Transport in superlattices on single-layer graphene

Burset, Pablo; Yeyati, A. Levy; Brey, L.; Fertig, H. A.

doi:10.1103/physrevb.83.195434

Cited by 74 publications

(96 citation statements)

References 55 publications

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“…Recently, a number of theoretical studies predicted that the chiral nature of charge carriers results in highly anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials and generates new Dirac points at energies E SD = ±ћν F |G|/2 in graphene superlattice (here ν F is the Fermi velocity of graphene and G is the reciprocal superlattice vector) [13][14][15][16]. Despite these suggestive findings [13][14][15][16] and many other interesting physics [17][18][19][20][21][22] in graphene superlattice, the experimental study of this system is scarce due to the difficulty in fabricating graphene under nano-scale periodic potentials [23]. Until recently, it was demonstrated that graphene superlattice (corrugated graphene or moiré pattern) induced between the top graphene layer and the substrate (or the underlayer graphene) acts as a weak periodic potential, which generates superlattice Dirac points at an energy determined by the period of the potential [24][25][26].…”

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Superlattice Dirac points and space-dependent Fermi velocity in a corrugated graphene monolayer

et al. 2013

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Recent studies show that periodic potentials can generate superlattice Dirac points at energies ±ћν F |G|/2 in graphene (ν F is the Fermi velocity of graphene and G is the reciprocal superlattice vector). Here, we perform scanning tunneling microscopy and spectroscopy studies of a corrugated graphene monolayer on Rh foil. We show that the quasi-periodic ripples of nanometer wavelength in the corrugated graphene give rise to weak one-dimensional (1D) electronic potentials and thereby lead to the emergence of the superlattice Dirac points. The position of the superlattice Dirac point is space-dependent and shows a wide distribution of values. We demonstrated that the space-dependent superlattice Dirac points is closely related to the space-dependent Fermi velocity, which may arise from the effect of the local strain and the strong electron-electron interaction in the corrugated graphene.Since the laboratory realization of graphene in 2004 [1], this two-dimensional honeycomb lattice of carbon atoms has motivated intense theoretical and experimental investigations of its properties [2][3][4][5][6][7][8]. It was demonstrated that the electronic chirality (the spinorlike structure of the wavefunction) is of central importance to many of graphene's unique electronic properties [3,[9][10][11][12]. Recently, a number of theoretical studies predicted that the chiral nature of charge carriers results in highly anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials and generates new Dirac points at energies E SD = ±ћν F |G|/2 in graphene superlattice (here ν F is the Fermi velocity of graphene and G is the reciprocal superlattice vector) [13][14][15][16]. Despite these suggestive findings [13][14][15][16] and many other interesting physics [17][18][19][20][21][22] in graphene superlattice, the experimental study of this system is scarce due to the difficulty in fabricating graphene under nano-scale periodic potentials [23]. Until recently, it was demonstrated that graphene superlattice (corrugated graphene or moiré pattern) induced between the top graphene layer and the substrate (or the underlayer graphene) acts as a weak periodic potential, which generates superlattice Dirac points at an energy determined by the period of the potential [24][25][26]. These seminal experiments provide a facile method to realize graphene superlattice and open opportunities for superlattice engineering of electronic properties in graphene.In this Letter, we address the electronic structures of a corrugated graphene monolayer on Rh foil. We show that the quasi-periodic ripples of nanometer wavelength give rise to a weak one-dimensional (1D) electronic potential in graphene. This 1D potential leads to the emergence of the superlattice Dirac points E SD , which are manifested by two dips in the density of states, symmetrically placed at energies flanking the pristine graphene Dirac point E D . The position of E SD is space-dependent and shows a wide distribution of values. Our experimental result demonstrates tha...

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Superlattice Dirac points and space-dependent Fermi velocity in a corrugated graphene monolayer

et al. 2013

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“…The advent of graphene has rapidly sparked interest in its superlattices, too [13][14][15][16][17][18][19][20][21][22] . The principal novelty in this case is the Dirac-like spectrum and the fact that charge carriers are not buried deep under the surface, allowing a relatively strong superlattice potential on a true nanometer scale.…”

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Cloning of Dirac fermions in graphene superlattices

Пономаренко

Gorbachev

et al. 2013

Nature

1,249

1,186

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Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional (2D) electron systems and, ultimately, create materials with tailored electronic properties 1-8 . Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits 1-4 . Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly 9 ) has been limited to the observation of new low-field oscillations 5 and an internal structure within Landau levels 6-8 . Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential 10-12 leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points 13-22 appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning 23 of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems 7-9,22-24 and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures 25 .Since the first observation of Weiss oscillations 1,2 , 2D electronic systems subjected to a periodic potential have been studied in great detail [3][4][5][6][7][8] . The advent of graphene has rapidly sparked interest in its superlattices, too [13][14][15][16][17][18][19][20][21][22] . The principal novelty in this case is the Dirac-like spectrum and the fact that charge carriers are not buried deep under the surface, allowing a relatively strong superlattice potential on a true nanometer scale. One promising avenue for making nanoscale graphene superlattices is the use of a potential induced by another crystal. For example, graphene placed on top of graphite or hexagonal boron nitride (hBN) exhibits a moiré pattern [10][11][12]26 , and graphene's tunneling density of states becomes strongly modified 12,26 indicating the formation of superlattice minibands. The spectral reconstruction occurs near the edges of superlattice's Brillouin zone (SBZ) that are characterized by wavevector G =4/ D and energy E S =v F G/2 (D is the superlattice period and v F graphene's Fermi velocity) 12,22 .To observe moiré minibands in transport properties, graphene has to be doped so that the Fermi energy reaches the reconstructed part of the spectrum. This imposes severe constraints on the misalignment angle  of graphene relatively to hBN. Indeed, D is given by  and the 1.8% difference between the two lattice constants ...

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“…These semiconductor NDR systems can also show interesting phenomena, such as intrinsic bistability due to charge accumulation 14 . Pursuing the recent interest in graphene superlattices transport and thermal properties [15][16][17][18][19][20][21][22][23][24] , it is a natural question to ask whether a graphene superlattice could exhibit similar features.…”

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Low-bias negative differential resistance in graphene nanoribbon superlattices

et al. 2011

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We theoretically investigate negative differential resistance (NDR) for ballistic transport in semiconducting armchair graphene nanoribbon (aGNR) superlattices (5 to 20 barriers) at low bias voltages VSD < 500 mV. We combine the graphene Dirac hamiltonian with the Landauer-Büttiker formalism to calculate the current ISD through the system. We find three distinct transport regimes in which NDR occurs: (i) a "classical" regime for wide layers, through which the transport across bandgaps is strongly suppressed, leading to alternating regions of nearly unity and zero transmission probabilities as a function of VSD due to crossing of bandgaps from different layers. (ii) a quantum regime dominated by superlattice miniband conduction, with current suppression arising from the misalignment of miniband states with increasing VSD; and (iii) a Wannier-Stark ladder regime with current peaks occurring at the crossings of Wannier-Stark rungs from distinct ladders. We observe NDR at voltage biases as low as 10 mV with a high current density, making the aGNR superlattices attractive for device applications.

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Transport in superlattices on single-layer graphene

Cited by 74 publications

References 55 publications

Superlattice Dirac points and space-dependent Fermi velocity in a corrugated graphene monolayer

Superlattice Dirac points and space-dependent Fermi velocity in a corrugated graphene monolayer

Cloning of Dirac fermions in graphene superlattices

Low-bias negative differential resistance in graphene nanoribbon superlattices

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