Localization of Charge Carriers in Monolayer Graphene Gradually Disordered by Ion Irradiation (original) (raw)
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Irradiation-induced metal-insulator transition in monolayer graphene
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A brief review of experiments directed to study a gradual localization of charge carriers and metal-insulator transition in samples of disordered monolayer graphene is presented. Disorder was induced by irradiation with different doses of heavy and light ions. Degree of disorder was controlled by measurements of the Raman scattering spectra. The temperature dependences of conductivity and magnetoresistance (MR) showed that at low disorder, conductivity is governed by the weak localization and antilocalization regime. Further increase of disorder leads to strong localization of charge carriers, when the conductivity is described by the variable-range-hopping (VRH) mechanism. It was observed that MR in the VRH regime is negative in perpendicular fields and is positive in parallel magnetic fields which allowed to reveal different mechanisms of hopping MR. Theoretical analysis is in a good agreement with experimental data.
Hopping magnetoresistance in ion irradiated monolayer graphene
Physica E-low-dimensional Systems & Nanostructures, 2016
Magnetoresistance (MR) of ion irradiated monolayer graphene samples with variable-range hopping (VRH) mechanism of conductivity was measured at temperatures down to T = 1.8 K in magnetic fields up to B = 8 T. It was observed that in perpendicular magnetic fields, hopping resistivity R decreases, which corresponds to negative MR (NMR), while parallel magnetic field results in positive MR (PMR) at low temperatures. NMR is explained on the basis of the orbital model in which perpendicular magnetic field suppresses the destructive interference of many paths through the intermediate sites in the total probability of the long-distance tunneling in the VRH regime. At low fields, a quadratic dependence (|∆R/R| ∼ B 2) of NMR is observed, while at B > B * , the quadratic dependence is replaced by the linear one. It was found that all NMR curves for different samples and different temperatures could be merged into common dependence when plotted as a function of B/B *. It is shown that B * ∼ T 1/2 in agreement with predictions of the orbital model. The obtained values of B * allowed also to estimate the localization radius ξ of charge carriers for samples with different degree of disorder. PMR in parallel magnetic fields is explained by suppression of hopping transitions via double occupied states due to alignment of electron
Hopping magnetoresistance in strongly disordered monolayer graphene
Magnetoresistance (MR) of ion irradiated monolayer graphene samples with variable-range hopping (VRH) mechanism of conductivity was measured at temperatures down to T = 1.8 K in perpendicular and parallel magnetic fields up to B = 8 T. It is shown that in perpendicular magnetic fields, conductivity increases, or negative MR (NMR) is observed, while parallel magnetic field results in positive MR (PMR) at low temperatures. NMR is explained on the basis of the " orbital " model in which magnetic field suppresses the destructive interference of many paths through the intermediate sites in the total probability of the long-distance tunneling in the VRH regime. Samples with different degree of disorder were studied systematically. It is found that all NMR curves for different samples and different temperatures are merged into one common curve when plotted as a function of B/B * , where B * is experimentally determined magnetic field at which the quadratic dependence of NMR on B ...
Non-ohmic behavior of carrier transport in highly disordered graphene
Nanotechnology, 2013
We report measurements of disordered graphene probed by both a high electric field and a high magnetic field. By applying a high source-drain voltage, V sd , we are able to study the current-voltage relation I-V sd of our device. With increasing V sd , a crossover from the linear I-V sd regime to the non-linear one, and eventually to activationless-hopping transport occurs. In the activationless-hopping regime, the importance of Coulomb interactions between charged carriers is demonstrated. Moreover, we show that delocalization of carriers which are strongly localized at low T and at small V sd occurs in the presence of high electric field and perpendicular magnetic field.
Weak localization and universal conductance fluctuations in multi-layer graphene
We have performed magneto transport measurements on a multi-layer graphene device fabricated by conventional mechanical exfoliation. Suppression of weak localization (WL) as evidenced by the negative magnetoresistance (NMR) centered at zero field, and reproducible universal conductance fluctuations (UCFs) are observed. Interestingly, it is found that the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are longer than those determined from fitting the amplitudes of the UCFs to theory in the low temperature regime (T 8 K). In the high temperature regime (T > 8 K), the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory. Our new results therefore indicate a difference in the electron phase-breaking process between the two models of WL and UCFs in graphene. We speculate that the presence of the capping and bottom graphene layers, which leads the enhancement of disorder in-between, improves the localization condition for WL effect during carrier transportation in the low temperature regime. With increasing temperature, the localization condition for WL in multi-layer graphene becomes much weaker due to strong thermal damping. Therefore, the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory at high temperatures.
Localization and field-periodic conductance fluctuations in trilayer graphene
We have systematically studied quantum transport in a short trilayer-graphene field-effect transistor. Close to the charge neutrality point, our magnetoconductance data are well described by the theory of weak localization in monolayer graphene. However, as the carrier density is increased we find a complex evolution of the low field magnetoconductance that originates from a combination of the monolayer-like and bilayer-like band structures. The increased phase coherence length at high hole densities takes our shortest devices into the mesoscopic regime with the appearance of significant conductance fluctuations on top of the localization effects. Although these are aperiodic in gate voltage, they exhibit a quasi-periodic behaviour as a function of magnetic field. We show that this is consistent with the interference of discrete trajectories in open quantum dots and discuss the possible origin of these in our devices.
C Y Cheah et al 2013 J. Phys.: Condens. Matter 25 (46), 465303 doi:10.1088/0953-8984/25/46/465303 (pre-print arXiv:1305.0315)
This paper is cited by: 15. Muhin, A. (2024). PhD Thesis, Technischen Universität Berlin. 14. Ruiz, E. (2023). PhD Thesis, Université Clermont Auvergne. 13. Lemesh, N. V. et al. (2023). Low Temp. Phys. 49, 1050–1057. https://doi.org/10.1063/10.0020598 12. Berlin. V. (2022). Graphene oxide reduction and decoration with lead sulphide nanoparticles for gas sensing application. Master's Thesis, Politecnico di Milano. 11. C¸ınar, M. N. et al. (2022). Nano Lett., 22, 2202. https://doi.org/10.1021/acs.nanolett.1c03883 10. Kovtun, A. et al. (2021). ACS Nano, 15, 2654. https://doi.org/10.1021/acsnano.0c07771 9. Leardini, F. et al. (2019). 2D Mater., 6, 035015. https://doi.org/10.1088/2053-1583/ab175c 8. Turmaud, J. P. (2018). Variable range hopping conduction in the epitaxial graphene buffer layer on SiC (0001). PhD Thesis, Georgia Institute of Technology. 7. Gómez, J. et al. (2017). Mater. Res. Express, 4, 105020. Available at doi.org/10.1088/2053-1591/aa8e11 6. Matis, B. R. et al. (2017). Electronic transport in bilayer MoS2 encapsulated in HfO2. ACS Appl. Mater. Interfaces, 9, 27995–28001. 5. Kusiak-Nejman, E. et al. (2017). Catal. Today, 287, 189–195. 4. Gillgren, N. A. (2017). Quantum Transport Properties of Atomically Thin Black Phosphorus. PhD Thesis, Uni California Riverside. https://escholarship.org/content/qt48k9x0s3/qt48k9x0s3\_noSplash\_134d8a6348e785ef6fa76c7c838d847f.pdf 3. Liu, C.-I. et al. (2016). Semicond. Sci. Technol., 31, 105008. 2. Hang, S. (2015). Irradiation-based defect engineering of graphene devices. PhD Thesis, University of Southampton, UK. 1. Lippert, G. et al. (2014). Carbon, 75, 104-112. _______________________________________________________________________________________ We report an analysis of low-temperature measurements of the conductance of partially disordered reduced graphene oxide, finding that the data follow a simple crossover scenario. At room temperature, conductance is dominated by two-dimensional (2D) electric field-assisted, thermally-driven (Pollak-Riess) variable-range hopping (VRH) through highly-disordered regions. However, at lower temperatures T, we find a smooth crossover to follow the exp(-E_0/E)^(1/3) field-driven (Shklovskii) 2D VRH conductance behaviour when the electric field E exceeds a specific crossover value E_C (T)_2D = (E_a E_0^(1/3) /3)^(3/4) determined by the scale factors E_0 and E_a for the high-field and intermediate field regimes respectively. Our crossover scenario also accounts well for experimental data reported by other authors for three-dimensional disordered carbon networks, suggesting wide applicability.
Influence of Disorder on Conductance in Bilayer Graphene under Perpendicular Electric Field
Nano Letters, 2010
Electron transport in bilayer graphene placed under a perpendicular electric field is revealed experimentally. Steep increase of the resistance is observed under high electric field; however, the resistance does not diverge even at low temperatures. The observed temperature dependence of the conductance consists of two contributions: the thermally activated (TA) conduction and the variable range hopping (VRH) conduction. We find that for the measured electric field range (0-1.3 V/nm) the mobility gap extracted from the TA behavior agrees well with the theoretical prediction for the band gap opening in bilayer graphene, although the VRH conduction deteriorates the insulating state more seriously in bilayer graphene with smaller mobility. These results show that the improvement of the mobility is crucial for the successful operation of the bilayer graphene field effect transistor.
Weak localization in graphene: theory, simulations, and experiments
TheScientificWorldJournal, 2014
We provide a comprehensive picture of magnetotransport in graphene monolayers in the limit of nonquantizing magnetic fields. We discuss the effects of two-carrier transport, weak localization, weak antilocalization, and strong localization for graphene devices of various mobilities, through theory, experiments, and numerical simulations. In particular, we observe a minimum in the weak localization and strong localization length reminiscent of the minimum in the conductivity, which allows us to make the connection between weak and strong localization. This provides a unified framework for both localizations, which explains the observed experimental features. We compare these results to numerical simulation and find a remarkable agreement between theory, experiment, and numerics. Various graphene devices were used in this study, including graphene on different substrates, such as glass and silicon, as well as low and high mobility devices.
Physical Review B, 2014
We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior computational efficiency. Using these data, we demonstrate the applicability of the one-parameter scaling theory of localization length and propose an analytical expression for the scaling function, which provides a reliable method of computing the two-dimensional localization length. This method is found to be consistent with another widely used method which relates the two-dimensional localization length to the elastic mean free path and the semiclassical conductivity. Abnormal behavior at the charge neutrality point is identified and interpreted to be caused by finite-size effects when the system width is comparable to or smaller than the elastic mean free path. We also demonstrate the finite-size effect when calculating the two-dimensional conductivity in the localized regime and show that a renormalization group beta function consistent with the one-parameter scaling theory can be extracted numerically. For graphene with vacancy disorder, we show that the proposed scaling function of localization length also applies. Lastly, we discuss some ambiguities in calculating the semiclassical conductivity around the charge neutrality point due to the presence of resonant states.