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Physica B 284}288 (2000) 649 } 650

Superconductor}insulator transition in amorphous In}O "lms
V.F. Gantmakher*, M.V. Golubkov, V.T. Dolgopolov, G.E. Tsydynzhapov, A.A. Shashkin
Institute of Solid State Physics RAS, 142432 Chernogolovka, Russia

Abstract From experiments with amorphous InO "lms, three conclusions are made: (i) The pattern of the superconducV tor}insulator transition (SIT) seen before for 2D electron gas in normal magnetic "eld can be reproduced under di!erent experimental conditions, with "eld parallel to the "lm; (ii) The negative magnetoresistance (NMr) observed in high "elds is due to breaking of localized pairs and transformation of bosons into fermions, the latter having higher mobility; hence, NMr is a con"rmation of the conception of localized pairs.; (iii) Assumption of existence near the SIN of two complementary groups of electrons, paired, i.e. bosons with density n , and unpaired fermions with density n (2n #n "n, the total density), can explain the nonuniversality of the critical resistance R seen before and its temperature dependence which we found in "lms with comparatively high n. 2000 Elsevier Science B.V. All rights reserved.
Keywords: Localized electron pairs; Pseudogap; Quantum transitions; Scaling relations; Superconductor}insulator transitions

In Ref. [1], Fisher proposed a scenario of the "eldinduced SIT with three main components. (a) It formulated some `boundary conditionsa for an experiment: the theory was elaborated for 2D electron gas and, as it was based on the vortex-boson duality, the magnetic "eld was assumed to be normal to the plane with electrons. (b) It predicted that the insulating state was arranged from localized pairs. (c) It predicted that at low temperature № in the vicinity of the critical "eld B the resistance R was a function of one scaling variable u"(B!B )/№W with y being a parameter: R(№, B)"R r(u), R "R (1#O(№)) (1)

with r(0)"1 and a universal constant R . This meant a horizontal separatrix R ,R(№, B ) in the (№, R) plane and a common crossing point for all isotherms in the (B, R) plane.

* Corresponding author. E-mail address: gantm@issp.ac.ru (V.F. Gantmakher)

Experiments done on amorphous InO [2] and MoGe V [3] "lms matched the conditions (a). They con"rmed prediction (c) } existence of the scaling relations in the vicinity of SIT (except of universality of R ). They did not deal with (b). In this work, we try to analyze our experiments regarding all three aspects and to clarify the points listed in the Abstract. The experiments were made with 200 A thick amorphous InO "lms. The oxygen s V content could be reversibly altered by heat treatment; all experimental procedures are described elsewhere [4,5]. Fig. 1 demonstrates that the change of the magnetic "eld direction practically does not a!ect the character of the function R(№, B) preserving the crossing of the isotherms R(B) in one point. This crossing was previously regarded as the main evidence of the existence of SIT [1}3]. We conclude that the scenario [1] realizes not only when the boson-vortex duality holds and that it is more universal. The striking feature seen from Fig. 1 is the high-"eld NMr, strongly temperature-dependent but not sensitive to the "eld direction, which returns the resistance R(BPR) to the level of R where the isotherms cross.

0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 3 0 5 - 4


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V.F. Gantmakher et al. / Physica B 284}288 (2000) 649 } 650

Fig. 1. Low-temperature isotherms R(B) for an amorphous In}O "lm at the "eild normal to the "lm (a) and parallel to it (b). The di!erence in behavior exists only below the crossing point (B , R ) where the resistance in the normal "eld con"guration is determined by the vortex dynamics.

Fig. 2. Isomagnetic R(№) curves (a) and isotherms R(B) (b) of the function R(№, B) for the "lm from Fig. 1 with increased through heat treatment carrier density n. Comparing with Fig. 1, note lower resistance values and decreased relative maximum magnitude on the isotherms.

This feeds the idea of the localized pairs and permits to propose a self-consistent description. The binding depletes the density n and leads to a gap (or a soft gap, or a pseudogap) at the Fermi-level in the one-particle density of states. As the bosons are localized in random positions they have di!erent binding energies . The larger is , the higher "eld is needed to break the pair. Hence, in each "eld the bosons and the fermions coexist. The density n goes down with increase of the "eld and n goes up and the gap shrinks. Bosons are localized above B and their hopping conductivity is very small. The fermions are localized at low n too but endure a Mott transition as n increases. Such "eld-induced insulator}metal transition was seen in Ref. [4]. Increase of n leads to NMr. NMr exists even when both groups are localized, because fermions do not need activation energy in the hopping processes while a bound electron needs. Existence of two complementary groups may complicate scaling relations (1). There are no special reasons why the conductance of both groups should not depend on temperature in the region where the scaling relations

hold. Then the function R (№) gets a "nite slope and the isotherms do not have a common crossing point. We see this on samples with higher total density n, which are deeper in the superconducting region (Fig. 2). However, the scaling relations may be saved by introducing compensation of the slope. Expanding R (№) and r(u), we get instead of (1) R(№, B)"R (1# №#2)(1# u#2) (2)

and not R but R"R! № remains a one-parametric I function until the product of the linear terms is small, № u;1 [5].

References
[1] [2] [3] [4] [5] M.P.A. Fisher, Phys. Rev. Lett. 65 (1990) 923. A.F. Hebard, M.A. Paalanen, Phys. Rev. Lett. 65 (1990) 927. A. Yazdani, A. Kapitulnik, Phys. Rev. Lett. 74 (1995) 3037. V.F. Gantmakher et al., JETP Lett. 68 (1988) 345. V.F. Gantmakher et al., cond-mat/9806244.