Possible vortex phase diagram at zero temperature in disordered 2D superconductors

Physica C 357±360 (2001) 556±559

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Possible vortex phase diagram at zero temperature in disordered 2D superconductors S. Okuma *, M. Morita Research Center for Very Low Temperature System, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku, Tokyo 152-8551, Japan Received 16 October 2000; accepted 13 January 2001

Abstract We study transport properties of highly disordered thin ®lms of amorphous Mox Si1 x at low temperatures. For superconducting ®lms we observe an anomalous peak in the magnetoresistance suggesting the presence of localized Cooper pairs on the insulating side (B > BC ) of the ®eld-driven superconductor±insulator transition. In contrast, for thick ®lms, or for thin ®lms in parallel ®elds the MR is always positive. These results may suggest the presence of insulating quantum-vortex-liquid (QVL) phase in the region B > BC . In B < BC the metallic QVL phase is not evident, most likely absent, which is in contrast to the results reported by other groups. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.25.Dw; 74.40.‡k; 74.60.Ec Keywords: Superconductor±insulator transition; Vortex glass; Bose glass; LTSC

The superconductor±insulator transition (SIT) in two-dimensions (2D) has been actively studied during recent years [1±12]. Despite numerous efforts, the vortex states at low temperatures have not been fully understood. For some 2D superconductors with microscopic or mesoscopic disorder an anomalous insulating regime suggestive of the presence of the localized Cooper pairs has been observed on the insulating side of the zero®eld [3,11] and ®eld-driven [1,3,4,10,12] SITs. Several authors have interpreted this regime as the Bose-glass phase (or insulating quantum-vortex-

* Corresponding author. Tel.: +81-3-5734-3252; fax: +81-35734-2749. E-mail address: [email protected] (S. Okuma).

liquid [QVL] phase), where Cooper pairs are localized and vortices are Bose condensed [13]. On the other hand, for other 2D systems (amorphous ®lms) with microscopic disorder the existence of the metallic QVL phase has been reported just below the ®eld-driven ``SIT'' (B < BC ) [5,6], which challenges the basic picture of the SIT. Experimentally, quality (or morphology) of the sample is essential, because the presence of inhomogeneity (or granularity) in the ®lms may signi®cantly a€ect the transport properties at low temperatures. For example, it is known that in some granular ®lms the ®nite temperature-independent resistance appears at T ! 0 even in B ˆ 0. In this paper, we present the measurements of the low-temperature resistance for a series of thin (2D) homogeneous ®lms with various disorder and, for comparison,

0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 3 0 7 - 0

S. Okuma, M. Morita / Physica C 357±360 (2001) 556±559

for thicker (3D) ®lms in which the vortex-glass transition is observable [14]. We construct the T ˆ 0 phase diagram for the zero-®eld and ®elddriven SITs in 2D and discuss possible vortex states at T ˆ 0 [15]. The samples for which we present data in this paper are amorphous (a-)Mox Si1 x ®lms prepared by coevaporation of pure Mo and Si [8,9,16]. The good quality of the sample has been guaranteed from the sharp (resistive) superconducting transition curves down to our experimental resolution R…T †  10 2 X [8,9]. The resistance was measured by four-terminal dc and ac locking methods. The ®eld was applied both perpendicular B and parallel Bk to the plain of the ®lm. For parallel ®elds the current was also parallel to the ®eld direction. An Arrhenius-type resistance R…T † is commonly observed in perpendicular ®elds B lower than the critical ®eld BC for the ®eld-driven SIT. In Fig. 1, we plot the ®eld dependence of the slope (i.e., activation energy U) extracted from the log R vs 1=T plots for two thin (4 nm) ®lms with Rn ˆ 0.79 (TC0 ˆ 1:8 K) and 1.79 kX (TC0 ˆ 0:47 K). Here, Rn

Fig. 1. Activation energy U plotted vs log B for two thin (4 nm) ®lms with TC0 ˆ 1:8 K (solid squares) and 0.47 K (solid circles). Slopes (open circles) derived from the Arrhenius plot of R…T † in parallel Bk are also shown for the ®lm with TC0 ˆ 0.47 K.

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is the normal-state resistance at 10 K and TC0 the mean-®eld transition temperature. Despite rather di€erent values of Rn , the slope (U) for each ®lm follows the log B formula predicted by the dislocation model [17]. Seemingly activated resistance is also seen in parallel ®elds Bk . However, for Bk the slope never obeys the log B formula, indicating that the resistance in the presence of perpendicular B is indeed dominated by ¯ux motion. With increasing B, the activation energy U decreases and extrapolates to zero at certain B0 that is very close to BC . Thus, in our 2D system the metallic QVL phase below BC is not so distinct, most likely absent [15]. This is in contrast to the result for other thin-®lm superconductors [5,6], 1 in which B0 is substantially lower than BC and on basis of which the existence of the metallic QVL phase has been claimed. Furthermore, for some systems the apparent temperature-independent resistance, the so-called ¯at tail, is observed at low T and is attributed to quantum tunneling of vortices [5,7]. In our system the ¯at tail is not observed for any ®lm studied. Instead, in high-resistance ®lms the activation energy U exhibits a discontinuous drop below about 0.1 K [15]. Such behavior is no longer visible for less resistive ®lms, suggesting that disorder may play a role in the reduction of U at low temperatures. The origin of this is not clear at present. However, we can say that it is not related to ¯ux motion, because the decrease in the slope is also seen for parallel ®elds Bk . Thus, to claim the existence of the metallic QVL, it is necessary to perform the transport measurements in parallel ®elds for other superconductors [5,7] 1 in which the ¯attening of the resistance is observed in perpendicular ®elds. For thicker ®lms, on the other hand, the ¯at tail at low T is clearly visible in a certain B region. This result, together with the ®nding of the vortex-glass transition from ac measurements,

1 For these ®lms it is dicult to reject de®nitely the possibility that the metallic behavior at T ˆ 0 may originate from granularity of the sample. We suggest that the ac resistivity measurements [14], as well as the dc measurements with parallel ®elds, will prove the existence of QVL more convincingly.

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S. Okuma, M. Morita / Physica C 357±360 (2001) 556±559

Fig. 2. MR for the (a) thin ®lm (4 nm) and (b) thick ®lm (100 nm) at di€erent T. The ®eld is applied perpendicular (solid symbols) and parallel (open symbols) to the ®lm surface. High R region is enlarged and shown in the upper panels.

implies that the T ˆ 0 metallic QVL phase is present in 3D. We reported previously [8,9] the anomalous peak and subsequent decrease in the magnetoresistance (MR) at low T higher than BC (Fig. 2(a)). The origin of this is attributed to the localized Cooper pairs present on the insulating side of the ®eld-driven SIT. As depicted in Fig. 2(a), the peak in MR observed in perpendicular B is no longer visible with parallel-®eld orientation, suggesting that the peak may be associated with the ¯ux motion. For thicker (100, 300 nm) ®lms the peak in R…B† is not visible down to the lowest T for any ®lm studied (Fig. 2(b)). This result indicates that the 2D plays an important role in the appearance of the MR peak [15]. We have also performed detailed measurements of MR for an insulating ®lm which lies near the zero-®eld SIT. At low T (0.05 K), a steep rise in MR is observed in low ®elds (B  0±0:1 T), as shown in the inset of Fig. 3. This cannot be explained in the framework of the localization theory

Fig. 3. B±Rn (10 K) phase diagram for the zero-®eld and ®elddriven SITs in 2D at T ˆ 0. Inset: MR of the thin insulating ®lm at T ˆ 0:05 K. A steep rise in R…B† is visible at B  0±0:1 T.

S. Okuma, M. Morita / Physica C 357±360 (2001) 556±559

for fermions. We suggest that it is due to localized Cooper pairs present on the insulating side of the zero-®eld SIT. On the basis of these data, we construct the ®eld-disorder (B±Rn ) phase diagram for the zero®eld and ®eld-driven SITs in 2D at T ˆ 0 [15]. As seen in Fig. 3, there is an unusual insulating regime with localized Cooper pairs just above BC . According to the theory of Fisher [13], at BC there is a Bose-glass (BG) insulator with localized Cooper pairs and mobile vortices. At some ®eld (BC2 ) that is higher, either at Bp , where the peak in R…B† occurs, or BkC , where R…Bk † at low T is temperature independent, the BG goes to the Fermi insulator. The ®eld region BC < B < BC2 is characterized by a ®nite amplitude of the order parameter and strong phase ¯uctuations in 2D. On the other hand, for parallel ®elds, Bk couples to only the order parameter amplitude and does not a€ect the phase ¯uctuations. Therefore, above BkC there is no order parameter amplitude and hence no BG insulator. Finally, we comment on alternative interpretations of the data. The peak in the MR has been also reported for granular ®lms [2]. The origin of this is sought in the single-particle tunneling at BC and subsequent destruction of energy gap within the grain at Bp (or BkC ). We have no experimental proof suggesting the granular structure of our ®lms; however, we cannot completely reject the possibility of the presence of small superconducting clusters which cannot be detected within our experimental resolutions. In addition, there are some models [18] which have addressed the formation of the superconducting clusters (``physical clusters'') near the SIT even in a homogeneous system. Assuming these models, the above interpretation based on the morphology of the ®lm could be derived from intrinsic e€ects. In any event, in order to prove the existence of the BG

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phase more convincingly, further experiments including direct detection of ¯ux motion is necessary.

Acknowledgements We wish to acknowledge V.F. Gantmakher and R. Ikeda for useful discussions and S. Shinozaki for technical assistance. This work was supported by a Grant-in-Aid for Scienti®c Research (B) from the Ministry of Education, Science, Sports, and Culture.

References [1] M.A. Paalanen, A.F. Hebard, R.R. Ruel, Phys. Rev. Lett. 69 (1992) 1604. [2] T. Wang, et al., Phys. Rev. B 47 (1993) 11619. [3] S. Okuma, N. Kokubo, Phys. Rev. B 51 (1995) 15415. [4] S. Okuma, N. Kokubo, Phys. Rev. B 56 (1997) 410. [5] D. Ephron, et al., Phys. Rev. Lett. 76 (1996) 1529. [6] J.A. Chervenak, J.M. Valles Jr., Phys. Rev. B 54 (1996) R15649. [7] P.H. Kes, M.H. Theunissen, B. Becker, Physica C 282±287 (1997) 331. [8] S. Okuma, T. Terashima, N. Kokubo, Solid State Commun. 106 (1998) 529. [9] S. Okuma, T. Terashima, N. Kokubo, Phys. Rev. B 58 (1998) 2816. [10] Y. Kuwasawa, K. Kato, M. Matsuo, T. Nojima, Physica C 305 (1998) 95. [11] N. Markovic, et al., Phys. Rev. Lett. 81 (1998) 701. [12] V.F. Gantmakher, et al., JETP Lett. 71 (2000) 473. [13] M.P.A. Fisher, Phys. Rev. Lett. 65 (1990) 923. [14] S. Okuma, M. Arai, J. Phys. Soc. Jpn. 69 (2000) 2747. [15] S. Okuma, S. Shinozaki, M. Morita, Phys. Rev. B 63 (2001) 54523. [16] S. Okuma, N. Kokubo, Phys. Rev. B 61 (2000) 671. [17] M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, Physica C 167 (1990) 177. [18] A. Ghosal, M. Randeria, N. Trivedi, Phys. Rev. Lett. 81 (1998) 3940.