Short-range Scatterers Research Articles

Doped graphene characterized via Raman spectroscopy and magneto-transport measurements

Functionalizing graphene beyond its intrinsic properties has been a key concept since the first successful realization of this archetype monolayer system. While various concepts, such as doping, co-doping, and layered device design, have been proposed, the often complex structural and electronic changes are often jeopardizing simple functionalization attempts. Here, we present a thorough analysis of the structural and electronic properties of co-doped graphene via Raman spectroscopy as well as magneto-transport and Hall measurements. The results highlight the challenges in understanding its microscopic properties beyond the simple preparation of such devices. It is discussed how co-doping with N and B dopants leads to effective charge-neutral defects acting as short-range scatterers, while charged defects introduce more long-range scattering centers. Such distinct behavior may obscure or alter the desired structural as well as electronic properties not anticipated initially. Exploring further the preparation of effective pn-junctions, we highlight step by step how the preparation process may lead to alterations in the intrinsic properties of the individual layers. Importantly, it is highlighted in all steps how the inhomogeneities across individual graphene sheets may challenge simple interpretations of individual measurements.

Influence of Long Range and Short Range Scattering Mechanisms on Electron Transport in Double Layer Graphene System

Theoretically investigated electronic transport properties of Double Layer Graphene System (DLGS) at absolute zero temperature using Boltzmann Transport equation are reported here with varying different parameters like relative carrier concentration (n(c)/n(CI)), relative dielectric constant (εr) and interlayer distance d. The contributions from two different scattering mechanisms namely, short range and long range scattering have been evaluated and found that the short range scatterers have influenced the scattering rate and the conductivity, long range scattering rate is more dominating in both high and low density regime. The conductivity curve is showing superlinear behavior in absence of short range impurities while the sublinear nature when some short range point defects are added. The role of screening effect between two layers and thus the dielectric constant on conductivity reaches to maximum very rapidly as the interlayer distance d is increased from 0.5 nm to 5 nm. The mismatch between dielectric constants of middle layer and substrate enhances the conductivity value.

Photovoltaic Hall effect in the two-dimensional electron gas: Kinetic theory

We study theoretically transverse photoconductivity induced by circularly polarized radiation, i.e., the photovoltaic Hall effect, and linearly polarized radiation causing intraband optical transitions in the two-dimensional electron gas (2DEG). We develop a microscopic theory of these effects based on the analytical solution of the Boltzmann equation for arbitrary electron spectrum and scattering mechanisms. We calculate the transverse photoconductivity of 2DEG with parabolic and linear dispersion for short-range and Coulomb scatterers at different temperatures. We show that the transverse electric current is significantly enhanced at frequencies comparable to the inverse energy relaxation time, whereas at higher frequencies the excitation spectrum and the direction of current depend on the scattering mechanism. We also analyze the effect of thermalization processes caused by electron-electron collisions on the photoconductivity.

Relevance of weak and strong classical scattering for the giant negative magnetoresistance in two-dimensional electron gases

The giant negative magnetoresistance (GNMR), observed in two-dimensional electron gases of high mobility, is studied by controlled definition of additional short-range scatterers in form of two-dimensional Lorentz arrays of varying obstacle density, as well as in the presence of edge scattering. The results support models, which ascribe the temperature-independent regime of the GNMR to strong, classical scattering and the temperature-dependent regime to electron-electron interactions under the influence of mixed disorder. The threshold magnetic field, which separates the two regimes, is in rough agreement with the lower percolation transition of the Lorentz array. At large obstacle densities, interaction corrections are suppressed and memory effects become more relevant. Shape, amplitude, and width of the GNMR depend sensitively on the time scales of the contributing scattering mechanisms. This can lead to qualitatively similar shapes for quite different parameter values.

Electron and hole transport in disordered monolayerMoS2: Atomic vacancy induced short-range and Coulomb disorder scattering

Atomic disorder is a common limiting factor for the low-temperature mobility in monolayer transition-metal dichalcogenides (TMDs; $M{X}_{2}$). Here, we study the effect of often occurring atomic vacancies on carrier scattering and transport in $p$- and $n$-type monolayer ${\mathrm{MoS}}_{2}$. Due to charge trapping in vacancy-induced in-gap states, both neutral and charged vacancies resembling, respectively, short-range and combined short-range and long-range Coulomb scatterers must be considered. Using the $T$-matrix formalism, we demonstrate a strong renormalization of the Born description of short-range scattering, manifested in a pronounced reduction and a characteristic energy dependence of the scattering rate. As a consequence, carrier scattering in TMDs with charged vacancies is dominated by the long-range Coulomb disorder scattering, giving rise to a strong screening-induced temperature and density dependence of the low-temperature carrier mobility. For TMDs with neutral vacancies, the absence of intrinsic Coulomb disorder results in significantly higher mobilities as well as an unusual density dependence of the mobility which decreases with the carrier density. Our work illuminates the transport-limiting effects of atomic-vacancy scattering relevant for high-mobility TMD devices.

Multifractal spectra of extended states with gate tunable Rashba spin-orbit interaction in two-dimensional electron systems

In a two dimensional electron gas with disorder, subjected to a strong magnetic field and in the presence of homogeneous Rashba spin-orbit coupling (SOC), the extended states that lie close to the center of each spin resolved Landau level (LL) have multifractal nature. In this work, multifractal analysis has been performed to extended states that lie close to the center of the spin unresolved lowest LL and the spin resolved first LL. Using both, a gaussian white noise potential and a series of short range scatterers as the source of disorder, the numerical results are found to agree within the statistical deviation. We have found that the multifractal exponents of extended states close to the center of the spin unresolved lowest LL and the spin down oriented first LL, are independent of the SOC parameter αd. However, the multifractal exponents of extended states close to the center of the spin up oriented first LL depend on αd. For these states, the inverse participation number, which characterizes the extent of localization of a given state, is observed to be an increasing function of αd, indicating that these states are less extended for stronger SOCs. This is in contrast to the effects of SOC on weak localization physics, where it tends to increase the conductivity and reduce localization.

Thermoelectric and optical probes for a Fermi surface topology change in noncentrosymmetric metals

Noncentrosymmetric metals such as ${\mathrm{Li}}_{2}{({\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{Pt}}_{x})}_{3}\mathrm{B}$ have different Fermi surface topology below and above the band touching point where spin-degeneracy is not lifted by the spin-orbit coupling. We investigate thermoelectric and optical response as probes for this Fermi surface topology change. We show that the chemical potential displays a dimensional crossover from three-dimensional to one-dimensional characteristics as the descending Fermi energy crosses the band touching point. This dimensional crossover is due to the existence of different Fermi surface topology above and below the band touching point. We obtain an exact expression of relaxation time due to short-range scatterer by solving Boltzmann transport equations self-consistently. The thermoelctric power and figure of merit are significantly enhanced as the Fermi energy goes below the band touching point owing to the underlying one-dimensional-like nature of noncentrosymmteric bulk metals. The value of thermoelectric figure of merit goes beyond two as the Fermi energy approaches to the van Hove singularity for lower spin-orbit coupling. Similarly, the studies of the zero-frequency and finite-frequency optical conductivities in the zero-momentum limit reflect the nature of topological change of the Fermi surface. The Hall coefficient and optical absorption width exhibit distinct signatures in response to the changes in Fermi surface topology.

Thermoelectric and thermal transport properties of graphene under strong magnetic field

We investigate theoretically the thermoelectric and thermal transport properties of graphene under strong magnetic field in the presence of short-range scatterers. The numerical results are in good agreement with available experimental data for all thermoelectric quantities except for the Seebeck coefficient near zero chemical potential. This anomaly is attributed to the overestimation of the longitudinal resistivity. Furthermore, we find an anomalous oscillation in the transverse thermal conductivity at the lowest Landau level and double peaks in the longitudinal thermal conductivity at higher Landau levels, which are expected to be observed in future experiments on high mobility graphene samples. An important finding of our work is that the thermoelectric figure of merit ZT can be as high as 2.4 for a magnetic field under which the chemical potential is pinned to the n=1 Landau level. This finding can greatly advance the thermoelectric application of graphene.

Valley Hall Conductivity in Graphene: Effects of Higher-Order Scattering

The valley Hall conductivity, having opposite signs between the K and K′ valleys, is calculated in monolayer and bilayer graphenes with nonzero gap in the presence of short-range scatterers within a single-site approximation. In the case of small disorder, the Hall conductivity is quantized into ±e2/2h and ±e2/h in the monolayer and bilayer graphene, respectively, in the gap region, while it is enhanced over the results in the absence of scatterers in the band region. With the increase in the strength of each impurity potential, large asymmetry between the conduction and valence band appears. For scatterers with attractive potential, the disorder parameter is effectively enhanced and reduced in the conduction and valence band, respectively. The behavior is opposite for repulsive scatterers. Effects of skew scattering causing asymmetry in the scattering direction remain small and do not play significant role.

Focal Points at Infinity for Short-Range Scattering Trajectories

Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of that manifold.

Evidence for non-Markovian electron dynamics in the microwave absorption of a two-dimensional electron system

We have studied the absorption of monochromatic microwave radiation in high-quality two-dimensional electron systems for the frequency span from 10 to 380 GHz using a bolometric method. For frequencies above 100 GHz the absorption exhibits an anomalous magnetic field dependence. Minima form at harmonics of the cyclotron resonance frequency. The results contrast previously reported data for other frequency ranges. Quasiclassical memory effects originating from the non-Markovian dynamics of electrons in a disorder potential containing short-range scatterers on top of a smooth potential background favorably account for the observed behavior.

Scattering from spin-polarized charged impurities in graphene

We study the spin relaxation of charge carriers in graphene in the presence of spin-polarized charged impurities by calculating the time evolution of an initially polarized state. The spin relaxation time shows completely different energy behavior for short-ranged and long-ranged spin scatterers and can be used to identify the dominant source of spin scattering. Our results agree well with recent experimental findings and indicate that their spin relaxation is likely caused by long-ranged scatterers.

Pure spin current and perfect valley filter by designed separation of the chiral states in two-dimensional honeycomb lattices

We propose a realization of pure spin currents and perfect valley filter based on a quantum anomalous Hall insulator, around which edge states with up-spin and down-spin circulate. By applying staggered sublattice potential on the strips along the edges of sample, the edge states with down spin can be pushed into the inner boundaries of the strips while the other edge states with up spin remain on the outer boundaries, resulting in spatially separated chiral states with perfect spin polarization. Moreover, a valley filter, which is immune to short-range and smooth long-range scatterers, can be engineered by additionally applying boundary potentials on the outmost lattices of the sample. We also find that the boundary potential can be used to control the size effect induced oscillation of the inner chiral states. The connection of the boundary potential to size effect is revealed.

Long- versus Short-Range Scattering in Doped Epitaxial Graphene.

Tuning the electronic properties of graphene by adatom deposition unavoidably introduces disorder into the system, which directly affects the single-particle excitations and electrodynamics. Using angle-resolved photoemission spectroscopy (ARPES) we trace the evolution of disorder in graphene by thallium adatom deposition and probe its effect on the electronic structure. We show that the signatures of quasiparticle scattering in the photoemission spectral function can be used to identify thallium adatoms, although charged, as efficient short-range scattering centers. Employing a self-energy model for short-range scattering, we are able to extract a δ-like scattering potential δ = -3.2 ± 1 eV. Therefore, isolated charged scattering centers do not necessarily act just as good long-range (Coulomb) scatterers but can also act as efficient short-range (δ-like) scatterers; in the case of thallium, this happens with almost equal contributions from both mechanisms.

Charge transport in ion-gated mono-, bi-, and trilayer MoS2 field effect transistors.

Charge transport in MoS2 in the low carrier density regime is dominated by trap states and band edge disorder. The intrinsic transport properties of MoS2 emerge in the high density regime where conduction occurs via extended states. Here, we investigate the transport properties of mechanically exfoliated mono-, bi-, and trilayer MoS2 sheets over a wide range of carrier densities realized by a combination of ion gel top gate and SiO2 back gate, which allows us to achieve high charge carrier (>1013 cm−2) densities. We discuss the gating properties of the devices as a function of layer thickness and demonstrate resistivities as low as 1 kΩ for monolayer and 420 Ω for bilayer devices at 10 K. We show that from the capacitive coupling of the two gates, quantum capacitance can be roughly estimated to be on the order of 1 μF/cm2 for all devices studied. The temperature dependence of the carrier mobility in the high density regime indicates that short-range scatterers limit charge transport at low temperatures.

Charge transport in two dimensions limited by strong short-range scatterers: Going beyond parabolic dispersion and Born approximation

We investigate the conductivity of charge carriers confined to a two-dimensional system with the non-parabolic dispersion $k^N$ with $N$ being an arbitrary natural number. A delta-shaped scattering potential is assumed as the major source of disorder. We employ the exact solution of the Lippmann-Schwinger equation to derive an analytical Boltzmann conductivity formula valid for an arbitrary scattering potential strength. The range of applicability of our analytical results is assessed by a numerical study based on the finite size Kubo formula. We find that for any $N>1$, the conductivity demonstrates a linear dependence on the carrier concentration in the limit of a strong scattering potential strength. This finding agrees with the conductivity measurements performed recently on chirally stacked multilayer graphene where the lowest two bands are non-parabolic and the adsorbed hydrocarbons might act as strong short-range scatterers.

Quantum Hall Criticality and Localization in Graphene with Short-Range Impurities at the Dirac Point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

Boltzmann conductivity of ferromagnetic graphene with magnetic impurities

We investigate the electrical conductivity of spin-polarized graphene in the presence of short-ranged magnetic scatterers within the relaxation time approximation and the semi-classical Boltzmann approach. Spin-flip scattering of the itinerant electrons from the majority spin sub-band into the minority one results in a minimum in the electrical resistivity at a finite temperature. While this behavior is reminiscent of the renowned Kondo effect, it has an entirely different origin and differs from the Kondo effect in several aspects. In particular, unlike the Kondo effect, this is a single particle phenomena, and it does not require antiferromagnetic coupling between the magnetic moments of impurities and spins of the itinerant electrons.

Asymmetric Effect of Oxygen Adsorption on Electron and Hole Mobilities in Bilayer Graphene: Long- and Short-Range Scattering Mechanisms

We probe electron and hole mobilities in bilayer graphene under exposure to molecular oxygen. We find that the adsorbed oxygen reduces electron mobilities and increases hole mobilities in a reversible and activated process. Our experimental results indicate that hole mobilities increase due to the screening of long-range scatterers by oxygen molecules trapped between the graphene and the substrate. First principle calculations show that oxygen molecules induce resonant states close to the charge neutrality point. Electron coupling with such resonant states reduces the electron mobilities, causing a strong asymmetry between electron and hole transport. Our work demonstrates the importance of short-range scattering due to adsorbed species in the electronic transport in bilayer graphene on SiO2 substrates.

Electron spin relaxation in bilayer graphene

Electron spin relaxation due to the D'yakonov-Perel' mechanism is investigated in bilayer graphene with only the lowest conduction band being relevant. The spin-orbit coupling is constructed from the symmetry group analysis with the parameters obtained by fitting to the numerical calculation according to the latest report by Konschuh et al. [Phys. Rev. B 85, 115423 (2012)] from first principles. In contrast to single-layer graphene, the leading term of the out-of-plane component of the spin-orbit coupling in bilayer graphene shows a Zeeman-like term with opposite effective magnetic fields in the two valleys. This Zeeman-like term opens a spin relaxation channel in the presence of intervalley scattering. It is shown that the intervalley electron-phonon scattering, which has not been reported in the previous literature, strongly suppresses the in-plane spin relaxation time at high temperature whereas the intervalley short-range scattering plays an important role in the in-plane spin relaxation especially at low temperature. A marked nonmonotonic dependence of the in-plane spin relaxation time on temperature with a minimum of several hundred picoseconds is predicted in the absence of the short-range scatterers. This minimum is comparable to the experimental data. Moreover, a peak in the electron density dependence of the in-plane spin relaxation time at low temperature, which is very different from the one in semiconductors, is predicted. We also find a rapid decrease in the in-plane spin relaxation time with increasing initial spin polarization at low temperature, which is opposite to the situation in both semiconductors and single-layer graphene. A strong anisotropy between the out-of- and in-plane spin relaxations at high temperature is also revealed with the out-of-plane spin relaxation time being about two orders of magnitude larger than the in-plane one. Detailed comparisons of the temperature and electron density dependencies of the spin relaxation with the experiments of Yang et al. [Phys. Rev. Lett. 107, 047206 (2011)], Han and Kawakami [Phys. Rev. Lett. 107, 047207 (2011)], and Avsar et al. [Nano Lett. 11, 2363 (2011)] are reported.