfluid network of dislocation (?)
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Shevchenko state of quasi-1D SF random netwokS.I. Shevchenko, Sov. J. Low Temp. Phys. 14, 553 (1988).
Coreless vortices
Tc in the network T*a/D ~1/DT*~1K, nd ~ (a/D)2
Tc ~1mK for nd ~109cm-2
Tc ~10mK for nd ~1011 cm-2
a
“Incompressible vortex fluid” by P.W. Anderson, cond-mat/0705.1174
Tc <T<T* , wide range of quasi-superfluid frequency dispersive response
ω τ> superfluid response at T>Tc
ω τ< normal state at T>Tc
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21*
2 1*
110 10
SFKTs
T Tτ
−
− −� �−� �
� �� �
V.A. Kashurnikov, et al, PRB, 53, 13091 (1996); Yu. Kagan, et al, PRA,61, 045601 (2000).
KSF -Luttinger parameter; T* ~ 1K; K =0.205(20); Tc~0.1K
time of phase slip in a single loop:
Not much is known about dynamics in the network!
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Edge and screw dislocations
ϕr
deformation vector u ~
2
bϕ
πstrain and stress /bu rσ∂ � �
b - Burgers vector
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Dislocation as almost free classical string
X
Y
Y(x,t)
J.Appl.Phys. 27,583; 789(1956)
Measurements of sound absorption and internal friction in solid He4
R.Wanner, I.Iwasa, S.Wales, Solid State Commun., 18,853(1976)Y.Hiki, F. Tsuruoka, Phys.Lett. 56A, 484; 62A, 50(1977); V.L.Tsymbalenko, JETP 47,787(1978); 49, 859(1979)I.Iwasa,K.Araki, H.Suzuki, J.Phys.Soc.Jpn 46, 1119(1979)J.Beamish, J.P.Frank, PRL 47,1736(1981).....................................................
Peierls barrier (still classical)
Peierls, Frenkel-Kontorova, in the book A. M. Kosevich, “The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices”, Wiley, 2005
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Quantum effects
Semiclassical tunneling of kinks: B.V. Petukhov and V.L. Pokrovsky, JETP 36, 336 (1973)
Kinks as quantum quasiparticles: A.Andreev, Soviet Uspekhi, 19, 137(1976)
Semiclassical description of dislocation dynamics in sound absorption: A. Y.Hiki, F. Tsuruoka, PRB 27, 696(1983)I.Iwasa, N.Saito, H.Suzuki, J.Phys.Soc. Japan 52, 952(1983)A.V.Markelov, JETP 61,118(1985)
Models of quantum kinks+ superfluid properties: P.G. de Gennes ,C.R. Physique 7, 561(2006)G.Biroli,J.P. Bouchaud, cond-mat 0710.3087
see review S. Balibar and F. Caupin, J. Phys.: Condens. Matter 20, 173201 (2008)
Role of deformations in inducing core SF :
V. M. Nabutovskii and V. Ya. Shapiro, JETP 48, 480 (1978)S. I. Shevchenko, Sov. J. Low Temp. Phys. 13, 61; 553 (1987)A. T. Dorsey,P.M. Goldbart, J. Toner PRL 96, 055301 (2006)J. Toner, PRL 100, 035302(2008)
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Deformations, structure and core superfluidity)M. Boninsegni, et al., PRL 99, 035301 (2007)L. Pollet, et al, cond-mat 08053713
Mechanically gapped dislocations andJ. Day & J. Beamish experiment
Nature 450, 853 (2007)
Main focus of the talk
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z-screw x-screw zy-edge xy-edge xz-edge
SF splits by I
ordertransition
SF SFstrongly
split
stronglysplit
insulator
insulator
Stable dislocations in hcp He4
83b a= 8
3b a=a
b a= b a= b a=
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Core splitting (partial dislocations) in He4
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Full edge dislocation
b- Burger’s vector
Z
X
two atoms in unit cell
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Full edge dislocation
b- Burger’s vector
Z
X
two atoms in unit cell
2~defE b
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Partial (split) edge dislocation
Z
X
fault
L
two atoms in unit cell
( )2 2
~ 2 ~2 2defb bE
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PIMC simulations (columnar view): split xy-edge dislocation
11 layers 11 layers
10 layers 10 layers
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bz
Z
X
L
bz /2
bz /2
A
A
A
B
B
B
C
Split ZY-edge dislocation
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A BY
X
Fault
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Fault: C-layerA B
½ cores
Y
X
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Columnar view of fault + split core: many layers
Y
X
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PIMC simulations (columnar view): zy-edge (SF) dislocation
½ cores
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Strong self-pinning of zy-edge dislocation
Z
X
bz/2 bz/2
L
gliding motion is pinned by the barrier ~ L
bx/2
bx/2
gliding motion is not pinned
split zy-edge dislocation
split xy-edge dislocationY
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Fault size
2
2
2
fault surface te
ln4
ln
nsi
8
, 8
on
full
split full L L
L
bE R
bE E
b
σ
μ
π
μ
π
μ
πσ
σ
=
− = − +
= −
o
o
3.7 A,
MC simulati
100 2
00b
ons
ar
: 0.1
75 150A
/K particle
L
b μ
σ
= ≈
> −
−
<
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Z-Screw
M. Boninsegni, et al., PRL 99, 035301 (2007)
condensate map
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X-screw
G. Soyler et al.
condensate map
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z-screw zy-edge
SF splits by I
order transition
SFstronglysplit and
selfpinned
Fully SF loops
+
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Splitting of z-screw dislocation makes it insulator
Z
L
bz/2
bz/2
split=insulator
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Z
L
bz/2
bz/2
insulator
superfluid
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(Preliminary) phase diagram for dislocation SF
superfluid screw dislocations
insulating screw dislocations
I order transition
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Strain and SF gap
2in t
2
( . . . ) | | . . . .
| | ~ ( . . . )
s y m m e try o f e la s t ic m o d u
;
l i
i j k l
i
i j i j k
jk l
i j
x x y y z z
i
l
i j i j kj j k l li
F r u uT
T T r T r
T
T
T
T
u
r u u u
ψ
ψ
⊥
= − − − +
− + + +
−
= = = �
no proximity to superfuidity of ideal crystal (no perfect supersolid)
Higher order terms in strain are equally important
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Density change and vacancy gap
/ 0.13 n nδ ≈
L. Pollet, et al, cond-mat 08053713
ii
xx yy zz
n u n
u u u
δ ≈ −
= =
No significant quadratic terms!!!
2 2 4 0zzzz xxyy xxxx xxzzT T T T+ + + ≈
V. M. Nabutovskii and V. Ya. Shapiro, JETP 48, 480 (1978)S. I. Shevchenko, Sov. J. Low Temp. Phys. 13, 61; 553 (1987)J. Toner, PRL 100, 035302(2008)
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ZY-edge dislocation: marginally SF
8, / 0., 2632ii
bu r a b n na
rδ
π≈≈ = = →
Splitting: / 2 / 0 13 .b n nb δ ≈→ →
XY-edge dislocation: Insulating
, , / 0.2
1 6 ii
bu r a b a
rn nδ
π≈≈ = = →
Splitting: / 2 / 0.08 0.13n nb b δ ≈ <→ →
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Anistropic compression
0xx yy zzu u u+ + =
L. Pollet, et al, cond-mat 08053713
No linear term!
r r⊥=�
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( )2
2 22
| | ~ ( / 2 / 2 2 ) 0.1
~ 1( 2)
zzzzzz xxyy xxxx xxzz zz
ur T T T T uψ
� �− + + + − −� �
� �
Anistropic compression
split ZY-edge is marginally SF
0.26
0.2
32 1/
zzz
zz
bu
au
π= ≈
≈
2 2 4 0zzzz xxyy xxxx xxzzT T T T+ + + ≈
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22 2
2| | ~ ( 4 ) ~
0.151 ,
( )zx
xzxz xz
ur T uψ
� �− − − −� �
� �
Lx
uz~x
Z
X
Shear strain
screw dislocation:2 2
22 22
2
2
0.22
0.22
0
8, ,
4 33
( )| | ~ 1 1 0,
( )
1 0
.15 0.15
0.11
0.
1 0
5
zzx zy z
zx zy
b au u r b a
r
u u
π
ψ
ψ
+ = ≈ = =
� �+ � �− − = − + >� � � �� � � �� �
� �− + < → =� �
� �insulating if split:
superfluid if unsplit:
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Quantum (non-)roughening and J.Day & J.Beamish experiment
J. Day & J. Beamish,Nature 450, 853 (2007)
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Quantum dislocation
X
Y
Y(x,t)
ratio K of phonon and kink energies becomes ~1
in He4:
Quantum rough dislocation Peierls barrier up is effectively zero at T=0Zero point wandering
K – Luttinger parameter
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Long-range interaction between kinks due to 3d elastic matrix
J.P.Hirth, J.Lothe, “ Theory of Dislocations”, McGraw-Hill, 1968A. M. Kosevich, “The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices”, Wiley, 2005
L
dislocation loop
Long-range space-time interaction suppresses quantum roughening
2 2( , )LR
gU x t
x t≈
+
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Coulomb gas mapping
Kostrelitz-Thouless transition is destroyed for arbitrary small g
Pairs are ionized into plasma state – Peierls barrier is relevant at T=0!!!
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RG
up grows at large L for any g(0) and K(0)
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MC simulations (of dual model) at T=0
KT
Monte Carlo Worm algorithm (Prokof’ev&Svistunov (1998)):http://montecarlo.csi.cuny.edu/umass/index.html
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Consequences
�No quantum roughening = no quantum macroscopic wandering
�Gapped spectrum rather than sound-like (gap << kink energy)
�Intrinsic hardening of shear modulus at T< gap (at pinning distances smaller than inverse concentration of thermal kinks)
2 2qω = + Δ
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If gap were zero: Thermal activation of He3
linear density of He3 in units a=1:
Lp – pinning length
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fit:nd~ 3.1011cm -2
nHe3~ 7.p.p.mactualnHe3~ 1.p.p.b
Single Arrhenius: poor fit
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Finite gap (and Lp-1 >> soliton density)
( )0
0
2( ) exp
1 g ln p
KT T
L
π� �� �Δ ≈ Δ −� �+ Δ� �
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data: courtesy of John Beamish,J. Day & J. Beamish,Nature 450, 853 (2007)
For 1p.p.b of He3, Lp=103: 2 from different curv6 s5 e DW KW D T → ≈= ≈
Modulus hardening
self-consistent!
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Summary
� Selfpinned SF loops (due to core splitting)
� Splitting as I order transition for Z-screw - hysteresis and metastability
�Strain criterion for SF and non-SF dislocations
� Preliminary phase diagram
� Self - pinning in the Peierls potential at low T: no quantum macroscopic wandering
� Bimodality in the modulus hardening due to Peierls gap