Pis'ma v ZhETF, vol.88, iss.ll, pp.785-790
© 2008 December 10
Hyperactivated resistance in TiN films on the insulating side of the disorder-driven superconductor-insulator transition
T. I. Baturina1 >, A. Yu.Mironov, V.M. Vinokurv, M.R.Baklanov+, C.Strunk*
Institute of Semiconductor Physics, 630090 Novosibirsk, Russia v Material Science Division, Argonne National Laboratory, Argonne, 111. 60439 USA + IMEC, B-3001 Leuven, Belgium *Institut für experimentelle und angewandte Physik, Universität Regensburg, D-93025 Regensburg, Germany
Submitted 28 October 2008
We investigate the insulating phase that forms in a titanium nitride film in a close vicinity of the disorder-driven superconductor-insulator transition. In zero magnetic field the temperature dependence of the resistance reveals a sequence of distinct regimes upon decreasing temperature crossing over from logarithmic to activated behavior with the variable-range hopping squeezing in between. In perpendicular magnetic fields below 2 T, the thermally activated regime retains at intermediate temperatures, whereas at ultralow temperatures, the resistance increases faster than that of the thermally activated type. This indicates a change of the mechanism of the conductivity. We find that at higher magnetic fields the thermally activated behavior disappears and the magnetoresistive isotherms saturate towards the value close to quantum resistance ft/e2.
PACS: 72.15.Rn, 73.50.^h, 74.40.+k, 74.78.^w
The subject of suppression of superconductivity by disorder in thin superconducting films can be traced back to a pioneering work of early forties by Shal'nikov [1], where it was noticed for the first time, that the superconducting transition temperature, Tc, decreases with the decrease of the film thickness. Later, a number of experimental works revealed a drastic suppression in Tc in thin films with the growth of sheet resistance [2-4], which is determined by either film composition or thickness and serves as a parameter measuring the degree of disorder. The observed behavior was in a good quantitative accord with theoretical predictions by Maekawa and Fukuyama [5] and the subsequent work by Finkel'stein [6]. The physical picture behind suppressing superconductivity by disorder is that in quasi-two-dimensional systems disorder inhibits electron mobility and thus impairs dynamic screening of the Coulomb interaction. This implies turning on the Coulomb repulsion between electrons which opposes Cooper attraction and, if strong enough, breaks down Cooper pairing and destroys superconductivity. Importantly, according to mechanism of [6], the degree of disorder at which the Coulomb repulsion would balance the Cooper pair coupling is not sufficient to localize normal carriers; thus at the suppression point superconductors transforms into a metal. The latter can be turned into an insulator
^e-mail: tatbat0isp.nsc.ru
upon further increase of disorder. Therefore this mechanism, which is referred to as a fermionic mechanism, results in a sequential superconductor-metal-insulator transition [6]. There exists a seemingly alternative picture of the transition, the so-called bosonic mechanism, where the intermediate metallic phase collapses to a single point, implying the direct disorder-driven superconductor-to-insulator transition (D-SIT) [7, 8]. Contrary to fermionic mechanism, the bosonic one realizes via localization of the Cooper pairs, which survive even at the nonsuperconducting side of the transition. However, numerical simulations by Ghosal, Randeria, and Trivedi [9] demonstrated that this distinction is not valid: near the D-SIT the homogeneously disordered film breaks up into superconducting islands separated by an insulating sea. Depending on the competition between the charging energy of a single island and the Joseph-son coupling between the neighboring islands, the film may become either superconducting or insulating, with the island-like structure maintaining at both sides of the transition. Yet the details of the microscopic mechanism of the D-SIT are far from being understood, and uncovering the nature of the phase resulting from suppression of the superconductivity by disorder remains one of the major challenges of condensed matter physics.
In this work we focus on the insulating side of the D-SIT. To begin with, we briefly summarize the up-to-date experimental findings on the subject. In the early
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experiments [2] with the very thinnest Pb films it was noticed that once on the nonsuperconducting side, the temperature dependence of resistance acquired an activated character:
R = Ro exp(T0/T). (1)
Study of the Bi films [10, 11] revealed three major regimes of the temperature resistance behavior in the insulator domain depending on the degree of disorder. The films closest to D-SIT exhibit comparatively weak insulating trend with conductance lowering as logT upon decreasing temperature. Moderately disordered films, that are more far from the D-SIT, demonstrate the Efros-Shklovskii (ES) behavior, R = Rx exp[{TES/T)1/2}, and the resistance in most disordered films is thermally activated (1). The direct D-SIT was found in InOa. films [12], exhibiting a sequence of temperature behaviors on the nonsuperconducting side: deep in the insulating regime, the conductivity shows Mott's variable range hopping (VRH) [12, 13], on approach to the transition with decreasing disorder it changes to ES law [13], and the films closest to D-SIT shows activation (1), which transforms to Mott's VRH at larger T [13]. Interestingly, the crossover from the activation to ES law, and eventually to Mott's VRH regime was also observed in InO^ composite films [14] upon increasing temperature. It was noticed in Ref. [12] that applying a relatively small perpendicular magnetic field (0.7 T) to the least disordered insulating films results in positive magnetoresistance, while more resistive samples show purely negative magnetoresistance. Gantmakher's group carried out measurements of the effect of the magnetic field up to 20 T on the insulating InO;,, films in the vicinity of the D-SIT [15] and revealed nonmonotonic magnetoresistance behavior: a positive magnetoresistance at low magnetic fields turning into a negative magnetoresistance upon increasing the field. Importantly, several works, starting from the earliest [12, 15] and ending by recent [16] demonstrate that in the zero magnetic field the resistance of insulating films closest to the transition deviates downward from the Arrhenius activated behavior at lowest temperatures. At high magnetic fields, the charge transfer mechanism appears the same as that at the zero field but high temperatures and follows Mott's VRH law [15]. Another recent finding worth noticing is the dependence of the activation energy in InO;,, films on the linear size of the film (the distance between the leads) [17]. The D-SIT in TiN was found for the first time on the films prepared by magnetron sputtering [18]. On the insulating side close to the transition, the resistance exhibited thermally activated behavior till lowest temperatures available. In our preceding works [19, 20], where we were dealing with the thin TiN films grown by
atomic layer chemical vapor deposition, an exceptionally sharp D-SIT was found. At zero and low magnetic fields the resistance displayed thermally activated behavior with the nonmonotonic dependence of activation temperature on the magnetic field. Here we present the novel results on identically prepared samples showing that at the lowest temperatures the resistance deviates upward from the Arrhenius activated dependence (1) in a contrast to observation in InO;,, films [12, 15, 16]. Hereafter we will referring to this behavior as to hyperactivation. This behavior holds at low magnetic fields. At higher magnetic fields, instead of this low-temperature upturn, the resistance shows downward deviation from the Arrhenius activation. The analysis of the corresponding magnetoresistance shows that it decays exponentially with field towards the finite value close to the quantum resistance Rq = h/e2.
The resistance was measured by the four-terminal technique in the linear I-V regime even at very low temperatures. The width of the film was 50 pm, the distance between the voltage probes was 100 pm, thus the sample comprised two squares. All the data are presented as resistance per square. The samples were cooled down in the Oxford 200 TLE dilution refrigerator. Magnetic fields up to 10 T were applied perpendicular to the film surface.
We start with the zero magnetic-field results obtained during the cooling the cryostat down from room temperature. Shown in Fig. la are the temperature dependences of the resistance R(T) of two samples, S and I. At room temperature, their resistances are close (-R300 = 4.48kO and JZ300 = 4.76kO, respectively), but diverge upon decreasing temperature. Namely, the S-sample falls into a superconducting state, whereas the I-sample becomes an insulator. Upon cooling down to 3K both samples exhibit nearly identical logarithmic temperature dependence of the conductance (see inset in Fig.la), which is well described by the formula G(T)/G00 = Aln(kBTT/h), where G(T) = 1/R(T) is the conductance, Goo = e2/(7rh), and A = 2.55 for both samples. This behavior is in accord with the theory of quantum corrections for quasi-two-dimensional disordered systems and can be attributed to localization and repulsive electron-electron interaction corrections [21]. To characterize the behavior of the I-sample at low temperatures we replot R(T) versus 1/T in Fig.lb. In the temperature interval between 0.25 and 0.9 K, the resistance is well fitted by a thermally activated dependence of Eq. (1), with T0 = 0.63 K being the activation temperature, and Rq « 17kO. Plotting the same data as log R versus 1/T1/2 one can see that the resistance can be nicely fitted by the ES-law in the higher
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