Phenomena in layered metals that coexist on a short spatial scale

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15 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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Phenomena

in

layered

metals

that

coexist

on

a

short

spatial

scale



Lev

P
.

Gor’kov,

NHMFL,

FSU


Discussion of few phenomena where two (almost) independent components coexist


on atomic or
mesoscopic

scale
-

the need of local tool
s

I. Superconductivity: unpaired electrons on Fermi surfaces


a) Strong e
-
ph interaction:
dHvA

oscillations below
Tc
; the CDW transition

b) Magnetism and superconductivity: similar features in some Heavy Fermions.


Phase diagram of CeCoIn5

II. “Peak effect” and
dHvA

oscillations

III. Phase diagram of Fe
-
based superconductors as function of
doping/pressure

I
.

Superconductors

with

strong

e
-
ph

interactions
:

2
H
-
NbSe
2
,

2
H
-
TaSe
2
,

Nb
3
Sn,

V
3

Si,

CeRu
2


,

borocarbides







In 1976
Graebner

and Robins observed in the superconducting state

of 2H
-
NbSe
2


dHvA

oscillations at H<Hc2 (down to 0.2Hc2 !) :

Oscillation were identified with 3D Se
-
pocket.

The main FS were
not

seen by
dHvA


!

For concreteness: 2H
-
NbSe
2
, 2H
-
TaSe
2

1)
Superconductivity

T.
Tokoya

et al, Science, 2001


Numerous theoretical attempts to derive
dHvA

oscillations in the SC state with non
-
zero gap
:


K. Maki (1991); A. Wasserman& M.
Springford

(1994);

S.
Dukan
& Z.
Tesanovic
(1995); M.
Vavilov&V
.

Mineev(1997);;
L.Gor’kov&J.Schrieffer

(1998),…

But!!Could it be that
the gap is
identical
ly

zero on this FS?

ARPES on
“zero gap”
at the small FS at the
Γ
-
point

The data obtained at T=5.3 K

(Normal state data at 10K)


The question arises whether indeed

this gap is zero down to T=0?
(
77
Se?)

The overall structure of the energy spectrum was recently
confirmed by ARPES (Borisenko et al) .


No conclusion
concerning the “sharpness” of FS from ARPES.”
N
o

CDW gap !

Attenuation of the
dHvA

signal comes
about due to motion of
quasiclassical

electron on the background of
inhomogeneous magnetic field

of the flux lines due to
SCon

other FS


dHvA

below Hc2 in other phonon superconductors

0.2Hc2,

0.6 Hc2

0.5Hc2

Masses of the order of the bare
electronic mass !

2)
What is Charge Density Wave (CDW) ??

SC on the CDW background !!!???

No nesting, no gaps on the F surfaces?

T
CDW
= 122K(Ta); = 33.5K(
Nb
)

CDW does not affect FS . However, CDW strongly
changes some inner electronic band states

S. V.
Borisenko

et al, PRL 102,166402 (2009)

ARPES

Tunneling: non
-
linear
dI
/
dV

(at ~4K):

Gaps: 60
meV

~18T
CDW

(
Nb
)


90meV~ 7 T
CDW

(Ta)

Is SC in NbSe2 formed on the large cylindrical FSs?

Can different bands have different strengths of the
e
-
ph
coupling?

(
Λ
2
~ 0.3 (Se),
Λ
2
~ 1.8 (
Nb
)
, Corcoran et al
).




(
Λ
2
is the dimensionless
e
-
ph

constant)


Different physics for different bands?

Local potential
U
(u)

for the ion at a given site


(
u

is the displacement).


At the structural transformation T=T
CDW.


t
he ion

gradually shifts from the center.

93
Nb NMR ?

Λ
2
<1

Consider how e
-
ph interaction changes the local environment for motion of an ion depending on

Λ
2


The potential U(u) at each local site has the two deep minima ,
u(+,
-
)
.



Equivalent to the
Ising

spin system
(Gor’kov
;

2011)

U

U(
u
)

+

-

u
+,
-

=0.5Å

Λ
2

>1

u

The two components, at least: CDW is formed on

the
Nb

bands


千S 瑨t b慣歧a潵nd映䍄W

⡓(
潲o楴慬a

no琠楮v潬ved 楮⁓䌩

Λ
2
>1 :

Ising

spins interact via the inter
-
site exchange by electrons


Above T
CDW
positions are random. Below T
CDW

ions occupy
the
superlattice

pattern of the
u(+,
-
)
minima .


Since the structural vector, Q is determined by the
inter
-
site interactions, Q is not related to FS sizes,
hence, no nesting and no energy gaps on FS! The
material remains metallic.


Large CDW gaps


瑨攠敮敲杩敳go映瑨攠e浩湩浡m

d䡶H

on 瑨攠浡mn⁣祬楮i物r慬 F匠慲攠no琠獥敮sb散慵獥a
o映瑨攠污rg攠業i杩湡g礠y慲琠o映瑨攠䝲敥渠晵nc瑩tn:


1)
Superconductivity

CeCoIn
5

:
dHvA

below Hc2

R.
Settai

et al
J.Phys
. Cond. Matter,
13,
L427(2001)


II. Superconductors (magnetic materials):
CeCo

In
5
; URu2Si2; UPd2Al3…

!

Large
Λ
2

break the
Migdal’s

adiabatic approximation


敬散瑲潮o
and ions form the local bound complex (the
polaronic

effect)

Unlike 2H
-
NbSe2, there are no ARPES data confirming zero SC gap independently

Indirect evidences in favor of zero SC gap on small FS in CeCoIn5:

For CeCoIn5 there are data for
non
-
zero residual normal component in the specific heat
(
R. Movshovich
et al.,
PRL. 86, 5152 (2001
)) and
on the heat transport
at low temperatures
that indicate existence of a FS with unpaired electrons (
M. A.
Tanatar

et al, PRL95(2005
))

2)
IWhat

is the background phase for SC in heavy fermions? Any
analogy to CDW ?

URu2Si2:
Tc
=1.4K ,T
N
=17.5K

UPd2Al3:
Tc
=2K, T
N
=14K

For CeCoIn5(
Tc
= 2.3 K): the so
-
called Kondo temperature “T
K
“~30
-
50K is temperature of crossover


into a “Two Fluid “ or “Kondo Liquid “ state

)
/
)
(
)(
(
)
/
)
(
)](
(
1
[
/
)
(
T
T
C
T
f
T
T
C
T
f
T
T
C
HF
KI
MAG



)
/
)
(
)(
(
)
/
)
(
)](
(
1
[
/
)
(
T
T
T
f
T
T
T
f
T
T
HF
KI
MAG






Phenomenology

S.
Nakatsuji
, D. Pines,
Z.Fisk
, PRL,92(2004))

Relation to bands is not
resolved

( ) ( )
K T T


The multi
-
components character of low T (<30K) physics in CeCoIn5 is best
manifested by the NMR data (N .J.
Curro

et al (PRB64 (2001); PRB70 (2004))


The broken proportionality

50K

T

0

Temperature dependence of Knight shifts interpreted as due to


temperature dependence of the transferred hyperfine

coupling constants , A(T). (H. Sakai et al, PRB 82,020501(R)(2010))


AFM fluctuations?

III. The peak effect
-
max
J
c

(H,T)

Peak effect is about changes in the

collective flux pinning close to Hc2(T)

It is a widespread effect, but in Q2D

2H
-
NbSe2 there are singular features,

possible due to the crossover

from the flux
-
lines to the pancakes

NMR options?

H (
kG
)

T(K)

the
local DOS is ~ 2D DOS in PM state

The distribution of local
DOS
and of
D
0

(x)
along

x
in the SP

x
0
~ few nm

n
w
(x)

Let the SDW phase be connected with the PM phase by the
1
st

order phase transition
that would result in
macroscopic
puddles

along the sample of each of the two phases.


Instead

--
>
a
gradual transition
between the two states :
domain walls, or

Discommensurations

occur(as stripes in
cuprates
) .


In theory, it was demonstrated on simple models.
Experimentally, observed in Co
-
doped BaFe2As2

III.
Pnictides
: 1
st

order phase transition
versus

non
-
linear modulated SDW ground
state as function of doping (
or pressure)

The order parameter for the SDW (CDW) in its simplest form is:

The
Soliton

phase
has the periodically modulated amplitude
(Gor’kov&Teitel’baum,2010)

)
cos(
)
(
0
Qx
D
S
x
D



)
(
0
x
D
)
(
0
x
D
Mőssbauer

spectroscopy


EPL,
89 (2010) 67008




c

PM

SDW

T
tcp

T
c0

T

SP

The periodic SP:

from weak IC modulation

to rarified domain walls

The components
do not communicate with each other being separated by large energy
barriers; “proximity” is very
weak :
the electronic tunneling between

components is a collective process.

Conclusions

Two or more distinctly different components may coexist in a correlated electronic system

a) The SC state of one group of electrons is not seen by electrons from other band.


b) This occurs for SC both of the e
-
phonon or of a magnetic origin.

c) The onset of SC is preceded by formation of the new phase in the system
above
Tc
. For the phonon mechanism it is the CDW state. For spins, it is a
magnetic phase, or the crossover into the HF state (CeCoIn5).


d) In the new phase electrons are strongly bound with other degrees of
freedom in the system. Details of this phase remain still poorly understood,
even experimentally.




It seems that local probes, such as NMR could be very instrumental in studying

these and other puzzles mentioned in the talk .