Two-dimensional Weak Localization Research Articles

Formation of Two-Dimensional Electronic System and Weak Localization in Conducting Langmuir-Blodgett Film of BEDO-TTF with Stearic Acid

Formation of Two-Dimensional Electronic System and Weak Localization in Conducting Langmuir-Blodgett Film of BEDO-TTF with Stearic Acid

Two-dimensional weak localization effects in high temperature superconductor Nd2−x CexCuO4−δ

A systematic study of the resistivity and Hall effect in single crystal Nd{2-x}Ce{x}CuO{4-d} films (0.12 < x < 0.20) is presented, with special emphasis on the low-temperature dependence of the normal state conductance. Two-dimensional weak localization effects are found both in a normally conducting underdoped sample (x = 0.12) and in situ superconducting optimally doped (x = 0.15) or overdoped (x = 0.18) samples in a high magnetic field B > B{c2}. The phase coherence time and the effective thickness of a CuO{2} conducting layer {d} (~ 1.5 A) have been estimated by fitting 2D weak localization theory expressions to the magnetoresistivity data for magnetic fields perpendicular to the {ab} plane and in plane. Estimates of the parameter {d} ensure the condition of strong carrier confinement and justify a model consisting of almost decoupled 2D metallic sheets for the Nd{2-x}Ce{x}CuO{4-d} single crystal.

A- and c-axis resistivity and magnetoresistance in graphite intercalation compounds

The a-axis electrical resistivity and the transverse magnetoresistance (aT-MR ) of stage-2 to 6 graphite intercalation compounds (GICs) have been measured in the temperature (T) range between 4.2 and 300 K and magnetic field (H) range between 0 and 7 kOe. The data are analysed together with the results of c-axis resistivity and the longitudinal magnetoresistance (cL-MR ) reported in our previous work. For stage-2 to 5 GICs shows a metallic-like T dependence and exhibits no logarithmic behaviour, while shows a metallic-like behaviour for low stage (2), a logarithmic behaviour for the intermediate stages (3, 4) and a semiconductor-like behaviour for high stages (5, 6). For all stages the sign of aT-MR is positive, while the sign of cL-MR is negative for the intermediate stages (3-5) and positive for low stages in low T and weak H. The resistivity is formed of a series connection of G-I-G (G: graphite layer, I: intercalate layer) and G-G resistivity, while is formed of a parallel connection of each layer contribution. The behaviour difference between and is discussed in the light of the role of the interior G layer forming a bottleneck to the c-axis conduction. The logarithmic behaviour and negative magnetoresistance in arise from the two-dimensional weak localization occurring in these interior G layers.

Magnetoresistance of an entangled single-wall carbon-nanotube network

The resistivity $\ensuremath{\rho}(T)$ and magnetoresistance (MR) $(\ensuremath{\Delta}\ensuremath{\rho}/\ensuremath{\rho})$ of an entangled single-wall carbon-nanotube network are investigated. The temperature dependence of the resistivity shows a negative $d\ensuremath{\rho}/dT$ from $T=4.3--300 \mathrm{K}$ with no resistivity minimum, which is fitted well to the two-dimensional variable-range-hopping (VRH) $(\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\mathrm{exp}[{(T}_{0}{/T)}^{1/3}])$ formula with ${T}_{0}=259.2 \mathrm{K}.$ The MR shows a negative ${H}^{2}$ behavior at low magnetic field. At $Tl~3.8 \mathrm{K}$ and high magnetic field, the negative MR becomes positive. The positive MR tends to be saturated for $Hg10 \mathrm{T}.$ The negative MR with a positive upturn can be decomposed into a positive contribution from the two-dimensional spin-dependent VRH and a negative contribution from the two-dimensional weak localization, with some contribution of the Ni impurities in the sample found with the transmission electron microscope and by energy dispersive spectrometer analysis.

C-axis resistivity of graphite intercalation compounds

The c-axis resistivity of stage-2, 3, 4, 5, 6, 7, and 9 graphite intercalation compounds (GICs) has been measured in the temperature range between 4.2 and 300 K with and without an external magnetic field along the c-axis. In these compounds the c-axis conduction is dominated by the in-plane conduction because of the highly anisotropic resistivity. The temperature dependence of strongly depends on the stage number. The stage-2 and 3 GICs show a metallic behaviour: increasing with increasing temperature. The logarithmic behaviour in is observed in a limited temperature range for stages 5 and 6, and negative longitudinal magnetoresistance is observed for stages 3 to 7, indicating that the two-dimensional weak localization effect may occur mainly in the interior graphite layers with a small charge transfer. The c-axis resistivity of stage-3 to 9 GICs shows a unusual thermal hysteresis in the temperature range between 180 and 240 K. It has two local minima at critical temperatures - 210 K) and (= 223 - 231 K) depending on the stage number. The carriers in the bounding graphite layers with a large charge transfer are scattered by enhanced fluctuations due to electric dipole moments of molecules. There may occur a two-dimensional- (2D-) like dipole ordered phase below and a 3D-like dipole ordered phase below .

Nanowire bonding with the scanning tunneling microscope

We have developed a reliable lithographic method to pattern thin gold films by locally exposing a thin layer of an electron beam resist with the tip of a scanning tunneling microscope (STM). The exposure of the resist layer is induced by applying a voltage difference of ca. −10 V between the STM tip and the gold film on top of which the resist layer has been deposited with the Langmuir-Blodgett technique. Our resist material is omega-tricosenoic acid which acts as a negative resist. After development, the unexposed areas of the gold film can be removed via argon ion milling. We have been able to obtain continuous gold lines having a width down to 15 nm, the linewidth being determined by the exposure dose. When reducing the tunneling voltage < 5 V, exposure of the Langmuir-Blodgett resist layer no longer occurs and one switches to the classical topographic imaging mode. This switching provides us with the unique possibility to attach electrical contacts to existing nanostructures. As a nice example of this nanowire bonding, gold contacts have been attached to individual multiwalled carbon nanotubes. We have made detailed measurements of the nanotube resistance as a function of temperature down to 10 mK and in magnetic fields up to 14 T. At low temperatures a pronounced negative magnetoresistance is observed which is consistent with the two-dimensional weak electron localization occurring in the cylindrical graphite layers forming the nanotubes. The nanotubes also show reproducible fluctuations of the magnetoresistance which can be related to the Aharonov-Bohm effect in the nanotubes.

C-axis resistivity of MoCl5 graphite intercalation compounds.

The c-axis resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ of stage-2, -3, -4, -5, and -6 ${\mathrm{MoCl}}_{5}$ graphite intercalation compounds (GIC's) has been measured in the temperature range between 4.2 and 300 K with and without an external magnetic field along the c axis. The resistivity for stage-3, -4, and -5 ${\mathrm{MoCl}}_{5}$ GIC's shows a logarithmic increase (lnT) with decreasing temperature at low temperatures. The stage-4, -5, and -6 ${\mathrm{MoCl}}_{5}$ GIC's show a negative longitudinal magnetoresistance (MR), while the stage-2 and -3 ${\mathrm{MoCl}}_{5}$ GIC's show a positive longitudinal MR. Because of high anisotropy in resistivity, the c-axis conduction is dominated by the in-plane conduction. The logarithmic behavior and negative MR in ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ are discussed in terms of the two-dimensional weak localization effect occurring in the graphite basal plane. The possibility of the Kondo effect is not ruled out because of possible exchange interactions between conduction electrons and ${\mathrm{Mo}}^{5+}$ spins having an effective magnetic moment of 1.83--1.95${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$. The temperature dependence of ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ varies with the stage number: metallic behavior for stage-2 and semiconductorlike behavior for stage-5 ${\mathrm{MoCl}}_{5}$ GIC. The resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ of stage-3 ${\mathrm{MoCl}}_{5}$ GIC has a local maximum around 267 K. These behaviors of ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ are also discussed in terms of conduction mechanisms including conduction paths, phonon- and impurity-assisted hopping, and small polaron effect. \textcopyright{} 1996 The American Physical Society.

Electron localization in band-tail transport of high-mobility poly-Si TFTs

The results of low-temperature transport properties on high-mobility poly-Si thin film transistors (TFTs) have been examined by measurement of the resistance as a function of temperature, magnetoresistance (MR) and Hall effect. It has been shown that the transition between the two-dimensional (2D) weak and strong localization (WL and SL) occurs around the sheet resistance R = π h ̵ /e 2 (⋍ 13 kΩ), where ( 1 2 )k F l ∼ 1 , in the band-tail states, caused by potential fluctuations in the inversion layer of TFTs. In the barely SL regime, R at low temperatures is found to obey the Efros-Shklovskii variable-range hopping (VRH) law in the presence of the Coulomb gap in the density of states. In both regimes of WL and SL, a negative MR has been observed and interpreted by the quantum interference effect in each regime.

Resistance of ceramic samples: 2D localization and time dependence

In this paper, we report results of giant magnetoresistance obtained in a ceramic sample. The results show that between 40 mK and 30 K, the resistance increases as log(T) when temperature decreasing, which could be associated with the two-dimensional weak localization effect. The time dependence of the resistance after changing the magnetic field was also measured at different temperatures. At temperatures higher than 2 K, the decay of resistance is associated with the decay of the magnetization. Bellow this temperature, however, the observed large variation of the resistance with time after changing the magnetic field may be associated with the reconfiguration of magnetic structure.

Quantum transport in a multiwalled carbon nanotube.

We report on electrical resistance measurements of an individual carbon nanotube down to a temperature $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}20\mathrm{mK}$. The conductance exhibits a $\mathrm{ln}T$ dependence and saturates at low temperature. A magnetic field applied perpendicular to the tube axis increases the conductance and produces aperiodic fluctuations. The data find a global and coherent interpretation in terms of two-dimensional weak localization and universal conductance fluctuations in mesoscopic conductors. The dimensionality of the electronic system is discussed in terms of the peculiar structure of carbon nanotubes.

Systematic evolution of electron localization in Bi2Sr2CuOy

The electronic transport properties in Bi2Sr2CuOy crystals have been investigated with the focus on the localized behaviours at low temperature. It is found that in the passage of transition from metallic to insulating states the samples first show two-dimensional weak localization behaviour, and cross over to the variable-range hopping conduction corresponding to the strong-localization regime. We analyse the experimental results and suggest that the metal-insulator transition is caused by the effects of both disorder in the lattice and electron correlations.

Magneto-Transport Properties of Epitaxial Iron-Silicides

AbstractThe phase-breaking time τφ'. in thin α-FeSi2 films was obtained from the analyses of the lowtemperature magnetoresistance (MR). The films were grown by molecular beam epitaxy (MBE) on Si(111) and capped with epitaxial Si. The MR behavior is interpreted in terms of two-dimensional (2D) weak localization with strong spin-orbit interaction and electron-electron interaction (EEI). By fitting the MR data we obtained the temperature dependence of τφ. The results indicate the phase-breaking time to vary as T− over a large temperature range from 1.7 to 15 K, in agreement with the dependence predicted by the EET in 2D systems.

LOCALIZATION OF ELECTRONS IN Bi_2Sr_2CuO_y CRYSTALS

The ab-plane resistivity of Bi2Sr2CuO, crystals as a function of temperature has been measured. In the process of metal-insulator transition, the crystals at low temperature exhibit the two-dimensional weak localization behavior at first, and cross over to the variable-range-hopping conduction of the strong localization regime gradually. Discussions on the nature of the metal-insulator transition are presented based on the experimental results.

Weak localization and electron-electron interactions in a two-dimensional grid lateral surface superlattice.

Low-field magnetoresistance measurements were performed on a two-dimensional grid lateral surface superlattice (LSSL) fabricated on a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction. From a one-parameter fit to the two-dimensional weak-localization theory we have obtained the effective inelastic scattering length at different temperatures. By subtracting the weak-localization term, we have also investigated the electron-electron interactions in this system. Both localization and interaction effects saturate at low temperatures when the inelastic scattering length and thermal diffusion length are longer than the period of the LSSL. At higher temperatures, when the thermal diffusion length becomes comparable to the period of the LSSL, the electron-electron interaction term causes the conductivity to decrease logarithmically with temperature. These results can be explained in terms of coherent backscattering of the electrons in a fraction of the electron puddles formed below the superlattice gate. Disorder ensures that the cells showing these results are not neighbors, so that this effect is an ensemble average of many unit cells several periods apart.

Resistance anisotropy in strongly anisotropic high- Tc superconductors

Non-superconducting metallic single crystals from the n-type high- T c system Pr 2− x Ce x CuO 4 exhibit a two-dimensional weak-localization behavior at low temperatures. We use the negative magnetoresistance from the coherent backscattering of electrons in the CuO 2 planes as a probe for the microscopic current paths, when the macroscopic current direction is along the c-axis. The anisotropy of the magnetoresistance for the magnetic field parallel and perpendicular to the CuO 2 planes provides clear evidence that the voltage drop develops mainly in the ( ab) planes. Hence metallic bridging defects between the CuO 2 layers are of dominant importance for the c-axis conductivity. We demonstrate that the peculiar anisotropy of ϱ c ( T, H) at the superconducting transition of Bi(2212) crystals can be explained following the same lines.

Quantum transport of buried single-crystalline CoSi2 layers in (111)Si and (100)Si substrates.

Magnetoresistance data for clean crystalline ${\mathrm{CoSi}}_{2}$ layers were analyzed in terms of weak localization, Coulomb interactions, and superconducting fluctuations. The ${\mathrm{CoSi}}_{2}$ layers with thicknesses of 11.5 nm in (111)Si and 23 nm in (100)Si were fabricated by high-dose ion implantation and subsequent annealing in a rapid thermal annealer (known as ion-beam synthesis or mesotaxy). The magnetic-field dependence of the resistance is interpreted in terms of two-dimensional weak localization with strong spin-orbit interaction and an addtional classical contribution proportional to ${\mathrm{H}}^{2}$. No indication of magnetic scattering was found, which is a sign of the ``cleanness'' of the samples. Long phase-coherence lengths of ${\mathit{l}}_{\mathrm{\ensuremath{\varphi}}}$\ensuremath{\approxeq}0.75 \ensuremath{\mu}m in (111)Si and ${\mathit{l}}_{\mathrm{\ensuremath{\varphi}}}$\ensuremath{\approxeq}2.3 \ensuremath{\mu}m in (100)Si at 4.2 K were determined by fitting the magnetoresistance data. The inferred inelastic-scattering time is interpreted as a sum of a clean-limit electron-electron process (dominant at temperatures below \ensuremath{\approxeq}6 K) and an electron-phonon process dominant at higher temperatures. We further observed a general orientation dependence of the electrical transport properties of mesotaxial ${\mathrm{CoSi}}_{2}$ layers, such as anisotropy in the residual resistance, Hall coefficient, and the prefactor for the classical ${\mathrm{H}}^{2}$ dependence of the magnetoresistance. This is probably related to multiple-band effects in ${\mathrm{CoSi}}_{2}$.

Two-dimensional weak localization in combined perpendicular and parallel magnetic fields.

We have studied the magnetoresistance of thin films of Au, Ag, and Au(Fe) (Au doped with small concentrations of Fe) at low temperatures. Magnetic fields both perpendicular and parallel to the plane of the film were employed, and in some experiments these two fields were applied simultaneously and independently. Our results are compared in detail with the predictions of weak-localization theory. The agreement between theory and experiment for purely perpendicular fields is reasonably good, but some of the behavior in parallel fields, especially for Au(Fe), cannot be reconciled with the usual theory. Our results can be qualitatively understood if one assumes that the spin-orbit-scattering length is field dependent, or that the phase-breaking length becomes shorter in large parallel fields. Either of these results would be contrary to conventional beliefs.

Inhomogeneous magnesium hydride synthesized by low temperature ion implantation: weak localization effect

Metastable MgHx hydride was prepared by H ion implantation into Mg films at 5 K. The resistivity and magnetoresistance temperature dependence reveal weak localization effects due to atomic disorder. At low hydrogen concentrations, x ≤0.3, the conductivity varies as σ∼log (T), typical of two-dimensional weak localization behaviour. The resistivity is also very sensitive to the sample inhomogeneity, due to H diffusion, which can be modelled by introducing a temperature-dependent geometrical percolating factor G. At higher H concentrations, 0.7 ≤x ≤3, after annealing at 20 K, 50 K and 110 K, the samples also exhibit weak localization but with three-dimensional behaviour i.e. a $\sigma \sim \sqrt{T}$. Our analysis is consistent with the existence of an inhomogeneous system formed by a mixture of two phases with contrasted conduction properties, one of which is a well-behaved metal, while the other displays the localization properties. The results lead us to identify the former phase to a non percolating superconducting phase at low temperature.

Negative Magnetoresistance in Activated Carbon Fibers Heat-Treated Above 2000°C

ABSTRACTActivated carbon fibers (ACFs) were heat-treated at temperatures above 2000°C to study both the effect of heat treatment on the order development in ACFs and the effect of granularity on the transport properties of granular materials in general. The electrical conductivity σ(T) and Magnetoresistance (MR) were measured as a function of temperature for ACFs Made of two different precursors and heat-treated at different temperatures. While the field dependence of the observed negative MR could be fit to the two-dimensional weak localization (2D WL) theory at each measurement temperature, σ(T) showed only a weak temperature dependence, inconsistent with the ln (T) dependence predicted by the same theory. Even More interesting is the observation of a negative MR, which is a quantum-Mechanical phenomenon, near room temperature. It is thought that the grain boundaries might be responsible for such deviations from the standard 2D WL theory.

Weak localization and hole-hole interaction effects in silicon-boron delta layers

Measurements of sheet resistance and Hall coefficient between 0.3 K and 30 K have been used to infer two-dimensional weak localization and hole-hole interaction effects in Si:B delta-doped layers. It is found that the renormalized screening parameter in the interaction theory F* approximately 0.9 for samples of sheet concentrations 1.8*1013 cm-2 to 7.6*1013 cm-2 and is only weakly dependent on carrier concentration, in agreement with theory. The weak localization correction provides evidence for spin-orbit scattering, which appears to become increasingly important as the sheet concentration is increased.