Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene (original) (raw)
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Physical Review Letters, 2006
We study the effects of disorder in the electronic properties of graphene multilayers, with special focus on the bilayer and the infinite stack. At low energies and long wavelengths, the electronic selfenergies and density of states exhibit behavior with divergences near half-filling. As a consequence, the spectral functions and conductivities do not follow Landau's Fermi liquid theory. In particular, we show that the quasiparticle decay rate has a minimum as a function of energy, there is a universal minimum value for the in-plane conductivity of order e 2 /h per plane and, unexpectedly, the c-axis conductivity is enhanced by disorder at low doping, leading to an enormous conductivity anisotropy at low temperatures. PACS numbers: 81.05.Uw 73.21.Ac 71.23.-k
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.
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.
Electronic properties of bilayer and multilayer graphene
Physical Review B, 2008
We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent potential approximation and some analytical results. Within the model we compute the self-energies, the density of states and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the DC conductivity. The c-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.
The European Physical Journal B
We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path Le, the localization length ξ and the inelastic mean free path Li. Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature T. In BLG an additional characteristic distance l1 exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1%-2%, one has l1 ≤ Le ξ and the BLG has transport properties that differ from those of the MLG independently of Li(T). Whereas for larger concentration of defects Le < l1 ξ, and depending on Li(T), the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.
Minimal conductivity in bilayer graphene
The European Physical Journal B, 2006
Using the Landauer formula approach, it is proven that minimal conductivity of order of e 2 /h found experimentally in bilayer graphene is its intrinsic property. For the case of ideal crystals, the conductivity turns our to be equal to e 2 /2h per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value 1 − 2/π is close to the value 1/3 found earlier for the single-layer graphene.
Transport Spectroscopy of Symmetry Broken Insulating States in Bilayer Graphene
Bilayer graphene is an attractive platform for studying new twodimensional electron physics 1-5 , because its flat energy bands are sensitive to out-of-plane electric fields and these bands magnify electron-electron interaction effects. Theory 6-16 predicts a variety of interesting broken symmetry states when the electron density is at the carrier neutrality point, and some of these states are characterized by spontaneous mass gaps, which lead to insulating behaviour. These proposed gaps 6,7,10 are analogous 17,18 to the masses generated by broken symmetries in particle physics, and they give rise to large Berry phase effects 8,19 accompanied by spontaneous quantum Hall effects 7-9,20 . Although recent experiments 21-25 have provided evidence for strong electronic correlations near the charge neutrality point, the presence of gaps remains controversial. Here, we report transport measurements in ultraclean double-gated bilayer graphene and use source-drain bias as a spectroscopic tool to resolve a gap of ∼2 meV at the charge neutrality point. The gap can be closed by a perpendicular electric field of strength ∼15 mV nm 21 , but it increases monotonically with magnetic field, with an apparent particlehole asymmetry above the gap. These data represent the first spectroscopic mapping of the ground states in bilayer graphene in the presence of both electric and magnetic fields.
Transport Properties in Gapped Bilayer Graphene
2021
We investigate transport properties through a rectangular potential barrier in AB-stacked bilayer graphene (AB-BLG) gapped by dielectric layers. Using the Dirac-like Hamiltonian with a transfer matrix approach we obtain transmission and reflection probabilities as well as the associated conductance. For two-band model and at normal incidence, we find extra resonances appearing in transmission compared to biased AB-BLG, which are Fabry-Pérot resonance type. Now by taking into account the inter-layer bias, we show that both of transmission and anti-Klein tunneling are diminished. Regarding four band model, we find that the gap suppresses transmission in an energy range by showing some behaviors look like ”Mexican hats”. We examine the total conductance and show that it is affected by the gap compared to AA-stacked bilayer graphene. In addition, we find that the suppression in conductance is more important than that for biased AB-BLG.
Electrical Conductance of Graphene with Point Defects
Acta Physico-Chimica Sinica
Graphene is one of the most promising materials in nanotechnology and has attracted worldwide attention and research interest owing to its high electrical conductivity, good thermal stability, and excellent mechanical strength. Perfect graphene samples exhibit outstanding electrical and mechanical properties. However, point defects are commonly observed during fabrication which deteriorate the performance of graphene based-devices. The transport properties of graphene with point defects essentially depend on the imperfection of the hexagonal carbon atom network and the scattering of carriers by localized states. Furthermore, an in-depth understanding of the effect of specific point defects on the electronic and transport properties of graphene is crucial for specific applications. In this work, we employed density functional theory calculations and the non-equilibrium Green's function method to systematically elucidate the effects of various point defects on the electrical transport properties of graphene, including Stone-Waals and inverse Stone-Waals defects; and single and double vacancies. The electrical conductance highly depends on the type and concentration of point defects in graphene. Low concentrations of Stone-Waals, inverse Stone-Waals, and single-vacancy defects do not noticeably degrade electron transport. In comparison, DV585 induces a moderate reduction of 25%-34%, and DV55577 and DV5555-6-7777 induce significant suppression of 51%-62% in graphene. As the defect concentration increases, the electrical conductance reduces by a factor of 2-3 compared to the case of graphene monolayers with a low concentration of point defects. These distinct electrical transport behaviors are attributed to the variation of the graphene band structure; the point defects induce localized states near the Fermi level and result in energy splitting at the Dirac point due to the breaking of the intrinsic symmetry of the graphene honeycomb lattice. Double vacancies with larger defect concentrations exhibit more flat bands near the Fermi energy and more localized states in the defective region, resulting in the presence of resonant peaks close to the Fermi energy in the local density of states. This may cause resonant scattering of the carriers and a corresponding reduction of the conductance of graphene. Moreover, the partial charge densities for double vacancies and point defects with larger concentrations exhibit enhanced localization in the defective region that hinder the charge carriers. The electrical conductance shows an exponential decay as the defect concentration and energy splitting increase. These theoretical results provide important insights into the electrical transport properties of realistic graphene monolayers and will assist in the fabrication of high-performance graphene-based devices.