Philosophical Magazine Letters

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Variable-range-hopping-type transport near thesuperconductor-insulator transition observed inNd2−x,CexCuO4 thin films
Satoshi Tanda & Tsuneyoshi Nakayama
To cite this article: Satoshi Tanda & Tsuneyoshi Nakayama (1995) Variable-range-hoppingtype transport near the superconductor-insulator transition observed in Nd2−x,CexCuO4 thin films,
Philosophical Magazine Letters, 72:4, 223-229, DOI: 10.1080/09500839508242455
To link to this article: https://doi.org/10.1080/09500839508242455

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PHILOSOPHICALMAGAZINE
LETTERS,
1995, VOL.72, No. 4, 223-229

Variable-range-hopping-type transport near thesuperconductor-insulator transition observed in
Nd2 -,Ce,Cu04 thin films
By SATOSHITANDAand TSUNEYOSHI
NAKAYAMA
Department of Applied Physics, Hokkaido University, Sapporo 060,Japan[Received 24 May 1995 and accepted 12 June 19951

ABSTRACTElectrical transport properties of high-T, Nd2 - .CexCu04 single-crystal thinfilms were investigatedto reveal the conduction mechanism near the superconductor-insulator transition. We find that two different types of localized state exist inthe insulator side: one shows typical behaviour or weak localization and the otheris the variable-range-hopping(VRH)conduction type. We claim this to be a newtype of VRH conduction process with interlayer hopping by Cooper pairs.
The experimental and theoretical study of charged boson transport in twodimensional (2D) disordered systems has become a rapidly developing field ofcontemporary solid state physics, particularly since the discovery of high-temperature(high-T,) superconductors. An important issue is the influence of disorder on bosontransport. Variable-range hopping (VRH) conduction due to strongly localized
electrons has been studied theoretically by Mott (1968, 1978, 1993), Efros andShklovskii (1975) and Shklovskii and Efros (1984). The VRH is characterized by anactivation-type conductivity, which yields Mott’s famous law

where the exponent ci takes different values depending on the dimensionality and thedensity of states g(&) at the Fermi level EF.For 2D systems, one expects a = f wheng(&) is almost constant or a slowly varying function and a = when there is a parabolic
gap at the Fenni level (Efros and Shklovskii 1975). However, the behaviour for
localized bosons has not been revealed either experimentally and theoretically. Herewe report evidence of VRH for charged bosons, observed near the superconductorinsulator (SI) transition using high-T, Nd2- F e x C u 0 4single-crystal thin films. We findthat two different types of localized state exist in the insulator side: one shows typicalbehaviour of weak localization ( a In T ) and the other is the VRH conduction type dueto the formation of Bose-glass states. We claim this to be a new type of VRH conduction
with an interlayer hopping process by Cooper pairs in the Bose-glass states.
It is well known that the high-T, oxide superconductor Nd2 - .CexCu04 is peculiar
among Cu-based oxide superconductors with perovskite structures. Ordinary copperoxide high-T, superconductors have Cu02 networks with pyramidal or octahedral
arrangements, and, in addition, the charge carriers in the normal state are holes.
The Ndz -.CexCuO4 system consists of 2D CUOZlayers with no apical 0 atoms. TheCuOz layers form an ideal 2D conducting sheet as verified by the observation that thenormal-state transport properties of the single-crystal films show the typical095&0839/95 $10 00 0 1995 Taylor & Francs Ltd224

S. Tanda and T. Nakayama

characteristics of weak localization associated with two-dimensionality (Anderson
1958, Abrahams, Anderson, Licciardello and Ramakrishnan 1979, Tanda, Honma andNakayama 1991).
Nd2 -,CexCu04 single-crystal films were grown on SrTi03( 100) single crystals bymolecular beam epitaxy using Knudsen cell sources for Nd, Cu and Ce. After
deposition, the 0 2 flow to the film surface was stopped immediately and the substrate
was cooled from 800°C to room temperature with a background pressure of 1 0 - 4 T o ~ .
The appearance of only (002n) peaks indicates that the (001) plane is oriented parallelto the film surface. These films were reduced with a background Ar pressure of 0.4 Torrwith the temperature ranging from 450 to 750°C over 20 min. This reduction in a partial
vacuum permits a reduction in the 0 concentration in the Nd2-,CexCu04 films, whichis required for the appearance of superconductivity. The film thickness, determinedfrom the cross-section of the films by electron microscopy, was l000A within an
accuracy of a few per cent.
The temperature dependence of the resistivities p(T) was measured by the standard
four-terminal method with evaporated Au electrodes. The current terminals werecovered with Au along the edge of the films in order to eliminate the ambiguity due
to inhomogeneous current flow arising from strong anisotropy. The current density wastaken as 10 A cm - 2 throughout our measurement. A sensitive voltmeter (Keithley 182)
was used to measure all resistances and magnetoresistances, and l o p 9resolution wasachieved. The temperature dependences of the resistivities p(T) for the Nd2 - .Ce,Cu04
films at various stages of oxygen reduction are shown in fig. 1. The residual resistivity
was 75 pQ cm for sample H (n = 0.16). This value is small compared with that of bulk
single crystals (Hidaka and Suzuki 1989, Hagen et al 1992). This is due to the easier
reduction of 0 impurities in thin films compared with bulk samples. These
vacuum-annealed films, with optimum reduction, are characterized by a sharp
superconducting transition with T,(p = 0) = 15 K and a transition width of less that0.9 K. The curve of sample H ( k d = 19) agrees fairly well with the theory by Azlamazovand Larkin 1968, indicating that 2D superconducting fluctuations are relevant for thisless-disordered sample.
0-rich non-superconducting samples (A-C) clearly show behaviour typical of weakAnderson localization in two dimensions (Tanda el al. 1991). We find that thetemperature dependence of the sheet resistance changes from the In T form of weak
localization to that for the 2D VRH-type conduction. As seen from the curves E andF in fig. 1, the separation between the insulating state (Rm increases as T+ 0) and thesuperconducting state (RDdecreases as T +0) occurs in the range between 8 and 9 kQ,
which is close to the value h/4e2. The sheet resistances (curves C-E) shown in fig. 1
are replotted in fig. 2. One sees from fig, 2 ( u )that only curve C follows a In Tbehaviour
indicative of 2D fermion weak localization. A remarkable feature is that curves D andE close to the SI transition take the functional form exp [ - (TdT)$ of the 2D VRH typc,
as seen from fig. 2 (b).This implies that a new type of localized state exists when R,
approaches a value close to h/4e2. The precise value of E was obtained by transforming
the expression for the sheet resistance Ro = Roexp [(TdT)"]intolog(w)(9+= (E - 1 ) log -log (ET;),

where d(1og R)/d( 1/T) corresponds to the characteristic hopping energy or generaliLed
activation energy. In fig. 3 we have plotted d(logR)Id( IIT) as a function of IIT on alog-log scale for sample D. The straight line represents a least-squares fit to the data.

Electrical transport in Nd2 - .CexCu04

225Fig. 1!--InEucU

Q%

010203040T (K)
Temperature dependence of resistivities (left-hand scale) for Ndz - .CexCu04 single-crystal films
at various stages of disorder controlled by the annealing process. Curves (samples) A-G
correspond to x = 0-18, and curve (sample) H to x = 0.16. The temperatures for a 20 min
anneal in a partial vacuum were as follows: curve A, 450°C; curve B,5OO"C; curve C,550°C; curve D, 600°C; curve E, 650°C;curve F, 700"C, curve G, 750°C; curve H,750°C. The right-hand scale refers to the sheet resistance per CuOz layer (see text).

The slope rn is related to tl through the relation m = a - 1. The observed value of m gives
a = 0.312 0-05.We have obtained a = 0.33 -t 0.05 for sample E. Electrical transport
in the strongly disordered regime is attributable to VRH. In VRH transport, the valueof a depends on both the dimensionality d of the system and the density of states at theFermi level (tl = f in two dimensions (Mott 1968)). In addition, a is related to theelectron correlation. Altshuler, Lee, Kheml'nitzkii and Larkin (1979) have shown thatthe density of states has a minimum (but finite) value at the Fermi level in disordered
metals. If the disorder increases, the electronic states at the Fermi level are stronglylocalized. Efros and Shklovskii (1975) have claimed that the minimum becomes a gap(the Coulomb gap) and that the conductivity is described by VRH with o r = * ,independent of dimensionality. Our results for samples D and E (a=i: 4) show thecharacteristics of 2D localization arising from induced disorder and not from theCoulomb correlation effect. We claim in the following that the charged carriers arebosons.
To determine the nature of the charge carriers we investigated the field-tuned

226

S . Tanda and T. Nakayama
Fig. 2

1000
900--I

cv

Gb

800

700v

600-.
600
O

OV
500

400
400

The temperature dependenceof conductances u for sample C , D and E. (a)c against log T(weak(VRH conduction).
localization): (b) u on a logarithmic scale against - Ttransport properties for the superconducting sample F. Figure 4 shows the resistanceof sample F measured as a function of magnetic field at various temperatures. Below
the critical field B, = 2.9 T, the resistance decreases with decreasing temperature
whereas, above B,, the resistance increases with increasing magnetic field B. The
resistance Ro at B, is 8.5 kQ. According to Fisher's scaling theory, the slopes of theRo(B) curves at B, should follow a T power-law dependence. ZB and V B are thedynamical critical exponent and the static critical exponent respectively for thesuperconducting correlation length &. Scaling theory predicts that the resistances
should scale, under a magnetic field B, as (Fisher 1989, 1990)

where cois a non-universal constant, where tB ( B - B,) - and QB x & - Z B , f2e beinga characteristic frequency. Near the SI transition, one expects that the length scale
diverges, which sets < B as the length scale characterizing the system. With increasing
magnetic field, the remarkable possibility arises that vortices can become delocalizedand undergo a Bose condensation at some critical field B,. When the slopes of the Ro(B)curves at B, are plotted against 1/T on a double-logarithmic plot, we find a straight linein the range 1-6K S T =S 8 K. From the reciprocal of the slope of this straight line, wedetermine ZBVS = 1.2 5 0.1 (Tanda, Ohzeki and Nakayama 1992). This value isconsistent with theoretical expectations ZBVB 2 1. The observed resistivities near thefield-tuned SI transition thus provide evidence for a Bose-glass-vortex-glass phasecE227

Electrical transport in Nd2 - ,Ce,CuO,
Fig. 3

0.1

0.05

0.1

0.2

Logarithmic plot of d(logR)/d(l/T) as a function of 1/T. The exponents ( a = rn + 1) wereextracted from the slope rn as CI = 0.31 2 0.05 (sample D) and CI = 0-33 ? 0.05 (sample E).
transition, indicating that the boson phase is formed on the insulator side of the SI
transition.
Resistivities on the insulating side of fig. 4 show a conductance varying as
exp [ - (TdT)"],indicating that VRH is the dominant process for transport. In fig. 5 wehave plotted d(1og R)/d( 1/T) against 1/T on a log-log scale for the field-tuned sample
F (a field B = 5 T was applied perpendicular to the film surface). The straight line
represents a least-squares fit to the data. The observed value of rn gives rise toa = 0-49 2 0.05 and not a = 3 as obtained for samples D and E. This suggests that underhigh magnetic fields the boson transport occurs along a quasi-one-dimensional path (inwhich case a = 4).
From the data on samples D and E we estimate TO= 5.0 and 4-5 K respectively.
These values are much smaller than those observed for disordered fennion systems suchas doped semiconductor materials. According to the expression for the Mott 2D VRH,
one has ksTo = 27/rcg(E~)(*,
where 5 is the localization length. By taking $to accountthe experimental value of y = 30 mJ mol - K - in specific-heat measurements(Ghamaty et al. 1989, Tigheza et al. 1990), one can estimate ( 2 0 0 0 a from theobserved TO.The value of 5 is the same order as that for the weakly localized regime.
It is natural that this localization length 5 does not represent the size of Cooper pairs(the coherence length is about 70a), but rather the correlation length of the superconducting region, that is the size of the local superconductor. Scaling theory predicts
that the characteristic energy TOrepresents the deviation of the parameter characterizing
the SI transition from the right of the SI transition, namely TOa 6 - A,, where 6 is theparameter characterizing the disorder (Fisher 1990). This suggests that To takes a'-228

S. Tanda and T. NakayamaFig. 4

5.8

5.7

sample F\ \nE&) 5.6/--$I

0T-iv

a.

5.5

5.4

ipi'

5.3
1-2

2.O(Tesla)

34- 5678T (EoThe temperature dependence of the resistivities of sample F under magnetic fields ranging from
2-0 to 5.OT. The magnetic fields are 2.0,2.4,2.6, 2.8,2.9,3.0, 3.1,3.2,3.4, 3.6,4.0 and
5.OT in order of increasing resistivity and are applied perpendicular to the film surface.
The critical field B, of the SI transition is 2-9T.
sufficiently small value near the SI transition. The above arguments are, however, basedon the assumption of ideal 2D VRH. Recently, Chakraverty, Sudbo, Anderson andStrong (1993) suggested that the interlayer tunnelling of Cooper pairs is important for
high-T, superconducting cuprate. If ( diverges over the sample size, the interlayer
tunnelling coupling (Josephson coupling) becomes perfect, and the system has globalcoherence. When is finite, interlayer hopping between local coherence regions of eachlayer take place. In this respect, our findings favour the quasi-2D VRH of Cooper pairs.
ACKNOWLEDGMENTS
The authors acknowledge S. Ohzeki f:x experimental support. H. Takahashi of EikoEngineering Company is thanked for his aid. This work was supported in part by theKurata Research Grant and by a Grant-in-Aid for Scientific Research on Priority Areas,'Science of High T, Superconductivity' given by the Ministry of Education, Science,and Culture, Japan.

229Electrical transport in Nd2 -,CexCu04
Fig. 50.03--IIIII

1l/r (1/K)
Logarithmic plot of d(log R)ld( 1/T) as a function of l/T. Th exponent ( a = m + 1) was extracted
from the slope rn as a = 0.49 t 0.05 (for field-tuned sample F).

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