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Mech
an
ical an
d S
up
erf
luid
Pro
pert
ies
of
Dis
locati
on
s in
So
lid
4H
e
An
ato
ly K
uklo
v(C
UN
Y,C
SI)
SP
N,
CU
NY
, M
arc
h,1
4,
200
9
support
: N
SF
Massim
o B
onin
segni(U
niv
of A
lbert
a)
Lode P
olle
t(U
MA
SS
,ET
HZ
)
Nik
ola
yP
rokof’ev
(UM
AS
S )
Gunes
So
yle
r(U
MA
SS
)
Boris S
vis
tunov
(UM
AS
S)
Matthia
s T
roye
r(E
TH
Z)
First princip
les Q
MC
of
He4
Model stu
die
s o
f str
uctu
ral defe
cts
Dary
aA
lein
ikava
(CU
NY
,CS
I)
Eugene D
edits
(CU
NY
,CS
I)D
avid
Schm
eltzer
(CU
NY
,CC
NY
)
PR
L 1
01, 097202 (
2008
)
PR
L 9
9, 035301 (
2007)
PR
L 9
8, 135301 (
2007)
PR
L 9
7, 080401 (
2006)
arX
iv:0
81
2.0
98
3
•H
ott
est
issu
es i
n s
olid
He4
•N
um
eri
cal
evid
en
ce f
or
su
perf
luid
ity
of
dis
locati
on
co
res
•S
up
erf
luid
netw
ork
of
cro
ss-l
inked
dis
locati
on
s?
??
•M
ech
an
ical
str
ain
an
d v
aca
ncy g
ap
•Q
uan
tum
an
d c
lassic
al
rou
gh
en
ing
of
glid
ing
dis
locati
on
•T
herm
al
kin
ks a
nd
co
re s
up
erf
luid
ity
•S
um
mary
an
d f
utu
re s
tud
ies
Outlin
e
Tors
iona
lo
scill
ato
r and N
CR
I (K
im &
M.C
ha
n)
Mg d
isk
He f
illin
g lin
e
So
lid h
eliu
m in
ann
ula
r chann
elA
l she
ll
Channel
OD=10mm
Width=0.63mm
Drive
Dete
ctio
n
3.5 cm
Torsion rod
Torsion cell
Sci
ence
305
, 19
41
(2
004)
f 0=912Hz
Sup
erf
luid
deco
up
ling
in s
olid
He
4
51bar
Tota
l m
ass loadin
g =
3012ns
Measure
d d
ecouplin
g, -∆
τ o=
41ns
NC
RIF
= 1
.4%
Andre
ev-L
ifshitz-C
heste
r-T
houle
ss
Supers
olid
!!!!?
??
?
D. J.
Thoule
ss, A
nn. P
hys.5
2, 403
(1969)
Ideal H
e4 c
rysta
l is
insula
tor
First princip
le M
C:
PR
L 9
7,
080
401 (
20
06)
J.
Da
y &
J.
Beam
ish e
xp
erim
ent
(Natu
re45
0,
853 (
200
7))
Z-S
cre
w
M. B
onin
segni, e
t al., P
RL 9
9, 035301 (
2007)
conde
nsate
map
X-s
cre
w
G. S
oyle
ret al.
conde
nsate
map
z-s
cre
wzy-e
dge
SF
S
F
Fully
SF
lo
ops in h
pc
He
4
+
Netw
ork
of
sup
erf
luid
dis
locations ?
??
Shevche
nko
sta
te o
f quasi-1
D S
F r
andom
ne
twok
S.I
. S
hev
chen
ko, S
ov.
J. L
ow
Tem
p.
Phy
s. 1
4, 553 (
1988).
Core
less
vort
ices
a
“Inco
mpre
ssib
le v
ort
ex f
luid
”by
P.W
. A
nder
son, co
nd-m
at/0
705.1
174
wid
e r
ange o
f th
e d
isp
ers
ive r
esponse
ωτ
>superf
luid
ωτ
<norm
al
Tc~
T* a
/D
T*(
a/D
) <
T<
T*
nd
~ (
a/D
)2
Tc
~10m
K f
or
nd
~10
11
cm
-2
Str
ain
and v
acancy g
ap
(PR
L 1
01, 097202 (
20
08))
hyd
rost
atic
(d
e)co
mp
ress
ion
/
0.1
3n
nδ
≈
Lx
uz~
x
Z
X
anis
otr
opic
shear
str
ain
:
Quantu
m (
glid
ing)
dis
locatio
n
X
Y
Y(x
,t)
KT
tra
nsitio
n:
Lutt
inger
para
mete
rK
~ (
phono
n e
nerg
y)/
(kin
k e
nerg
y)
~1
in H
e4:
Quantu
m r
oug
h d
islo
cation:
Peie
rls
barr
ier
up~
0 a
t T
=0
Long-r
ang
e inte
raction b
etw
een k
inks d
ue t
o 3
d e
lastic m
atr
ix
J.P
.Hirth
, J.L
oth
e, “
Theory
of D
islo
cations”,
McG
raw
-Hill
, 1968
A.
M. K
osevic
h, “T
he C
rysta
l Lattic
e: P
honons, S
olit
ons, D
islo
cations, S
uperlatt
ices”,
Wile
y,
2005
22
(,
)L
R
gU
xt
xt
≈+
x
1(
)~
||
Vx
x
Mappin
g t
o c
lassic
al gas
Pe
ierls
barr
ier
is a
lwa
ys r
ele
vant
at
T=
0 !!!
PB
C:
(
,)
(,
),
,
,1,
2..
.
yx
nL
my
xn
mT
τβ
τβ
++
==
=ℏ
RG
up
gro
ws a
t la
rge L
for
an
y g
(0)
and K
(0)
Dual
rep
rese
nta
tion:
J-cu
rren
t m
odel
iJ�
-in
teg
er b
ond
curr
ents
form
ing
clo
sed l
oop
s
,
1(
)2
ij
ij
d
ij
SU
nJ
xx
JJ
n+
−∇
−
−=
=
×
∑
�
����
�
��
()
()
2
212
()
,
()
()
d
P
Uq
Uq
qu
Uq
Kπ
−=
+∼
Space
Tim
e
,
y(
)'
)'
(,
yx
xτ
τ
configura
tion u
pdate
s b
y c
orr
ela
tor
Mo
nte
Carl
o W
orm
alg
ori
thm
: h
ttp:/
/mcw
a.c
si.cun
y.e
du/u
mass/inde
x.h
tml
Renorm
aliz
ed s
tiff
ness, T
=0
01
23
45
67
89
1011
1213
140.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
1020
3040
5060
7080
9010
00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
0
K(Nx,C)
CLn
(Nx)
3.4
2.8
2.6
1.6
1.4
0.8
0.3
5 0
.2
0.5
1.1
2
1.2
5
0.0
5
1.8
0.6
5 0.9
5
3 3
.2 2
.2 2
.4
K(Nx)N
x
BK
T
gln
(Nx)
K(g
,Nx)
Selfpin
ned
dis
location n
etw
ork
and s
hear
modulu
s G
(T)
00
2
11
(,
)(0
,0)
()
xL
idea
l
yz
dx
dy
xy
GT
G
b LL
β
λτ
τ
λ
=+
≈
∫∫
ℏ
Lx
y(x
,t)
Ly
Lz
2
()
,
11
...
(,
)(
)
xid
eal
Jx
GT
G
τ
τ
τ
=
+
∑
density o
f kin
ks n
(T)
data
: D
ay &
J. B
eam
ish,N
atu
re4
50, 853 (
2007)
Shear
mod
ulu
s h
ard
en
ing
(,
,,
)x
TT
KC
Nα
∆
Kin
k e
nerg
y
Ho
w s
up
erf
luid
an
d m
ech
an
ica
l re
sp
on
se
s c
an
be
sim
ilar?
Str
ong s
uppre
ssio
n o
f S
F b
y s
tructu
ral kin
ks
24
2(
)|
|
||
'(
)
||
c
kink
Fa
TT
Ba
nT
ψψ
ψ=
−+
+
actu
al S
F t
ransitio
n:
()
'(
)0
cki
cnk
ca
TT
aT
nT
T−
+=
<<
→ɶ
ss
()
()
1(0
),
)
(
ki
nk
c
kink
c
nT
TT
Tn
Tρ
ρ
=
−<
ɶɶ
(0)
()
;
0.0
50.
1(
)1
()
kink
kink
GG
Tn
T
n
γγ
=≈
−
+∞
()
()
()
()
()
1(0
)(
)(
)(0
)
cki
nk
s
cki
nk
cs
GT
GT
nT
Tg
TG
GT
nT
ρ ρ
−=
≈−
=−
ɶ ɶɶ
rela
tive c
hang
es o
f th
e m
odulu
s a
nd S
F d
en
sity:
Sum
mary
and
open q
uestio
ns
�S
train
crite
rion fo
r co
re s
uperf
luid
ity
�Long-r
ange inte
ractions =
no q
uantu
m r
oughenin
g
�C
rossover
from
quantu
m s
moo
th to c
lassic
ally
rou
gh s
tate
–in
trin
sic
mechanis
m
for
shea
r m
odulu
s s
oftenin
g
�K
inks s
uppre
ss c
ore
superf
luid
ity
�R
ole
of H
e3
�Q
uan
tum
dynam
ics o
f clim
bin
g (
superf
luid
core
!) d
islo
cations
�M
icro
scopic
sfo
r kin
k-S
F inte
raction
�Q
uantu
m m
eta
llurg
y in H
e4
Happy B
irth
day Z
henya!!!