Coulomb drag of massless fermions in graphene

Abstract

Using a novel structure, consisting of two, independently contacted graphene single layers separated by an ultra-thin dielectric, we experimentally measure the Coulomb drag of massless fermions in graphene. At temperatures higher than 50 K, the Coulomb drag follows a temperature and carrier density dependence consistent with the Fermi liquid regime. As the temperature is reduced, the Coulomb drag exhibits giant fluctuations with an increasing amplitude, thanks to the interplay between coherent transport in the graphene layer and interaction between the two layers.PACS numbers: 73.22.Gk Bilayer systems formed by two layers of carriers in close proximity are a fascinating testground for electron physics. In particular, the prospect of electron-hole pair (indirect exciton) formation, and dipolar superfluidity 1 has fueled the research of electron-hole bilayers in GaAs/AlGaAs heterostructures 2,3 . Graphene 4,5 is a particularly interesting material to explore interacting bilayers. The symmetric conduction and valence bands, and the large Fermi energy favor correlated electron states at elevated temperatures 6,7 . The zero energy band-gap allows a seamless transition between electrons and holes in each layer, and obviates the large inter-layer electric field required to simultaneously induce electrons and holes in GaAs bilayers 3 . Coulomb drag, a direct measurement of inter-layer electron-electron scattering 8 can provide insight into the ground state of two-9 and one-10 electron systems, as well as correlated bilayer states 11,12 . Here we demonstrate a novel, independently contacted graphene bilayer, and investigate the Coulomb drag in this system. Two main ingredients render the realization of independently contacted graphene bilayers challenging. First, an ultra-thin yet highly insulating dielectric is required to separate the two layers. Second, a method to position another graphene layer on a pre-existing device with minimum or no degradation is needed to create the second layer of the structure investigated here. The fabrication of our independently contacted graphene bilayers is described in Fig. 1. First, the bottom graphene layer is mechanically exfoliated onto a 280 nm thick SiO 2 dielectric, thermally grown on a highly doped Si substrate. E-beam lithography, metal lift-off, and etching are used to define a Hall bar on the bottom layer [ Fig. 1(a)]. A 7 nm thick Al 2 O 3 is then deposited on the bottom layer using a 2 nm oxidized Al interfacial layer, followed by 5 nm of Al 2 O 3 atomic layer deposition 13 . The second, top graphene layer is also mechanically exfoliated on a similar SiO 2 /Si substrate. A poly methyl metacrylate (PMMA) film is applied on the top layer and cured. Using an NaOH etch 14 , the PMMA film along with the graphene layer, and the alignment marks are detached from the host substrate, forming a free standing membrane. The membrane is placed face down on the substrate containing the bottom graphene layer [ Fig. 1(b)], and aligned with it. A Hall bar is subsequently defined on th...

Hydrodynamics in graphene: Linear-response transport

“…Moreover, in the degenerate regime, A( ) → A(μ). Such a description is completely equivalent to the standard linearresponse theory [1], but is more natural in situations where one passes a current through a sample rather than applies an electric field, for example, in drag measurements [16][17][18][19].…”

“…It is well known [32], however, that the traditional Fermi-liquid theory of Coulomb drag is applicable only for very large densities, far beyond the current experimental range [16][17][18][19].…”

“…[9,10] and then extended to double-layer graphene-based structures in Ref. [11], which allowed for a description of the Coulomb drag effect [16][17][18][19] in graphene. An extension of this approach to mesoscopic (finite-size) samples was suggested in Ref.…”

“…In Sec. V, we apply our theory to double-layer graphene-based systems [16][17][18][19]. Concluding remarks can be found in Sec.…”

A complete laboratory for transport studies of electron-hole interactions in GaAs/AlGaAs ambipolar bilayers

“…Such experiments have been performed on devices based on GaAs 13,[16][17][18] and graphene structures. [19][20][21][22][23] An anomalous increase of the drag at low temperature was reported in several cases, suggesting the approach of a non-Fermi liquid phase; however, some unanswered questions still exist about the nature of this effect.…”