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JETP Letters, Vol. 71, No. 11, 2000, pp. 473­476. From Pis'ma v Zhurnal èksperimental'nooe i Teoreticheskooe Fiziki, Vol. 71, No. 11, 2000, pp. 693­697. Original English Text Copyright © 2000 by Gantmakher, Golubkov, Dolgopolov, Shashkin, Tsydynzhapov.

Observation of the Parallel-Magnetic-Field-Induced Superconductor­Insulator Transition in Thin Amorphous InO Films1
V. F. Gantmakher, M. V. Golubkov, V. T. Dolgopolov, A. A. Shashkin, and G. E. Tsydynzhapov
Institute of Solid-State Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia e-mail: gantm@issp.ac.ru
Received April 25, 2000

We study the response of a thin superconducting amorphous InO film with variable oxygen content to a parallel magnetic field. A field-induced superconductor­insulator transition (SIT) is observed that is very similar to the one in normal magnetic fields. As the boson-vortex duality, which is the keystone of the theory of the fieldinduced SIT, is obviously absent in the parallel configuration, we have to draw a conclusion about the theory's insufficiency. © 2000 MAIK "Nauka / Interperiodica". PACS numbers: 74.80.Bj; 74.76.Db

A good deal of work was performed on the investigation of the magnetic-field-induced superconductor­ insulator transition (SIT) on superconducting amorphous films of InO [1­3], MoGe [4], and MoSi [5] with thickness comparable to the superconducting coherence length. It was found that with increasing field B the resistance R of all studied films rises abruptly at a magnetic field Bc and then passes through a maximum followed by a drop in high magnetic fields [2, 3]. The film state just above Bc was identified as insulating, although at the lowest temperatures, about 30 mK, the maximum resistance does not exceed 100 k and the temperature dependences of 1/R correspond to the activation energies which do not exceed by far the lowest temperatures. Near Bc, at sufficiently low temperatures, the resistance R(T, B) was found to be a function of the single scaling variable u = (B ­ Bc)/Ty with exponent y 0.8. The above experimental findings are regarded as confirming the theory of the quantum SIT [6] in twodimensional (2D) superconducting films subjected to a normal magnetic field. This theory exploits the concept of the hypothetical system of charged bosons in a random potential and is based on the boson-vortex symmetry of the model Hamiltonian. In the vicinity of the SIT point (T = 0, B = Bc), the film resistance R(T, B) is expected to be a universal function of the single scaling variable, which is defined as the ratio of the correlation length (B ­ Bc)­ and the dephasing length L T­1/z, where and z are the critical indices. The form of the scaling variable implies that the value 1/z has to be identified with exponent y. The concept of the localization of electron pairs, or bosons [6], has been supported recently by the work of [7]. There, it is shown that for a
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This article was submitted by the authors in English.

2D superconducting film with strong disorder, the region of fluctuation superconductivity, where the electron pairs occur, should extend down to zero temperature. In this region, the unpaired electrons are supposed to be localized, whereas the bosons can be either localized or delocalized, depending on the value of the magnetic field. Other experimental results were interpreted within the model of electron pair localization: (i) A crossing of Hall isotherms Rxy(B) was observed at a field Bc0 > Bc and attributed to a transition between the Bose insulator and a Fermi insulator that consists of localized single electrons; i.e., pairing was presumed to be destroyed at Bc0 [1]. (ii) The resistance drop in high fields was explained in terms of the electron pair breaking which occurs gradually with increasing B owing to the different binding energies of bosons in a random potential [2, 3]. However, a very similar SIT has been observed recently on amorphous MoSi films with the thickness d = 1700 å, which is an order of magnitude larger compared to the superconducting coherence length sc [8]. This fact causes one to think that either the theory is inadequate or its restrictions are too severe. Here, we investigate the influence of a parallel magnetic field on the superconducting properties of a thin amorphous InO film with variable oxygen content. For all film states we find a complete similarity in the behavior of the resistance R(T, B) for both parallel and perpendicular magnetic fields. The sample is an amorphous InO film with thickness 200 å that was grown by electron-gun evaporation of a high-purity In2O3 target onto a glass substrate [9]. Oxygen deficiency compared to fully stoichiometric insulating compound In2O3 causes the film conductiv-

0021-3640/00/7111-0473$20.00 © 2000 MAIK "Nauka / Interperiodica"


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Fig. 1. Isotherms R(B) for (a) normal and (b) parallel magnetic field. The dashed lines separate regions I, II, and III and correspond to the critical field Bc and the resistance maximum at the lowest temperatures.

ity. By changing the oxygen content, one can cover the range from a superconducting material (sc 500 å) to an insulator with activated conductance [10]. The procedures to change the film state reversibly are described in detail in [2]. To reinforce the superconducting properties of the film, we used heating in vacuum up to a temperature from the interval 70­110°C until the sample resistance became saturated. To shift the film state in the opposite direction, we made an exposure to air at room temperature. As the film remains amorphous during these manipulations, it is natural to assume that the treatment used results mainly in a change of the carrier density n and that the value n is inversely proportional

Fig. 2. Scaling plot for the (a) normal and (b) parallel magnetic field.

to the room temperature resistance Rr of the sample. Seven superconducting states of the film were studied. The film was mounted into the top loading system of a dilution refrigerator; it was set either parallel or normal to the magnetic field within 1° accuracy. A four-terminal lock-in technique at a frequency of 10 Hz was used to measure the resistance of the sample. The ac current through the sample was equal to 1 nA. The experimental dependences R(B) for two close states of the film in the normal and parallel field orientations are presented in Fig. 1. As seen from the figure, for both field orientations the isotherms cross at the critical field Bc, which separates the superconducting region I and the insulating region II. The resistance drop with B in region III down to values of about h/e2 indicates that at high magnetic fields the film state is metallic. The critical field Bc is found to vary with field direction by about a factor of two. Nevertheless, near Bc, the experimental data collapse onto a single curve equally well for both perpendicular and parallel magnetic fields, with close values of exponent y, see Fig. 2. Figure 3 displays the behavior of the relative resistance maximum Rmax/R14T at the lowest temperature and of the critical field Bc with changing film state. As seen from the figure, the resistance ratio decreases and approaches unity as one goes deeper into the superconducting phase. The value Bc for both field directions increases when departing from the zero-field SIT, being higher in the parallel configuration. The mean free path of the normal electrons in our film is small compared to the film thickness [3], and, hence, the metal­insulator transition expected in region III should be three-dimensional. In this case, the conductance 1/R in the vicinity of metal­insulator transiJETP LETTERS Vol. 71 No. 11 2000


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Fig. 3. Change of the relative resistance maximum at T 30 mK and of the critical magnetic field with changing film state, as determined by the room temperature resistance of the film. The dashed lines are guides to the eye.

Fig. 4. The temperature dependence of 1/R near the threedimensional metal­insulator transition in the (a) normal and (b) parallel magnetic field.

tion is expected to change linearly with T1/3 and extrapolation of the linear dependence to T = 0 should reveal whether the phase is metallic or insulating, as judged by the offset sign [11, 12]. Such a data analysis is shown in Fig. 4. For both field configurations, the experimental data behave similarly: the offset of the linear dependence increases with B, passing through zero at the transition point. The crucial point of the theory of the magneticfield-driven SIT [6] is the boson-vortex duality for vortices induced by an external magnetic field penetrating the film, which is not the case for a parallel magnetic field. The experimentally observed complete similarity of the SIT properties in the perpendicular and parallel
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magnetic fields forces one to conclude that the theory is not directly applicable to actual superconducting systems with disorder. Nonetheless, assuming that the parallel magnetic field is capable of localizing the fluctuation-induced Cooper pairs in the paraconductivity region, one can translate all experimental findings into the language of localized bosons. We emphasize that the speculations below are very attractive but do not have a sound experimental basis so far. One can reckon that the resistance rise with B in region II is caused by decreasing boson localization length. Assuming additionally that the magnetic field not only localizes, but also breaks, electron pairs, it is easy to interpret the resistance drop in region III: breaking the correlations in localized electron pairs results in an increase in the electron hopping probability [2] and eventually electron delocalization at high fields [3]. For sufficiently deep film states in the superconducting phase; i.e., sufficiently high Bc, at B > Bc, the localized bosons coexist with delocalized normal electrons, so that the state never becomes insulating. In other words, as one advances into the superconducting phase, a fraction of the localized bosons reduces. As a result, the relative amplitude of the resistance maximum Rmax/R14T tends to unity (Fig. 3), and the SIT should transform into an ordinary superconductor to normal metal transition. In summary, we have investigated the response of a thin superconducting amorphous InO film to a parallel magnetic field. At a critical field Bc, a SIT has been observed that is very similar to the one in normal magnetic fields. That the boson-vortex duality is absent in the parallel configuration points to the insufficiency of the theory of the field-induced SIT [6]. We find that the behaviors of the film resistance at fields above the transition are also similar for parallel and normal magnetic fields. This work was supported by the Russian Foundation for Basic Research, project no. 99-02-16117; the Russian Foundation for Basic Research-PICS, project no. 98-02-22037; and the program "Statistical Physics" of the Russian Ministry of Sciences. REFERENCES
1. A. F. Hebard and M. A. Paalanen, Phys. Rev. Lett. 65, 927 (1990); M. A. Paalanen, A. F. Hebard, and R. R. Ruel, Phys. Rev. Lett. 69, 1604 (1992). 2. V. F. Gantmakher, M. V. Golubkov, J. G. S. Lok, and A. K. Geim, Zh. èksp. Teor. Fiz. 109, 1765 (1996) [JETP 82, 951 (1996)]. 3. V. F. Gantmakher, M. V. Golubkov, V. T. Dolgopolov, et al., Pis'ma Zh. èksp. Teor. Fiz. 68, 345 (1998) [JETP Lett. 68, 363 (1998)]; Pis'ma Zh. èksp. Teor. Fiz. 71 (2000) (in press) [JETP Lett. 71, 160 (2000)].


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GANTMAKHER et al. 8. A. V. Samoilov, N.-G. Yeh, and C. C. Tsuei, Phys. Rev. B 57, 1206 (1998). 9. The films were kindly presented by A. Frydman and Z. Ovadyahu from Jerusalem University. 10. D. Shahar and Z. Ovadyahu, Phys. Rev. B 46, 10 917 (1992). 11. Y. Imry and Z. Ovadyahu, Phys. Rev. Lett. 49, 841 (1982). 12. V. T. Dolgopolov, Pis'ma Zh. èksp. Teor. Fiz. 68, 807 (1998) [JETP Lett. 68, 848 (1998)].

4. A. Yazdani and A. Kapitulnik, Phys. Rev. Lett. 74, 3037 (1995). 5. S. Okuma, T. Terashima, and N. Kokubo, Solid State Commun. 106, 529 (1998). 6. M. P. A. Fisher, G. Grinshtein, and S. M. Girvin, Phys. Rev. Lett. 64, 587 (1990); M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990); S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997). 7. A. I. Larkin, Ann. Phys. (Leipzig) 8, 785 (1999).

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2000