Transport and Elastic Scattering Times as Probes of the Nature of Impurity Scattering in Single-Layer and Bilayer Graphene

Abstract

Both transport τtr and elastic τe scattering times are experimentally determined from the carrier density dependence of the magnetoconductance of monolayer and bilayer graphene. Both times and their dependences on carrier density are found to be very different in the monolayer and the bilayer. However, their ratio τtr/τe is found to be close to 1.8 in both systems and nearly independent of the carrier density. These measurements give insight on the nature (neutral or charged) and range of the scatterers. Comparison with theoretical predictions suggests that the main scattering mechanism in our samples is due to strong (resonant) scatterers of a range shorter than the Fermi wavelength; likely candidates being vacancies, voids, ad-atoms or short-range ripples.PACS numbers: 63.22. Np, 73.23.Hk, 73.21.Ac Since the discovery of the fascinating electronic properties of graphene [1] due to its electronic spectrum with linear dispersion and a perfect electron-hole symmetry at the Fermi level [2], the nature of defects has been shown to play an essential role in determining the carrier density (n c ) dependence of the conductance. The wavevector and energy dependences of the impurity potential are known to determine the characteristic scattering times of the carriers. It is important to distinguish the transport time τ tr , which governs the current relaxation and enters the Drude conductivity (σ), from the elastic scattering time τ e , which is the lifetime of a plane wave state [3]. Since τ tr and τ e involve different angular integrals of the differential cross section, they differ as soon as the Fourier components of the potential depend on the wavevector q. A large ratio τ tr /τ e indicates that scattering is predominantly in the forward direction, so that transport is not affected much by this type of scattering. This is the case in 2D electron gases (2DEG) confined to GaAs/GaAlAs heterojunctions with the scattering potential produced by remote charged Si donors [4], where τ tr /τ e is found to be larger than 10.The nature of the main scattering mechanism limiting the carrier mobility in graphene is still subject to controversy. It has indeed been shown [5][6][7] that "white noise" (q independent) scattering leads to a weak (logarithmic) dependence of σ(n c ), in contradiction with experiments which typically find a linear increase. In contrast, scattering on charged impurities originates from a q dependent screened Coulomb potential described in the Thomas Fermi approximation [8][9][10]. This leads to a linear σ(n c ) both for a monolayer (ML) and a moderately doped bilayer (BL). Recent experiments performed to probe this question measured the change in σ upon immersion of graphene samples in high-K dielectric media. Their conclusions differ [11]. Alternate explanations involve resonant scattering centers with a large energy mismatch with the Fermi energy of carriers [7,12].In order to gain insight into the scattering mechanism in graphene, we have extracted τ e and τ tr from magnetotransport in monolayer and b...

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Optimal traps in graphene

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Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach

“…2,3 For example, both the strong short-range potential [4][5][6][7][8][9] and the long-range potential 7,[10][11][12] lead to similar linear density dependence of the conductivity commonly observed in experiments. [13][14][15][16][17][18][19] Experiments also often show strong deviations from this linear dependence and an asymmetry with respect to the polarity of carriers, which can be attributed to a number of factors such as the effect of realistic structural defects and impurities, 8,[20][21][22][23][24] effect of contacts, [25][26][27] effect of weak shortrange impurities, 4,[10][11][12] the ballistic or quasiballistic transport regimes, 7,[28][29][30] ripples, [30][31][32] and many others. Detailed studies of the density dependence of the conductivity in graphene often require exact numerical approaches for transport calculations combined with ab initio calculations for microscopic properties of realistic scatterers.…”