Weak Localization Measurements Research Articles

Strain control in graphene on GaN nanowires: Towards pseudomagnetic field engineering

Gallium nitride nanowire and nanorod substrates are prospective platforms allowing to control the local strain distribution in graphene films on top of them, resulting in an induction of pseudomagnetic fields. AFM measurements performed in a HybriD mode complemented by SEM allow for a detailed visualization of the strain distribution on graphene surface. Graphene in direct contact with supporting regions is tensile strained, while graphene located in-between is characterized by lower strain. Characteristic tensile strained wrinkles also appear in the areas between the supporting regions. A positive correlation between strain gradient and distances between borders of supporting regions is observed. These results are confirmed by analysis of the Raman D’ band intensity, which is affected by an enhancement of intravalley scattering. Furthermore, scanning tunneling spectroscopy shows a local modification of the density of states near the graphene wrinkle and weak localization measurements indicate the enhancement of pseudomagnetic field-induced scattering. Therefore, we show that nanowire and nanorod substrates provide strain engineering and induction of pseudomagnetic fields in graphene. The control of graphene morphology by modification of distances between supporting regions is promising for both further fundamental research and the exploration of innovative ways to fabricate pseudomagnetic field-based devices like sensors or filters.

New method of transport measurements on van der Waals heterostructures under pressure

The interlayer coupling, which has a strong influence on the properties of van der Waals heterostructures, strongly depends on the interlayer distance. Although considerable theoretical interest has been demonstrated, experiments exploiting a variable interlayer coupling on nanocircuits are scarce due to the experimental difficulties. Here, we demonstrate a novel method to tune the interlayer coupling using hydrostatic pressure by incorporating van der Waals heterostructure based nanocircuits in piston-cylinder hydrostatic pressure cells with a dedicated sample holder design. This technique opens the way to conduct transport measurements on nanodevices under pressure using up to 12 contacts without constraints on the sample at the fabrication level. Using transport measurements, we demonstrate that a hexagonal boron nitride capping layer provides a good protection of van der Waals heterostructures from the influence of the pressure medium, and we show experimental evidence of the influence of pressure on the interlayer coupling using weak localization measurements on a transitional metal dichalcogenide/graphene heterostructure.

Weak localization measurements of electronic scattering rates in Li-doped epitaxial graphene

Early experiments on alkali-doped graphene demonstrated that the dopant adatoms modify the conductivity of graphene significantly, as extra carriers enhance conductivity while Coulomb scattering off the adatoms suppresses it. However, conductivity probes the overall scattering rate, so a dominant channel associated with long-range Coulomb scattering will mask weaker short-range channels. We present weak localization measurements of epitaxial graphene with lithium adatoms that separately quantify intra- and intervalley scattering rates, then compare the measurements to tight-binding calculations of expected rates for this system. The intravalley rate is strongly enhanced by Li deposition, consistent with Coulomb scattering off the Li adatoms. A simultaneous enhancement of intervalley scattering is partially explained by extra carriers in the graphene interacting with residual disorder. But differences between measured and calculated rates at high Li coverage may indicate adatom-induced modifications to the band structure that go beyond the applied model. Similar adatom-induced modifications of the graphene bands have recently been observed in ARPES, but a full theoretical understanding of these effects is still in development.

Spin relaxation in fluorinated single and bilayer graphene

We present a joint experiment-theory study on the role of fluorine adatoms in spin and momentum scattering of charge carriers in dilute fluorinated graphene and bilayer graphene. The experimental spin-flip and momentum scattering rates and their dependence on the density of fluorine and carrier doping are obtained through weak localization and conductivity measurements, respectively, and suggest the role of fluorine as resonant magnetic impurities. For the estimated fluorine concentration of a few 100 ppm, the observed spin lifetimes are in the range of 1-10\,ps. Theoretically, we established tight-binding electronic structures of fluorinated graphene and bilayer graphene by fitting to density functional supercell calculations and performed a comprehensive analysis of the spin-flip and momentum scattering rates within the same devices, aiming to develop a consistent description of both scattering channels. We find that resonant scattering in graphene is very sensitive to the precise position of the resonance level, as well as to the magnitude of the exchange coupling between itinerant carriers and localized spins. The experimental data point to the presence of weak spin-flip scatterers that, at the same time, relax the electron momentum strongly, nearly preserving the electron-hole symmetry. Such scatterers would exhibit resonance energies much closer to the neutrality point than what density functional theory predicts in the dilute limit. The inclusion of a magnetic moment on fluorine adatoms allowed us to qualitatively capture the carrier density dependence of the experimental rates but predicts a greater (weaker) spin (momentum) relaxation rate than the measurements. We discuss possible scenarios that may be responsible for the discrepancies. Our systematic study exposes the complexities involved in accurately capturing the behavior of adatoms on graphene.

Weak localization and electron–electron interactions in few layer black phosphorus devices

Few layer phosphorene (FLP) devices are extensively studied due to their unique electronic properties and potential applications on nano-electronics. Here we present magnetotransport studies which reveal electron–electron interactions as the dominant scattering mechanism in hexagonal boron nitride-encapsulated FLP devices. From weak localization measurements, we estimate the electron dephasing length to be 30 to 100 nm at low temperatures, which exhibits a strong dependence on carrier density n and a power-law dependence on temperature (∼T−0.4). These results establish that the dominant scattering mechanism in FLP is electron–electron interactions.

Weak Delocalization in Graphene on a Ferromagnetic Insulating Film.

Graphene has been predicted to develop a magnetic moment by proximity effect when placed on a ferromagnetic film, a promise that could open exciting possibilities in the fields of spintronics and magnetic data recording. In this work, the interplay between the magnetoresistance of graphene and the magnetization of an underlying ferromagnetic insulating film is studied in detail. A clear correlation between both magnitudes is observed but through a careful modeling of the magnetization and the weak localization measurements, that such correspondence can be explained by the effects of the magnetic stray fields arising from the ferromagnetic insulator is found. The results emphasize the complexity arising at the interface between magnetic and 2D materials.

Enhanced quantum coherence in graphene caused by Pd cluster deposition

We report on the unexpected increase in the dephasing lengths of a graphene sheet caused by the deposition of Pd nanoclusters, as demonstrated by weak localization measurements. The dephasing lengths reached saturated values at low temperatures. Theoretical calculations indicate the p-type charge transfer from the Pd clusters, which contributes more carriers. The saturated values of dephasing lengths often depend on both the carrier concentration and mean free path. Although some impurities are increased as revealed by decreased mobilities, the intense charge transfer leads to the improved saturated values and subsequent improved dephasing lengths.

Limitations to carrier mobility and phase-coherent transport in bilayer graphene.

We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase-coherence times τϕ as well as the inter- and intravalley scattering times τi and τ*, respectively. While τϕ is in qualitative agreement with an electron-electron interaction-mediated dephasing mechanism, electron spin-flip scattering processes are limiting τϕ at low temperatures. The analysis of τi and τ* points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.

Weak localization and Berry flux in topological crystalline insulators with a quadratic surface spectrum

The paper examines weak localization (WL) of surface states with a quadratic band crossing in topological crystalline insulators. It is shown that the topology of the quadratic band crossing point dictates the negative sign of the WL conductivity correction. For the surface states with broken time-reversal symmetry, an explicit dependence of the WL conductivity on the band Berry flux is obtained and analyzed for different carrier-density regimes and types of the band structure (normal or inverted). These results suggest a way to detect the band Berry flux through WL measurements.

Magneto-transport in MoS2: Phase Coherence, Spin–Orbit Scattering, and the Hall Factor

We have characterized phase coherence length, spin-orbit scattering length, and the Hall factor in n-type MoS2 2D crystals via weak localization measurements and Hall-effect measurements. Weak localization measurements reveal a phase coherence length of ~50 nm at T = 400 mK for a few-layer MoS2 film, decreasing as T(-1/2) with increased temperatures. Weak localization measurements also allow us, for the first time without optical techniques, to estimate the spin-orbit scattering length to be 430 nm, pointing to the potential of MoS2 for spintronics applications. Via Hall-effect measurements, we observe a low-temperature Hall mobility of 311 cm(2)/(V s) at T = 1 K, which decreases as a power law with a characteristic exponent γ = 1.5 from 10 to 60 K. At room temperature, we observe Hall mobility of 24 cm(2)/(V s). By determining the Hall factor for MoS2 to be 1.35 at T = 1 K and 2.4 at room temperature, we observe drift mobility of 420 and 56 cm(2)/(V s) at T = 1 K and room temperature, respectively.

Tunable doping of a metal with molecular spins

The mutual interaction of localized magnetic moments and their interplay with itinerant conduction electrons in a solid are central to many phenomena in condensed-matter physics, including magnetic ordering and related many-body phenomena such as the Kondo effect, the Ruderman-Kittel-Kasuya-Yoshida interaction and carrier-induced ferromagnetism in diluted magnetic semiconductors. The strength and relative importance of these spin phenomena are determined by the magnitude and sign of the exchange interaction between the localized magnetic moments and also by the mean distance between them. Detailed studies of such systems require the ability to tune the mean distance between the localized magnetic moments, which is equivalent to being able to control the concentration of magnetic impurities in the host material. Here, we present a method for doping a gold film with localized magnetic moments that involves depositing a monolayer of a metal terpyridine complex onto the film. The metal ions in the complexes can be cobalt or zinc, and the concentration of magnetic impurities in the gold film can be controlled by varying the relative amounts of cobalt complexes (which carry a spin) and zinc complexes (which have zero spin). Kondo and weak localization measurements demonstrate that the magnetic impurity concentration can be systematically varied up to ∼800ppm without any sign of inter-impurity interaction. Moreover, we find no evidence for the unwanted clustering that is often produced when using alternative methods.

Aharonov–Bohm oscillations in a nanoscale dopant ring in silicon

We have fabricated a nanoscale ring of phosphorus dopants in silicon using a scanning tunneling microscope to pattern a hydrogen resist layer. Low-temperature magnetotransport measurements reveal both aperiodic universal conductance fluctuations and periodic Aharonov–Bohm oscillations. From the ratio of the h/e and h/2e components of the Aharonov–Bohm oscillations, we estimate a phase coherence length of ≃100 nm at a temperature T=100 mK. This is in agreement with previous results from weak localization measurements on low-dimensional dopant devices in silicon.

Character of electronic states in graphene antidot lattices: Flat bands and spatial localization

Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasiflat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy localized states compete with states induced by the superlattice-scale defects in this system, which have been proposed as hosts for electron-spin qubits. Furthermore, we suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.

High-field measurements of electron decoherence time in metallic nanowires: switching off magnetic impurity spins.

We report low-temperature measurements of electron decoherence time in a series of pure gold wires, 18 nm thick and 30 nm wide. At fields up to 15 T, large enough to polarize any concentration of magnetic impurity spins, conductance fluctuation measurements show almost no temperature dependence of the decoherence time below 300 mK, both in the correlation field for interference and the root-mean-square value of the fluctuations. Combined with previous low-field weak localization measurements on samples from similar material, our experiment suggests that the ubiquitous saturation of decoherence time in these samples is not due to any mechanism based on magnetic impurity spins.

Magnetic-field effects in energy relaxation mediated by Kondo impurities in mesoscopic wires

We study the energy distribution function of quasiparticles in short voltage biased mesoscopic wires in the presence of magnetic impurities and applied magnetic field. The system is described by a Boltzmann equation where the collision integral is determined by coupling to spin-$\frac{1}{2}$ impurities. We develop a theory of the coupling of nonequilibrium electrons to dissipative spins. This theory is valid as long as the characteristic smearing of the steps in the energy distribution function, which depends both on the bias voltage and the location of the probe, exceeds the Kondo temperature. We further address the renormalization of coupling constants by nonequilibrium electrons. Magnetic-field dependence of the energy relaxation rate turns out to be nonmonotonic. For low magnetic field an enhancement of energy relaxation is found, whereas for larger magnetic fields the energy relaxation decreases again meeting qualitatively the experimental findings by Anthore et al. (cond-mat/0109297). This gives a strong indication that magnetic impurities are in fact responsible for the enhanced energy relaxation in copper wires. Our theoretical results are in good agreement with the experiment at large bias voltages where the theory is applicable. At the same time, at small bias voltages there are substantial quantitative deviations. Furthermore, the concentration of the spins, which follows from the energy relaxation for Cu, seems to to be substantially higher than the concentration estimated from weak localization (dephasing rate) measurements. Since the approach presented is valid only above Kondo temperature, it does not apply to the related problem of weak localization at low temperature in equilibrium.

Frequency dependence of the Nyquist noise contribution to the dephasing rate in disordered conductors

We calculate the Nyquist noise contribution to the dephasing rate $1/{\ensuremath{\tau}}_{\mathrm{NN}}(\ensuremath{\omega},T)$ of disordered conductors in d dimensions in the regime where the frequency \ensuremath{\omega} is larger than the temperature T. For systems with a continuous spectrum we find at zero temperature $1/{\ensuremath{\tau}}_{\mathrm{NN}}(\ensuremath{\omega},0)\ensuremath{\propto}{\ensuremath{\nu}}_{d}^{\ensuremath{-}1}(\ensuremath{\omega}{/D)}^{d/2},$ which agrees qualitatively with the inelastic quasiparticle scattering rate. Here ${\ensuremath{\nu}}_{d}$ is d-dimensional density of states, and D is the diffusion coefficient. Because at zero frequency and finite temperatures $1/{\ensuremath{\tau}}_{\mathrm{NN}}(0,T)\ensuremath{\propto}[T/({\ensuremath{\nu}}_{d}{D}^{d/2}){]}^{2/(4\ensuremath{-}d)}$ for $d<2,$ the frequency dependence of $1/{\ensuremath{\tau}}_{\mathrm{NN}}(\ensuremath{\omega},0)$ in reduced dimensions cannot be obtained by simply replacing $\stackrel{\ensuremath{\rightarrow}}{T}\ensuremath{\omega}$ in the corresponding finite-temperature expression for $1/{\ensuremath{\tau}}_{\mathrm{NN}}(0,T).$ We also discuss the dephasing rate in mesoscopic systems with length L and show that for $\ensuremath{\omega}\ensuremath{\gtrsim}{D/L}^{2}$ the spectrum is effectively continuous as far as transport is concerned. We propose weak localization measurements of the ac conductivity in the GHz range to clarify the origin of the experimentally observed zero-temperature saturation of the dephasing rate.

Electron phase coherence length in a lattice of antidots

The temperature dependence of the phase coherence length Lϕ of electrons in a two-dimensional hexagonal lattice of antidots is investigated through weak localization (WL) measurements over a wide temperature range from 40mK to 30K. The magnetic field dependence of the WL can be perfectly described by the conventional theory for disordered conductors, with an additional magnetic-field-independent prefactor α. Using a two parameters fit of the WL, Lϕ can be extracted. An unusual T−1/4 dependence was found for Lϕ, which is contradictory with most of the models proposed for phase breaking processes. A saturation of Lϕ was observed below 1K. Finally, α was found to scale exponentially with the temperature. Surprisingly, the values obtained for α were particularly high, revealing mechanisms which enhance the WL in our system.

Kondo effect in systems of reduced dimensionality.

This paper describes a series of experiments concerning the Kondo effect in metal films and wires which have revealed some surprising aspects of the Kondo behavior in quasi-two- and quasi-one-dimensional systems. We have studied two different Kondo alloys, Au(Fe) and Cu(Fe), and found that in both cases the Kondo contribution to the resistivity \ensuremath{\Delta}${\mathrm{\ensuremath{\rho}}}_{\mathit{K}}$ is sensitive to the size of the sample, and is suppressed at length scales below about 1500 \AA{}. This critical length scale is observed in both quasi-two- and quasi-one-dimensional systems. Studies of bilayer samples composed of a Kondo film in contact with a layer of the pure host material [e.g., Cu(Fe) overcoated with Cu] reveal the existence of a Kondo proximity effect, which is also length scale dependent. Results for the spin scattering rate ${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ for conduction electrons, obtained via weak localization measurements, indicate that ${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ is suppressed in quasi-two-dimensional systems in a manner similar to that found for \ensuremath{\Delta}${\mathrm{\ensuremath{\rho}}}_{\mathit{K}}$. Finally, we find that disorder plays a central role; increasing the amount of disorder (i.e., elastic scattering) suppresses \ensuremath{\Delta}${\mathrm{\ensuremath{\rho}}}_{\mathit{K}}$. Surprisingly, the length scale which controls the Kondo behavior seems to be essentially independent of the Kondo temperature ${\mathit{T}}_{\mathit{K}}$. This implies that physics beyond that contained in the simplest Kondo models is responsible.

Dimensional Cross-Over in Thin Film Spin-Glasses

Measurements of the electrical transport in the presence of a magnetic field for very thin spin-glass films of AuMn, AgMn and AuFe alloys, are reported. The influence of the effective dimensionality on the spin-glass order is studied by varying the film thickness between 4nm and 40nm. Weak electron localization and spin-glass resistivity measurements only provide a qualitative picture of the transition from spin-glass to Kondo behaviour in the thinnest films. Measuring the temperature dependence of the Hall resistivity on the other hand directly reflects the thickness dependence of the freezing temperature Tf. Our results clearly indicate that dimensionality effects as well as the reduced elastic mean free path influence the spin-glass transition. The experimental correlation length exponent v = 0.8 is smaller than the theoretically predicted value.