Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long wavelength optical phonons of graphene. The EFE in this two dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and line-width demonstrate optically the particle-hole symmetry about the charge-neutral Dirac-point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of mass-less Dirac fermions.The interaction between electrons and quantized lattice vibrations in a solid is one of the most fundamental realms of study in condensed matter physics. In particular, the electron-phonon interaction in graphene and its derivatives plays an important role in understanding anomalies of photoemission spectra observed in graphite [1] and graphene [2], the non-linear high energy electron transport in carbon nanotubes [3,4,5,6,7], as well as phonon structures in graphite [8,9] and carbon nanotubes [9,10,11].Traditionally, electron-phonon interactions are investigated through chemical doping, in which the charge carrier density is varied by introduction of impurities. The electric field effect (EFE) is an alternative method for changing the charge carrier density effectively in lowdimensional systems. The EFE has proven very successful in graphene, a single atomic sheet of graphite, where unconventional integer quantum Hall effect [12,13] has revealed physics linked to the uniqueness of the electronic band structure near the charge neutral Dirac points ( Fig. 1(a)).We measured Raman spectra of optical phonons in graphene where large densities of free electrons or free holes are modulated by the EFE. We discovered that the even parity long wavelength optical phonon (the graphene G band) has marked dependence on gate voltage and the induced charge density. The dependence of phonon frequency and line-width on the EFE induced charge density demonstrates that the intriguing physics of mass-less Dirac fermions with particle-hole symmetry is encoded in the electron-phonon interaction.Raman studies of graphite [14] are at the forefront of research on carbon based materials. The recent availability of few-layer and single-layer graphene [15,16], has stimulated great interest in Raman scattering in such novel and exciting systems. For example, dimensional crossover was observed in Raman spectra of thin graphitic films as a function of multilayer thickness [17,18,19]. In the work reported here, Raman spectroscopy emerges as an insightful method to probe the EFE in a single atomic layer and the phonon dynamics that are associated with the two dimensional (2D) Dirac fermions.We focus on the doubly degenerate optical phonon of E 2g symmetry at ∼1580 cm −1 , known as the G band. We also report on the s...

In monolayer graphene, substitutional doping during growth can be used to alter its electronic properties. We used scanning tunneling microscopy, Raman spectroscopy, x-ray spectroscopy, and first principles calculations to characterize individual nitrogen dopants in monolayer graphene grown on a copper substrate. Individual nitrogen atoms were incorporated as graphitic dopants, and a fraction of the extra electron on each nitrogen atom was delocalized into the graphene lattice. The electronic structure of nitrogen-doped graphene was strongly modified only within a few lattice spacings of the site of the nitrogen dopant. These findings show that chemical doping is a promising route to achieving high-quality graphene films with a large carrier concentration.

At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity, which does not depend on carrier density. Here we show that modulating a two-dimensional electron gas with a long-wavelength periodic potential with honeycomb symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphenelike system and discuss an experimental realization in a modulation-doped GaAs quantum well. Graphene is a one-atom-thick two-dimensional ͑2D͒ electron system composed of carbon atoms on a honeycomb lattice.1 The lattice has two inequivalent sites in the unit cell that are analogous to the two spin orientations of a spin-1/2 particle. This observation opens the way to an elegant description of electrons in graphene as particles endowed with a pseudospin degree-of-freedom.1 At low energy, electrons in graphene are described by a 2D massless Dirac fermion ͑MDF͒ Hamiltonian, H D = v F · p, where v F is the bare Fermi velocity, which does not depend on carrier density, p is the 2D momentum measured from the corners of the Brillouin zone, and is the pseudospin operator constructed with two Pauli matrices ͕ i , i = x , y͖, which act on the sublattice pseudospin degree-of-freedom. It follows that the energy eigenstates are chiral, i.e., for a given p have pseudospins oriented either parallel ͑conduction band͒ or antiparallel ͑valence band͒ to p. The Dirac-like wave equation and the chirality of its eigenstates have a number of very intriguing implications.1 It would be highly desirable to have other materials with Dirac-like spectrum and a pseudospin degree-offreedom. One candidate is represented by HgTe/Hg͑Cd͒Te quantum wells ͑QWs͒ where MDFs are predicted to arise at a critical QW thickness.2 More recently, Park and Louie 3 proposed that MDFs can arise in any 2D electron gas ͑2DEG͒ if appropriately nanopatterned.Here we present an independent approach to the realization of "artificial graphene" in a nanopatterned 2DEG. We provide theoretical evidence for the occurrence of linearly dispersing energy bands in an artificially engineered honeycomb lattice, and we demonstrate a remarkable dependence of the Fermi velocity on the strength of the external potential in this system. We also define the conditions that the external periodic potential and the electron density must satisfy in order to achieve artificial MDFs. Finally we present the photoluminescence ͑PL͒ of the 2DEG confined in a highmobility modulation-doped GaAs/AlGaAs QW where a nanopatterning with honeycomb symmetry is achieved by dry etching. We believe that the development of patterned 2DEGs with tunable parameters will offer unprecedented opportunities to study fundamental interactions of MDFs in high-mobility semiconductor structures.We start our analysis by considering a 2DEG consisting of electrons with band mass m b = 0.067m ͑m is the bare electron mass in vacuum͒ confined in a GaAs/AlGaAs QW. The 2DEG is subjected to a...

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Stimulated optical emission from the lowest exciton state in atomically smooth semiconductor quantum wires is observed for the first time. The wires are formed by the T intersection of two 7 nm GaAs quantum wells. The optical emission wavelength is nearly independent of pump levels. This absence of band-gap renormalization in the laser emission indicates a marked increase in the stability of the exciton in one dimension. PACS numbers: 78.45.+h, 73.20.Dx, 78.55.Cr The superior performance of quantum well (QW) semiconductor lasers over heterostructure lasers has directed considerable attention towards lower-dimensionality quantum wire (QWR) and quantum box structures. Carrier confinement to one or even zero dimensions is expected to give rise to sharp peaks in the density of states. This should lead to a variety of interesting optical properties such as increased exciton binding [1,2], enhanced optical nonlinearities [3], narrower gain spectra, and higher differential gain [4]. These striking physical phenomena are of importance for novel optoelectronic devices. Quantum wire geometries have been proposed as a route to lower threshold lasers having reduced threshold temperature sensitivity and increased modulation bandwidth [4][5][6]. However, the fabrication of QWR structures with precisely controlled dimensions is a very challenging task. Growth on patterned substrates [7] has been used to fabricate QWRs exhibiting optical signatures of carrier confinement to one dimension. In that work, stimulated emission from QWRs was first demonstrated. However, the relatively large size (80-100 by 10 nm) of the structures results in the occupation of many one-dimensional (ID) subbands, and due to band-filling effects only the higher-order transitions were observed.The existence of QWR states was recently also demonstrated at the T intersection of two GaAs QWs [8]. The T concept originally proposed by Chang et al. [9] was realized by the cleaved edge overgrowth (CEO) method, a molecular beam epitaxy (MBE) technique that uses high-quality regrowth on the cleaved edge of a multilayer sample [10]. The method is capable of producing nearly perfect structures with atomic control in two dimensions. The quantum mechanical bound state of an electron at two intersecting QWs is illustrated in Fig. 1. Near the T intersection confinement is somewhat relaxed leading to a smaller kinetic contribution to the total energy. A carrier in such a bound state is free to move along the line defined by the intersecting planes of the two QWs.This Letter reports the first observation of stimulated optical emission using exciton recombination in QWRs formed at intersecting GaAs QWs. Exciton emission in the ID quantum limit, i.e., from the ground state exciton, is apparent in these structures at low optical pump power densities of 600 W/cm 2 , where the adjacent QWs show no stimulated emission. Equally striking is the near constancy of the photon emission energy of the QWRs under large changes of pump power, ranging over 2 orders of magnitude to 3 k...

Artificial crystal lattices can be used to tune repulsive Coulomb interactions between electrons. We trapped electrons, confined as a two-dimensional gas in a gallium arsenide quantum well, in a nanofabricated lattice with honeycomb geometry. We probed the excitation spectrum in a magnetic field, identifying collective modes that emerged from the Coulomb interaction in the artificial lattice, as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a Coulomb-driven ground state.

A long wavelength, low-energy excitation of the fractional quantum Hall state at v= j has been observed by inelastic light scattering. The mode appears as a very sharp peak with marked temperature and magnetic field dependence. Its energy is consistent with theoretical predictions for the collective gap excitations of the incompressible quantum fluid. Spectra interpreted as q =0 collective spin-wave excitations also display the strong dependence on field and temperature associated with the fractional quantum Hall state. PACS numbers: 73.40.Hm, 73.20.Dx, 73.20.Mf, 78.30.Fs The 2D electron gas in the incompressible states of the fractional quantum Hall effect (FQHE) should exhibit new collective charge-density /«^ra-Landau-level excitations which, in the absence of kinetic energy changes, are entirely due to electron-electron interactions in the condensate [1-3]. The excitations are associated with fractionally charged quasiparticles that obey fractional statistics [1][2][3][4][5]. The FQHE states should also have collective spin-wave excitations associated with changes of the spin degree of freedom in the lowest Landau level [6], In the spin-polarized states with v;S 1 the q =0 spin wave is required to be at the Zeeman energy by Larmor's theorem. The emergence of low-lying charge-density modes, or "gap excitations," is one of the most significant new behaviors in the fractional quantum Hall effect. These excitations display characteristic "magnetoroton" minima and the large wave-vector limit, ^-• oo^ represents the infinitely separated quasiparticle-quasihole pairs that are associated with the energy gaps of the incompressible quantum fluid [1][2][3][4][5][6][7].Gaps of the FQHE are obtained in activated magnetotransport experiments, where residual-disorder effects could be important even in the highest mobility systems [8]. Intrinsic [9,10] and extrinsic [11] photoluminescence spectra reveal anomalies in the FQHE regime. However, the quantitative interpretation of photoluminescence requires a detailed understanding of the complex dynamical response of the electron gas in optical recombination processes. The direct measurement of charge-density gap excitations in the FQHE states has not been reported. Optical experiments could access the long wavelength modes. However, at small wave vectors q<^\/lo, where lo^'ihc/eB)^^^ is the magnetic length, intra-Landaulevel excitations have vanishing oscillator strength and optical absorption methods are not expected to be effective [3].The structure of the ^=0 collective gap excitation of the FQHE is intriguing. Girvin, MacDonald, and Platzman [3] speculated that two gap excitations each near the magnetoroton minimum, at wave vectors ~l//o, could pair to produce a two-roton bound state with ^ =0. The (7=0 mode has also been discussed within the Landau-Ginzburg framework [12,13]. It was proposed that it consists of two dipole excitations in a configuration that has a quadrupole moment but no net dipole moment [13]. These considerations suggest to us that inelastic light sca...

The interaction of electron-hole pairs with lattice vibrations exhibits a wealth of intriguing physical phenomena such as the renowned Kohn anomaly. Here we report the observation in bilayer graphene of an unusual phonon softening that provides the first experimental proof for another type of phonon anomaly. Similar to the Kohn anomaly, which is a logarithmic singularity in the phonon group velocity [W. Kohn, Phys. Rev. Lett. 2, 393 (1959)], the observed phonon anomaly exhibits a logarithmic singularity in the optical-phonon energy. Arising from a resonant electron-phonon coupling effect, the anomaly was also expected, albeit not observed, in monolayer graphene. We propose an explanation for why it is easier to observe in bilayer samples.