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Could exist the Abrikosov vortex state in type-II superconductors without pinning?
Physlca C 235-240 (1994) 1945-1946
PHYSlCA
North-Holland
Could exist the Abrikosov vortex state in type-ll superconductors without p i n n i n g ? A.V.Nikulov ~, D.Yu.Remisova, and V.A.Oboznov b ~Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russian Federation. blnstitute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russian Federation The resistive properties of thin NbO, films above and below H~2 were investigated experimentally, it was shown that in thin amorphous films the vortex pinning appears much below H~> The position of the vortex pinning appearance moves up to He2 with film thickness increase and pinning value increase. A nonperturbative fluctuation theory of the mixed state of two-dimensional type-II superconductor in the lowest Landau level (LLL) approximation is proposed. 1. I N T R O D U C T I O N The results o f Maki-Takayama [1] theory have recently been the subject of an intense interest[2,3] It is followed from [|] that the thermal fluctuations destroy off-diagonal long-range order in the mixed state of type-ll superconductors. Since the offdiagonal long-range order is destroyed by the longwavelength fluctuations, any pinning of the flux l,nes by disorder will inhibit and slow the fluctuatmns. Therefore the fluctuatmn effects must be investigated on samples with weak pinning. It ~s followed from Maki-Takayama theory that for bulk sample of real size the fluctuatmn value Is big at H~2 only whereas for two- dlmensmnal superconductor one is big almost in whole mixed state region. The bulk superconductors with weak pinning we investigated earlier [4-7]. It was shown that the vortex pinning appears below H~2 on some percent [4,6] It take place at narrow transition [5,7] which we connect with transition into the Abrikosov vortex state [8]. Above the narrow transition the experimental dependencies are described very well by paraconductwity theory [5,7]. In this work thm films with weak pinning are investigated. The non-perturbatwe theory of fluctuation effects in mixed state of two-dlmensmnal type-ll superconductors m the lowest Landau level approximation is proposed m this work also.
gen contents x = 0 08-0 20 and 7",=5 7-2 K were investigated. At x=0.08 the film has small gram structure and at x=20 it is amorphous. The investigation shown that the paracopductlvity dependenmes above He2 m the hnear approximation region are well described by Am>Makl theory [9] adapted to a two-dimensional superconductors by one fit parameter Hc~ (T=0) From the characteristms of the IV curves three different B-T regimes can be dlstinguished [5,101tl) A high-field regime with zero cntmal current and ohmic i-V characteristms (2) A intermediate field regime m whmh the I-V behavior is hnear both at small and large current (3) A lowfield pmmng regime w~th a nondetcctable voltage below a fintte critical current The position of the (2) regime depends on film thmkness and on pinning value of the films. We have discovered that this position move down to very low magnetic field m thin (20 nm) amorphous Nb0sz O018 film. For example at T=I 6 K (T~ =2.3 K) the (2) regime take place at 80 Oe>H>10 Oc whereas H~:=16500 Oe m this case For excess conductivity dependencies m the (!) regnne a scahng law is observed These dependenctes are close to theorencal paracondactwity dependences obtained m Itartree appm-,lmatlon With film thmkness m~rcasc and with pruning valae increase the (2) re,,m, po~,ltlon nlo'v~_ up Io
2.EXPERIMENT The measurements was made on NbO~ films produced by magnetron sputtering of Nb in atmosphere of argon and oxygen The films wtth oxy0921-4534D4/S07 00 © 1994 - Elsevier Science B V. All nghts reserved SSD! 0921-4534(94)01539-2
H~2 •
It Is obvious that the (2~ regime is connected with the vortex pinmng appearance We think that the vortex pinning appearance is connected with a trans~tmn into Abnkosov vortex state This oplmon is based on Mak>Takayama theory results and on our theor3, written briefly below
1946
A, V Nikuloo et al IPhysica C 235-240 (1994) 1945-1946
3.THEORY In the lowest Landau level (LLL) approximation the GL free energy functional for two-dimensional superconductor may be write as [ 1 ! ]
L
¢
. - . - - -a
_j
/ (0)" V is the Ginsburg n u m b e r ; t = / T T ~~ ;h = H __/H,2 film area; [q~2 = I//V I d zrlv] 2 is the spatial average order parameter; I$<, = N'I a / l ' ~ 2 is the generalized Abnkosov parameter We use a dimensionless unit system in which cbo/H = I ~0 is the flux quantum Taking into account a entropy connected with I~l "~ and !3o values we obtain a new free energy expression
FCL k~T
= lvi + l__n,, 2
- nl@ - In S(n,, -
) (2)
The exact thermodynamic everages of the [qj~ and 13<, values are close to values corresponded to the Fx,,. mimmum 13 r = I [59.
I(
.
]:+ 1
2
<
7
(3)
(4)
The (3) relation coincide with one obtained in [1 I] At [3<,-13, <<1, f(~,,-pA4)~[3,,-pS1 Consequently below the H~2 critical region, at-a >> I
(5)
The Ginsburg number values of conventional type-I1 superconductors lie in the interval I0 11 < G~ < 10-5 . Therefore in the center of the mixed state region, at
t=O.5, h=0.25,
10 -5 < ( [ 3 < , - ~ 4 ) < i 0 -2 It may be shown that a critical [3,,- t3~ value exist. Below this value all states are situated near the Abrikosov solution whereas above one states exist which are distant from the Abrikosov solution. We suppose that this critical [3,,- [3A value determines the transition into Abrikosov vortex state. This value depends on a film area and is very small for a film area usually used by experimental investigations. Therefore the Abrikosov vortex state may be only at low T in the film without pinning. The pinning decreases a effective area and the transition into Abrikosov vortex state moves up to H¢2 This work is supported by the National Scientific Council on High Temperature Superconductivity, Project 93195. A.V.N. thanks the International Science Foundation for financial support.
REFERENCES 1. K.Makl and H.Takayama, Progr.Theor.Phys, 46 (1971) 1651 2. A.Houghton, R A Pelcovlts, A Sudbo, Phys.Rev. B42, (1990) 906 3 M.A Moore, Phys Rev B45, (1992) 7a36, R ikeda, T.Ohmi, T.Tsuneto J of Phys Society of Japan, 61 (1992) 254: G G.Sergeeva, FIz.Nizk. Temp., 20 (1994) 3. 4 V A.Marchenko and A V Nikulov, Soy Phys JETP, 53 (1981) 377. 5 V.A Marchenko and A.V.Nikulov, JETP Lett, 34 (1981) 17 6 V A Marchenko and A V Ntkulov, Soy Phys.JETP, 59 (1984) 815 7 V A Marchenko and A V Nlkulov, Physica C, 210 (1993) 466 8. A V Nikulov, Supercond.Sci Technol., 3 (1990) 377 9 S Aml and K MaM, Phys Rev. B18 (1978) 4714 !O P Berghu,s and P H Kes, Phys Rev B4'7 (1993) 262 1 I Zlatko l esanovm and A V Andrcev, Phys Rev B49 (1994) 4064
PHYSlCA
North-Holland
Could exist the Abrikosov vortex state in type-ll superconductors without p i n n i n g ? A.V.Nikulov ~, D.Yu.Remisova, and V.A.Oboznov b ~Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russian Federation. blnstitute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russian Federation The resistive properties of thin NbO, films above and below H~2 were investigated experimentally, it was shown that in thin amorphous films the vortex pinning appears much below H~> The position of the vortex pinning appearance moves up to He2 with film thickness increase and pinning value increase. A nonperturbative fluctuation theory of the mixed state of two-dimensional type-II superconductor in the lowest Landau level (LLL) approximation is proposed. 1. I N T R O D U C T I O N The results o f Maki-Takayama [1] theory have recently been the subject of an intense interest[2,3] It is followed from [|] that the thermal fluctuations destroy off-diagonal long-range order in the mixed state of type-ll superconductors. Since the offdiagonal long-range order is destroyed by the longwavelength fluctuations, any pinning of the flux l,nes by disorder will inhibit and slow the fluctuatmns. Therefore the fluctuatmn effects must be investigated on samples with weak pinning. It ~s followed from Maki-Takayama theory that for bulk sample of real size the fluctuatmn value Is big at H~2 only whereas for two- dlmensmnal superconductor one is big almost in whole mixed state region. The bulk superconductors with weak pinning we investigated earlier [4-7]. It was shown that the vortex pinning appears below H~2 on some percent [4,6] It take place at narrow transition [5,7] which we connect with transition into the Abrikosov vortex state [8]. Above the narrow transition the experimental dependencies are described very well by paraconductwity theory [5,7]. In this work thm films with weak pinning are investigated. The non-perturbatwe theory of fluctuation effects in mixed state of two-dlmensmnal type-ll superconductors m the lowest Landau level approximation is proposed m this work also.
gen contents x = 0 08-0 20 and 7",=5 7-2 K were investigated. At x=0.08 the film has small gram structure and at x=20 it is amorphous. The investigation shown that the paracopductlvity dependenmes above He2 m the hnear approximation region are well described by Am>Makl theory [9] adapted to a two-dimensional superconductors by one fit parameter Hc~ (T=0) From the characteristms of the IV curves three different B-T regimes can be dlstinguished [5,101tl) A high-field regime with zero cntmal current and ohmic i-V characteristms (2) A intermediate field regime m whmh the I-V behavior is hnear both at small and large current (3) A lowfield pmmng regime w~th a nondetcctable voltage below a fintte critical current The position of the (2) regime depends on film thmkness and on pinning value of the films. We have discovered that this position move down to very low magnetic field m thin (20 nm) amorphous Nb0sz O018 film. For example at T=I 6 K (T~ =2.3 K) the (2) regime take place at 80 Oe>H>10 Oc whereas H~:=16500 Oe m this case For excess conductivity dependencies m the (!) regnne a scahng law is observed These dependenctes are close to theorencal paracondactwity dependences obtained m Itartree appm-,lmatlon With film thmkness m~rcasc and with pruning valae increase the (2) re,,m, po~,ltlon nlo'v~_ up Io
2.EXPERIMENT The measurements was made on NbO~ films produced by magnetron sputtering of Nb in atmosphere of argon and oxygen The films wtth oxy0921-4534D4/S07 00 © 1994 - Elsevier Science B V. All nghts reserved SSD! 0921-4534(94)01539-2
H~2 •
It Is obvious that the (2~ regime is connected with the vortex pinmng appearance We think that the vortex pinning appearance is connected with a trans~tmn into Abnkosov vortex state This oplmon is based on Mak>Takayama theory results and on our theor3, written briefly below
1946
A, V Nikuloo et al IPhysica C 235-240 (1994) 1945-1946
3.THEORY In the lowest Landau level (LLL) approximation the GL free energy functional for two-dimensional superconductor may be write as [ 1 ! ]
L
¢
. - . - - -a
_j
/ (0)" V is the Ginsburg n u m b e r ; t = / T T ~~ ;h = H __/H,2 film area; [q~2 = I//V I d zrlv] 2 is the spatial average order parameter; I$<, = N'I a / l ' ~ 2 is the generalized Abnkosov parameter We use a dimensionless unit system in which cbo/H = I ~0 is the flux quantum Taking into account a entropy connected with I~l "~ and !3o values we obtain a new free energy expression
FCL k~T
= lvi + l__n,, 2
- nl@ - In S(n,, -
) (2)
The exact thermodynamic everages of the [qj~ and 13<, values are close to values corresponded to the Fx,,. mimmum 13 r = I [59.
I(
.
]:+ 1
2
<
7
(3)
(4)
The (3) relation coincide with one obtained in [1 I] At [3<,-13, <<1, f(~,,-pA4)~[3,,-pS1 Consequently below the H~2 critical region, at-a >> I
(5)
The Ginsburg number values of conventional type-I1 superconductors lie in the interval I0 11 < G~ < 10-5 . Therefore in the center of the mixed state region, at
t=O.5, h=0.25,
10 -5 < ( [ 3 < , - ~ 4 ) < i 0 -2 It may be shown that a critical [3,,- t3~ value exist. Below this value all states are situated near the Abrikosov solution whereas above one states exist which are distant from the Abrikosov solution. We suppose that this critical [3,,- [3A value determines the transition into Abrikosov vortex state. This value depends on a film area and is very small for a film area usually used by experimental investigations. Therefore the Abrikosov vortex state may be only at low T in the film without pinning. The pinning decreases a effective area and the transition into Abrikosov vortex state moves up to H¢2 This work is supported by the National Scientific Council on High Temperature Superconductivity, Project 93195. A.V.N. thanks the International Science Foundation for financial support.
REFERENCES 1. K.Makl and H.Takayama, Progr.Theor.Phys, 46 (1971) 1651 2. A.Houghton, R A Pelcovlts, A Sudbo, Phys.Rev. B42, (1990) 906 3 M.A Moore, Phys Rev B45, (1992) 7a36, R ikeda, T.Ohmi, T.Tsuneto J of Phys Society of Japan, 61 (1992) 254: G G.Sergeeva, FIz.Nizk. Temp., 20 (1994) 3. 4 V A.Marchenko and A V Nikulov, Soy Phys JETP, 53 (1981) 377. 5 V.A Marchenko and A.V.Nikulov, JETP Lett, 34 (1981) 17 6 V A Marchenko and A V Ntkulov, Soy Phys.JETP, 59 (1984) 815 7 V A Marchenko and A V Nlkulov, Physica C, 210 (1993) 466 8. A V Nikulov, Supercond.Sci Technol., 3 (1990) 377 9 S Aml and K MaM, Phys Rev. B18 (1978) 4714 !O P Berghu,s and P H Kes, Phys Rev B4'7 (1993) 262 1 I Zlatko l esanovm and A V Andrcev, Phys Rev B49 (1994) 4064