Friedel Oscillations, Impurity Scattering, and Temperature Dependence of Resistivity in Graphene

Abstract

We show that Friedel oscillations (FO) in grapehene are strongly affected by the chirality of electrons in this material. In particular, the FO of the charge density around an impurity show a faster, δρ ∼ r −3 , decay than in conventional 2D electron systems and do not contribute to a linear temperature-dependent correction to the resistivity. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice lead to a negative linear T-dependence of the resistivity. Screening strongly influences properties of impurities in metals and semiconductors. While Thomas-Fermi screening suppresses the long-range tail of a charged impurity potential, Friedel oscillations (FO) of the electron density around a defect [1] are felt by scattered electrons at a distance much longer than the Thomas-Fermi screening length. Friedel oscillations originate from the singular behavior of the response function of the Fermi liquid at wave vector 2k F . At zero temperature the decay of the amplitude δρ of these oscillations with distance r from the impurity obeys a power law dependence. In a nonrelativistic degenerate two-dimensional (2D) Fermi gas [2], δρ ∝ cos(2k F r + δ)/r 2 . In 2D electron systems Bragg scattering off the potential created by these long-range FO strongly renormalises the momentum relaxation rate, τ −1 for quasi-particles near the Fermi level, ǫ ≈ ǫ F , which leads to a linear temperature dependence of the resistivity [3, 4, 5, 6] in a 'ballistic' temperature range ǫ F > T > h/τ confirmed in recent experiments on semiconductor heterostructures and Si field-effect transistors [7].Graphene-based transistor [8,9] is a recent invention which attracts a lot of attention. Improvement of the performance of this device requires identification of the dominant source of electron scattering limiting its mobility. Those can be structural defects of graphene lattice (vacancies and dislocations), substitutional disorder, chemical deposits on graphene and, importantly, charges trapped in or on the surface of the underlying substrate.In this Letter we investigate the effects of screening of scatterers in graphene, and show how the phenomenon of FO can be used to gain insight into the microscopic nature of disorder. Graphene (a monolayer of graphite) is a gapless 2D semiconductor with a Dirac-like dispersion of carriers [10,11]. In this material, it is the Thomas-Fermi screening which is responsible [12] for the experimentally observed linear dependence of graphene conductivity on the carrier density [8,9]. Moreover, quasiparticles in graphene possess chiral properties related to the sublattice composition of the electron wave on a 2D honeycomb lattice [10]. Below we show that, due to the latter peculiarity of graphene, FO of the electron density decay as δρ ∼ r −3 at a long distance from an impurity [faster than in a usual 2D metal] and the linear temperaturedependent correction to the resistivity,

Diluted Graphene Antiferromagnet

“…The oscillating term proportional to 1/R 2 is present because the Kohn anomaly is not suppressed in the relevant response function. A similar behavior was found recently for Friedel oscillations, where the way in which the perturbation breaks the lattice symmetry determines whether they fall off as 1/R 2 or 1/R 3 [15]. While this 1/R 2 behavior is similar to that of the standard 2DEG, it nevertheless differs from the 2DEG in having a density dependent amplitude [18].…”

“…For doped graphene, we shall demonstrate similar behavior, with an important qualitative difference: the sign of the interaction depends on whether the two local moments couple to the honeycomb network on sites of the same sublattice or different ones, and when summed over both sublattices at a fixed distance, the 1/R 2 contribution to the RKKY coupling is cancelled, leaving behind a residue that falls off as 1/R 3 . Interestingly, analogous studies of the linear response to perturbations that do not distinguish between A and B sublattice sites also result in a 1/R 3 behavior [8,15,16]. We will show that the 1/R 3 behavior -and the absence of 1/R 2 behavior in density response functions -is a direct result of the chiral nature of electrons in graphene.…”

Hydrodynamics in graphene: Linear-response transport

“…Neglecting all quantum effects [34][35][36], we base our considerations on a set of macroscopic transport equations, which essentially generalize the usual Ohm's law to the case of collision-dominated transport in graphene. These equations can be derived from the kinetic equation (see Sec.…”

Dual-probe spectroscopic fingerprints of defects in graphene

“…Nanometer-scale STM measurements, yielding both local density of states (LDOS) and topographic details, are extensively used both theoretically [9][10][11][12][13][14][15][16] and experimentally [17][18][19][20][21][22] in the study of graphene. However, the STM measures only local properties, whereas we often want to obtain information about the transport properties for electrons traversing the sample.…”