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!!!