^{1,a)}and K. Y. Constantinian

^{1}

### Abstract

Electron transport and microwave properties of cuprate superconducting structures (bicrystal junctions and hybrid mesa heterostructures) are discussed here. Superconducting current in junctions from cuprate superconductors with the dominant *d _{x} *

^{2}

_{−}

_{ y }

^{2}-wave symmetry is determined by the barrier properties, characterized by the mid-gap bound states due to the multiple Andreev reflection. In bicrystal junctions it is revealed via linear dependence of critical current density on square root of the transparency, and an increase of spectral density of shot noise at low voltages are observed. The experiments demonstrate that the superconducting hybrid mesa-heterostructures have the critical current density

*j*= 1–700 A/cm

_{с}^{2}for an antiferromagnetic interlayer with thickness

*d*= 10–50 nm and the characteristic decay length of superconducting correlations on the order of 7 nm, due to the anomalous long range proximity effect, analyzed in the model of coupled superconductors via multilayer magnetic layer with antiferromagnetic ordering of magnetization in the layers. It is found that the hybrid mesa–heterostructures have much greater sensitivity to external magnetic field than conventional Josephson junctions because of the strong dependence of superconducting current on interlayer spin state.

_{M}We thank I. V. Borisenko, D. Winkler, V. V. Demidov, A. V. Zaitsev, Yu. V. Kislinsky, A. Kalabukhov, F. V. Komissinsky, V. K. Kornev, E. Myugind, A. M. Petrzhik, I. I. Soloviev, A. V. Shadrin for the help in conducting the experiment and the useful discussion. The study was supported through the OFN RAS ad the RAS Presidium programs, by the Ministry of Education and Science of Russia (Grant 02.740.11.0795), the Russian Presidential grant: Leading Scientific School (Grant NSh-2453.2012.2), by the project RFFI-11-02-01234 a, and Visby—the program of Russian-Swedish cooperation.

I. INTRODUCTION

II. ANDREEV STATES AND THE JOSEPHSON EFFECT IN SUPERCONDUCTING BICRYSTAL JUNCTIONS FROM CUPRATE SUPERCONDUCTORS

A. Experimental method

B. Electrophysical properties of bicrystal junctions

C. Current-phase relation of superconducting current

D. Shot noise in bicrystal junctions

III. HYBRID JOSEPHSON HETEROSTRUCTURES WITH AN ANTIFERROMAGNETIC LAYER

A. Experimental method

B. The superconducting current in HMS

C. The current-phase relation

D. Magnetic-field dependence

IV. CONCLUSION

### Key Topics

- Josephson junctions
- 41.0
- Superconductivity
- 37.0
- Critical currents
- 19.0
- Magnetic fields
- 16.0
- Superconductivity models
- 15.0

## Figures

Phase dependence of the Andreev levels in the tunnel junctions of S-superconductors (solid line) and low-energy Andreev levels of D-superconductors (dotted line) in the transparency of the boundary *D* = 0.1. The inset shows a diagram of the bicrystal junction of two D-superconductors with a symmetrical misorientation of axes and the direction of incidence of electrons and holes.

Phase dependence of the Andreev levels in the tunnel junctions of S-superconductors (solid line) and low-energy Andreev levels of D-superconductors (dotted line) in the transparency of the boundary *D* = 0.1. The inset shows a diagram of the bicrystal junction of two D-superconductors with a symmetrical misorientation of axes and the direction of incidence of electrons and holes.

The dependence of energies of the Andreev levels on the angle of incidence θ of quasiparticles with phase difference ϕ = π for three values of angle α, which is the angle of misorientation of bicrystal rotational junctions of D-superconductors

The dependence of energies of the Andreev levels on the angle of incidence θ of quasiparticles with phase difference ϕ = π for three values of angle α, which is the angle of misorientation of bicrystal rotational junctions of D-superconductors

Schematic representation of two types of bicrystal junctions: rotational (*a*) and tilted (*b*). The solid line indicates the bicrystal boundary, dotted line – the normal to the boundary or the plane of the substrate, shading is used to show the direction of the layers in cuprate superconductors.

Schematic representation of two types of bicrystal junctions: rotational (*a*) and tilted (*b*). The solid line indicates the bicrystal boundary, dotted line – the normal to the boundary or the plane of the substrate, shading is used to show the direction of the layers in cuprate superconductors.

Current-voltage characteristics of the bicrystal junction at *T* = 4.2 K. The inset on the left shows temperature dependences of the critical current *I _{c} *(

*T*) and the resistance of the junction. The inset on the right shows the dependence of the critical current (

*j*) density on the characteristic resistance of the boundary

_{c}*R*

_{N}S.Current-voltage characteristics of the bicrystal junction at *T* = 4.2 K. The inset on the left shows temperature dependences of the critical current *I _{c} *(

*T*) and the resistance of the junction. The inset on the right shows the dependence of the critical current (

*j*) density on the characteristic resistance of the boundary

_{c}*R*

_{N}S.Dependences of the Shapiro steps (the first *n* = 1 and the fractional *n* = 1/2) on the amplitude of the external electromagnetic radiation of frequency *f _{e} * = 100 GHz when

*T*= 4.2 K for two tilt angles of the bridge forming the TBJ. The dotted line represents dependences calculated within the framework of the resistive model for

*I*(ϕ) =

_{S}*I*sinϕ, the solid line represents

_{c}*I*(ϕ) = (1−

_{S}*q*)

*I*sinϕ +

_{c}*qI*sin 2ϕ,

_{c}*q*= 0.2. The inset shows the corresponding dependences of

*I*(ϕ) for

_{S}*q*= 0.2 (solid line) and

*q*= 0 (dotted line).

Dependences of the Shapiro steps (the first *n* = 1 and the fractional *n* = 1/2) on the amplitude of the external electromagnetic radiation of frequency *f _{e} * = 100 GHz when

*T*= 4.2 K for two tilt angles of the bridge forming the TBJ. The dotted line represents dependences calculated within the framework of the resistive model for

*I*(ϕ) =

_{S}*I*sinϕ, the solid line represents

_{c}*I*(ϕ) = (1−

_{S}*q*)

*I*sinϕ +

_{c}*qI*sin 2ϕ,

_{c}*q*= 0.2. The inset shows the corresponding dependences of

*I*(ϕ) for

_{S}*q*= 0.2 (solid line) and

*q*= 0 (dotted line).

Current-voltage characteristics for a symmetrical RBJ at *T* = 4.2 K (dotted line) and the noise power *P _{N} *(

*V*), given in degrees Kelvin (solid line). The dot-dashed line represents the dependence of shot noise

*T*(

_{SH}*V*) = (

*e*/2

*k*)

_{B}*I*(

*V*)

*R*. The inset shows the dependence of the effective charge

_{D}*Q*(

*V*) =

*S*(

_{I}*V*)/2

*I*in units of electron charge.

Current-voltage characteristics for a symmetrical RBJ at *T* = 4.2 K (dotted line) and the noise power *P _{N} *(

*V*), given in degrees Kelvin (solid line). The dot-dashed line represents the dependence of shot noise

*T*(

_{SH}*V*) = (

*e*/2

*k*)

_{B}*I*(

*V*)

*R*. The inset shows the dependence of the effective charge

_{D}*Q*(

*V*) =

*S*(

_{I}*V*)/2

*I*in units of electron charge.

(a) Cross section of the heterostructure with an AF (CSCO) interlayer, marked with the letter M. The thicknesses of the layers: YBCO–200 nm, CSCO–20-50 nm, Au–10-20 nm, Nb–200 nm. (b) A photograph of HMS from the top. The light color represents superconducting electrodes of the log-periodic antenna.

(a) Cross section of the heterostructure with an AF (CSCO) interlayer, marked with the letter M. The thicknesses of the layers: YBCO–200 nm, CSCO–20-50 nm, Au–10-20 nm, Nb–200 nm. (b) A photograph of HMS from the top. The light color represents superconducting electrodes of the log-periodic antenna.

Experimental data on the dependence of the density of superconducting current on the thickness for an HMS with an interlayer of CSCO (stars) *x* = 0.5. Filled circles correspond to heterotransitions without the M-interlayer. The dashed lines show the theoretical dependences of critical current on the thickness of the AF-interlayer for three values of normalized exchange field *H* _{ex}/π*k _{B}T*: 2 (

*1*), 5 (

*2*), 10 (

*3*). The normalization of the theoretical dependence in the critical current value and the interlayer thickness was chosen from the condition of best fit to the theory of experiment ξ

_{ AF }= 10 nm.

Experimental data on the dependence of the density of superconducting current on the thickness for an HMS with an interlayer of CSCO (stars) *x* = 0.5. Filled circles correspond to heterotransitions without the M-interlayer. The dashed lines show the theoretical dependences of critical current on the thickness of the AF-interlayer for three values of normalized exchange field *H* _{ex}/π*k _{B}T*: 2 (

*1*), 5 (

*2*), 10 (

*3*). The normalization of the theoretical dependence in the critical current value and the interlayer thickness was chosen from the condition of best fit to the theory of experiment ξ

_{ AF }= 10 nm.

(a) The family of CVC HMS at various values of the power of microwave impact and *T* = 4.2 K. The thin line shows the envelope of the critical current, arrows show the first (*hf _{e} */2

*e*) and fractional (

*hf*/4

_{e}*e*) Shapiro steps. (b) The dependence of critical current

*I*(circles) and the first Shapiro step

_{c}*I*

_{1}(triangles) on the normalized amplitude

*I*/

_{e}*I*of external influence of millimeter radiation with frequency of 56 GHz for

_{c}*T*= 4.2 K. The dashed line shows the theoretical dependence

*I*

_{1}(

*I*/

_{e}*I*), obtained from the resistive model of JJ. The solid line shows the calculated dependences calculated with the second CPR harmonic in mind for

_{c}*q*= 0.2.

(a) The family of CVC HMS at various values of the power of microwave impact and *T* = 4.2 K. The thin line shows the envelope of the critical current, arrows show the first (*hf _{e} */2

*e*) and fractional (

*hf*/4

_{e}*e*) Shapiro steps. (b) The dependence of critical current

*I*(circles) and the first Shapiro step

_{c}*I*

_{1}(triangles) on the normalized amplitude

*I*/

_{e}*I*of external influence of millimeter radiation with frequency of 56 GHz for

_{c}*T*= 4.2 K. The dashed line shows the theoretical dependence

*I*

_{1}(

*I*/

_{e}*I*), obtained from the resistive model of JJ. The solid line shows the calculated dependences calculated with the second CPR harmonic in mind for

_{c}*q*= 0.2.

(a) The magnetic field dependence of the critical current *I _{c} *(

*H*) (circles) for a HMS containing CSCO (

*x*= 0.5),

*d*= 50 nm, and

_{M}*L*= 10

*μ*m at

*T*= 4.2 K. The solid line represents the dependence of Eq. (3) under the normalization

*I*(0) =

_{c}*I*

_{c}^{0}. Dashed line shows calculated Fraunhofer dependence for

*L*= 10

*μ*m and London penetration depths λ

_{ L }

_{1}= 150 nm and λ

_{ L }

_{2}= 90 nm for YBCO and Nb, respectively. Filled circles – experimental data for a heterostructure without AF-interlayer with

*L*= 50

*μ*m. Inset: model

^{50}for an S–AF–S JJ. (b) Dependence of the first minimum

*H*

_{1}on the magnitude of HMS: without an AF-interlayer for a perpendicularly directed field (◯), for the parallel field (•); HMS with

*d*= 50 nm for a perpendicular field (□), for a parallel field (▪),

_{M}*d*= 20 nm (▵); solid line—approximation of the 1/

_{M}*L*type.

(a) The magnetic field dependence of the critical current *I _{c} *(

*H*) (circles) for a HMS containing CSCO (

*x*= 0.5),

*d*= 50 nm, and

_{M}*L*= 10

*μ*m at

*T*= 4.2 K. The solid line represents the dependence of Eq. (3) under the normalization

*I*(0) =

_{c}*I*

_{c}^{0}. Dashed line shows calculated Fraunhofer dependence for

*L*= 10

*μ*m and London penetration depths λ

_{ L }

_{1}= 150 nm and λ

_{ L }

_{2}= 90 nm for YBCO and Nb, respectively. Filled circles – experimental data for a heterostructure without AF-interlayer with

*L*= 50

*μ*m. Inset: model

^{50}for an S–AF–S JJ. (b) Dependence of the first minimum

*H*

_{1}on the magnitude of HMS: without an AF-interlayer for a perpendicularly directed field (◯), for the parallel field (•); HMS with

*d*= 50 nm for a perpendicular field (□), for a parallel field (▪),

_{M}*d*= 20 nm (▵); solid line—approximation of the 1/

_{M}*L*type.

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