A.A. Sinchenko Kotelnikov Institute of Radio-Engineering and Electronics, Russian Acad. of

Sci., Mokhovaya 11-7, Moscow 125009, Russia

INTERLAYER ELECTRONIC TRANSPORT IN QUASI-TWO-DIMENSIONAL COMPOUNDS

Collaborators

Yu. I. Latyshev, A.P. Orlov, A.M. Nikitina, V.N. Pavlenko, A.V. Frolov IRE RAS, Moscow, Russia P. Monceau, Th. Fournier Neel Institute-CNRS, Grenoble, France S. Brazovskii LPTMS-CNRS, Orsay, France S.-J. Kim, T. Yamashita, T. Hatano M.B. Gaifullin NIMS, Tsukuba, Japan M. Konczykowski, C. van der Beek Ecole Polytechn., Palaiseau, France D. Vignolles, W. Escoffier LNCMP, Toulouse A.A. Schekin, A.V. Bykov NT MDT, Zelenograd, Moscow A.N. Vasiliev, O.S. Volkova, D.A. Chareev MSU, Moscow P.D. Grigoriev ITP RAS, Chernogolovka, Russia

OUTLINE

1. Junction for interlayer transport studying.

2. Interlayer transport in HTSC: intrinsic Josephson effect and interlayer tunneling energy gap spectroscopy.

3. Interlayer transport in CDW compounds: CDW gap spectroscopy and intragap states.

4. Effect of high magnetic field: field induced CDW state in NbSe3 and graphite.

5. Interlayer transport in FeSe: detecting of inhomogeneous high-Tc superconductivity.

6. Conclusions.

FIB microetching method Yu.I. Latyshev, T. Yamashita, et al. Phys. Rev. Lett., 82 (1999) 5345. S.-J. Kim, Yu.I.Latyshev, T. Yamashita, Supercond. Sci. Technol. 12 (1999) 729.

FIB machine Seiko Instruments Corp. SMI-9000(SP) Ga+ ions 15-30 kV Beam current : 8pA – 50 nA Minimal beam diameter: 10nm

Stacked structures fabricated from layered materials by FIB methods

(a-c) Stages of the double sided FIB processing technique for fabrication of the stacked structure;

(d) SEM image of the structure. The structure sizes are 1µ x 1µ x 0.01 - 0.3µ

Yu. I. Latyshev et al. Supercond.Sci.Techn. 2007

single crystals with a thickness of 1-3 µm

Josephson effects on naturally layered crystalline structure of layered superconductors

Early ideas in 70-s:

W.E.Lawrence, S.Doniach 1971, L.N. Bulaevskii 1973

Further development in 90-s, after discovery of HTS

L.Bulaevskii, J.Clem, L.Glazman 1992

stationary IJE for short stacks L< 2λJ,

λJ = s λc /λab~ 1µm in Bi-2212

ehc

sLH

sLH

IHI cc 2|

)sin(|)( 0

0

00 =Φ

Φ

Φ= π

π

s L L L

intrinsic Josephson effects in HTS

Yu.I.Latyshev, N. Pavlenko, S-J.Kim, T.Yamashita ISS-99, Morioka Physica C, 2001

FIB fabricated Bi-2212 mesa, L=1.4 µm, s=1.5 nm, ∆H=1 T

DC Intrinsic Josephson effect

ehc

sLHx

xxIHI cc

2

sin)0()(

0

0

=Φ

Φ=

=

π

AC Intrinsic Josephson effect

H.B. Wang, T. Yamashita, P.H. Wu, PRL 2001

Quasiparticle tunneling over a gap: multibranched IVs, gap/pseudogap spectroscopy

Yu.I. Latyshev et al.ISS Conf. 1999, Physica C, 2001; V.M. Krasnov et al. PRL, 2000, 2001

NbSe3 Tp1=145K

Tp2=59K

Crystal structure

Interlayer transport in CDW compounds

The elementary prisms are assembled in elementary conducting layers with higher density of conducting chains (shaded layers in a figure) separated by a double barrier of insulating prism bases. That results in a very high interlayer conductivity anisotropy σa*/σb ~ 10-3 at low temperatures compared with intralayer anisotropy σc/σb ~ 10-1.

That provides the ground for interlayer tunneling spectroscopy of CDW layered materials..

-300 -200 -100 0 100 200 3000.8

1

10

50

4.2K 6K 8K 10K 12K 14K 16K 18K 20K 22K 24K 26K 28K 30K 32K 35K 40K 45K 50K 55K 60K 65K 70K 75K 80K 85K 90K 95K 100K 105K 110K 115K 120K 125K 130K 135K 140K 145K 150K 160K 170K

dI/d

V (k

Ohm

-1)

V (mV)

NbSe3 N1

-150 -100 -50 0 50 100 150 V (mv)

0 50 100 1500.0

0.5

1.0

1.5

S(T)

/S(1

60K)

T (K)

# 1

2∆1

2∆2

Temperature evolution of the spectra

4.2К→ 170К

Stacked junction behaves as a single junction. We consider that as the weakest junction in the stack.

0 20 40 60 80 100 120 140 1600

20

40

60

80

40 50 60 700.0

0.2

0.4

0.6

0.8

1.0

1.2

δ∆1,

∆ 2, ∆2 2,

norm

. unit

s

T (K)

α∗δ∆1

∆2

(∆2)2

∆ (m

V)

T(K)

∆1

∆2

NbSe3

BCS

δ∆1

Comparison with other techniques STM 70 190 Z.Dai et al. PRB 92, Optics 70 - A. Perucci et al. PRB 2004 ARPES 90 - J. Schafer et al. PRL 2003 MC 60 140 A.A. Sinchenko and P. Monceau PRB 2007

Intragap states

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.522

24

26

282∆1

2∆1/3

dI/d

V (k

Ohm

-1)

V/2∆1

T=100 K

Vt

CDWπ-soliton is a kind of atomic scale π-junction

The order parameter in the ground state is ∆0 =A cos (Qx + ϕ) with Q the CDW wave vector Q = 2kF and ϕ the arbitrary phase in the ICDW state and A=const. That means that ground state is degenerated with respect to A ↔ -A.

That leads to the possibility of configuration with accepting of one electron and formation of new ground state with A=tanh (x/ξ0) called amplitude soliton (AS).

AS is a self-localized state with an energy

Es= 2∆0 /π S.A. Brazovskii, Sov. Phys.-JETP, 1980

This state is more preferable since its energy is smaller than the lowest energy ∆0 of the free band electron by ≈∆0/3.

Yu.I. Latyshev, P. Monceau, S. Brazovskii, A.P. Orlov, Th. Fournier, PRL 2005, 2006

Magnetic field induced CDW state in NbSe3

magnetic field may increase CDW gap C.A. Balseiro and L.M. Falikov PR B 1986

Q Q

2K F 2K F

perfe c t im perfe c t

H=0 H

mechanism is related with improvement of CDW nesting by magnetic field L.P. Gor’kov and A. Lebed, 1984

A. Bjelis, D. Zanchi, G. Montambeaux PR B 1996 - also have shown the possibility to increase Tp by magnetic field.

(theory)

Interlayer tunneling spectra at pulsed magnetic field

LNCMP, Toulouse

Sweep current

~50ms

Field start

Field finish

55T

0.5ms Start DAC, 3 ADC

Stop DAC, 3 ADC

kth tr. pulse

~350ms

Full measurement time 500ms

H

I

~60ms

1000 IV

t

t

V

I, dI/dV

Fm=2MHz 1000 points in IV for Hk

+Imax

-Imax

Hmax

High speed acquisition system

0.00 4.92 9.79 14.73 19.65 24.40 29.31 34.38 39.05 44.00 48.93 53.71

T=65K Н+ layers

Н // layers

Field induceed CDW state

Non-monotonic behaviour of Tp(H) is defined by interplay between orbital and Pauli effects on CDW pairing. Orbital effect is realized in improving of nesting condition and, thus, in increase of ∆ and Tp, while Zeeman shift tends to destroy CDW pairing.

Experimental crossover field corresponds to H ≈ 30T, 2µBH0 ≈ kTp

is consistent with calculatons of Zanchi, Bjelis, Montambeau PRB 1996

Field induced CDW (?) gap in graphite

Observation H. Ochimizu et al., Phys. Rev. B46, 1986 (1992). Explanation was related with the CDW formation along the field axis D. Yoshioka and H. Fukuyama, J. Phys. Soc. Jpn. 50, 725 (1981).

We attempted to find CDW gap above 30 T

0 5 10 15 20 25 30 35 40 45 50 55 600

200

400

600

800

1000

1200

R (O

hm)

H (T)

G1 G3

Graphite mesa

T=1.4K

Effect nearly disappeares for 20 graphene layers

That means that it does not relate with individual graphene layers

Field induced CDW ?

The pictures for both compounds look very similar as well as the values of field induced gap are close 50-70 mV

graphite NbSe3

Phase diagram of the field induced CDW state in graphite

2∆/To = 3.1-3.5 close to the BCS value as in field induced CDW state in NbSe3.

The data are consistent with recent Hall effect data in graphite A. Kumar et al., J. Phys.: Condens. Matter 22(2010) 436004.

Yu.I. Latyshev, A.P.Orlov, P, Monceau, D.Vignolles, and W, Escscoffier, Physica B, 2012.

Coherent nonlinear transport across the chains in NbSe3 under perpendicular magnetic fields.

-200 -150 -100 -50 0 50 100 150 2001.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

dI/d

V(sm

)

V(mV)

F=108 MHzB=16 T

7 K

30 K

NbSe3 c-axis

Welcome to poster

FeSe a simple crystal structure consisting of the FeSe layer essential building block responsible for the superconductivity in the iron-based superconductors. Tc≈ 8 K at ambient pressure. structural tetragonal to orthorhombic transition around 90 K but without a magnetic transition

dramatic pressure dependence Tc enhanced up to 36.7 K under high pressure. Medvedev, et al., Nat. Mater. 8, 630 (2009) static magnetic order is observed M. Bendele et al., J Supercond Nov Magn 27, 965 (2014)

discovery of high temperature superconductivity in the single-layer FeSe/SrTiO3 films (Тс > 100 К) Ge, J.-F. et al. Nat. Mater. 14, 285-289 (2015).

Structures

two types of structures have been fabricated by the focused ion beam (FIB)

А in-plane bridge with a length 20 μm, width 2 μm and thickness equal to single crystal thickness.

B a bridge oriented transverse the layers (along c-axis) with a typical sizes 2μm × 2μm × 0.2 μm.

Experimental results

0 100 200 3000,00

0,02

0,04

ρ c (O

hm/c

m2 )

T (K)

0,0

1,0x10-4

2,0x10-4

3,0x10-4

ρ ab (O

hm/c

m2 )

50 100 150 200 250 300

200

300

400

500

ρ c/ρ(a

b)

T (K)

Temperature dependence of resistance. Anisotropy.

А B At room temperature ρc/ρab = 160-180; it increases with temperature and achieves ~ 500 at T = 12K.

growth of anisotropy in two stage:

-in the temperature range 300-90 K with the rate 0.25 – 0.30 K-1 and below 90 K the rate of growth increases more then order of magnitude and achieves 2.5-3.0 K-1

-0,02 -0,01 0,00 0,01 0,02

-0,005

0,000

0,005I (A)

V (V)

8.5 K 9.0 K10.0 K

0,0 2,0x10-5 4,0x10-50,0

4,0x104

8,0x104

j (A/c

m2 )

V (V)

T=8 K

I//c

I//(a,b)

10 150

2

4

6

R c (O

hm)

T (K)0,0

0,5

1,0

1,5

R ab (O

hm)

Experimental results Superconducting properties

In the direction transverse to layers superconductivity is stronger compare with intralayer superconductivity.

B A

no weak superconductivity and intrinsic Josephson effect

Tc and critical current density for B-type structures are larger

Fluctuation region

10 153

4

5

R c (Oh

m)

T (K)0.5

1.0

R ab (O

hm)

Normal state V=IR Joule heating V=I(R+ΔR)

linear R(T): dV/dI ~ V2

Supeconducting fluctuations excess conductivity deviation from square low

Fluctuation effects. A-type structures.

Experimental results

-0,010 -0,005 0,000 0,005 0,0101,2

1,4

1,6

1,8

2,0

10 K 12 K 14 K 16 K

dV/d

I (O

hm)

V (V)0 20 40 60 80

1.2

1.6

2.0

10 K 12 K 14 K 16 K

dV/d

I (O

hm)

V2 (mV2)

-4 -2 0 2 4

0.00

0.04

0.08

10 K 12 K 14 K 16 K

∆G (O

hm-1

)

I (mA)

-0,04 -0,02 0,00 0,02 0,046

8

10

dV/d

I (O

hm)

V (V)

25 K20 K

16 K

0,000 0,001 0,002 0,003

8

12

10K 12K 14K 16K 18K 20K 22K 25K 30K 35K

dV/d

I (O

hm)

V2 (V2)

-0.004 -0.002 0.000 0.002 0.004

0.00

0.02

0.04

0.06

0.08

10K 12K 14K 16K 18K 20K 22K 25K 30K 35K∆G

(Ohm

-1)

I (A)

Fluctuations or superconducting inclusions

???

Fluctuation effects. B-type structures. Experimental results

20 40 60

300

400

500

T (K)

ρ c/ρ(a

b)Indications of superconducting transition with Tc>40 K

How ???

35 40 45 50 550.16

0.18

0.20

0.22

dR/dT (Ohm/K)

T (K)

35 40 45 50

10

12

R c (O

hm)

T (K)2

3

R ab (O

hm)

0 50 100

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

10 100

10-3

10-2

4πχ'

T (K)

N ~ 0.5

-4πχ

'

T (K)

the existence of one-dimensional and two-dimensional 2D metallic domains with a crossover from a filamentary superconductivity mostly along the c axis to a 2D superconductivity in the bc-plane perpendicular to the most conducting direction. The formation of these domain walls may be related to the proposal of a soliton phase in the vicinity of the critical pressure of the TMTSF2PF6 phase diagram.

FeSe – the same???

model

two parallel ways for interlayer current to flow:

and the total conductivity is approximately a sum of two parts:

In the frame of such model:

Depending on the ratio η/φ the first or second part makes the main contribution to the interlayer conductivity in such inhomogeneous media.

In the limit of rare superconducting granules the volume fraction of superconducting islands φ≪ 1,

Maxwell’s approximation (1873)

conductivity in anisotropic media can be mapped to the problem of isotropic media with anisotropic coordinate dilations

spherical inclusions inside anisotropic media transform to elongated ellipsoids with axis ratio az/ax = 1/√η = σxx/σzz ≫ 1

anisotropy

the isotropic 3-dimensional media of conductivity σ1 with spherical inclusions (granules) of conductivity σ2 with small volume fraction φ≪ 1

Volume fraction of superconducting islands

10 15 20 25 30 35 40 455055

10-4

10-3

10-2

φ

T (K)Transport measurements Magnetic measurements

If inhomogeneous superconductivity in a anisotropic conductor first appears in the form of isolated superconducting islands, it reduces electric resistivity anisotropically with maximal effect along the least conducting axis.

General property ???

Inhomogeneous superconductivity in another compounds

LSCO Iguchi et al. (2001) Tl2Ba2CuO6+δ (Tc = 15K) Bergemann et al. (1998)

Pr-Doped CaFe2As2 Krzysztof Gofryk et al. 2014

organic superconductors (TMTSF)2PF6

(N. Kang et al. 2010) (TMTSF)2ClO4

(Ya. A. Gerasimenko et al. 2014)

YBa2Cu4O8 (N. E. Hussey et al. 1997)

Superconductivity in these compounds, probably, first appear in the form of small isolated superconducting islands,

which become connected and coherent with decreasing temperature

SUMMARY

The interlayer tunneling spectroscopy has been developed on a number of layered materials. Main results:

1. Intrinsic Josephson effects has been demonstrated on mesa type

structures of HTSC layered superconductors.

2. Energy gap has been studied in CDW compounds. We found intra gap states associated with excitation of amplitude and phase CDW solitons in NbSe3.

3. We found and studied magnetic field induced CDW states in NbSe3 and graphite predicted long time ago.

4. We found inhomogeneous (gossamer) high-T superconductivity in FeSe .