31 research outputs found
Broken symmetry states and divergent resistance in suspended bilayer graphene
Graphene [1] and its bilayer have generated tremendous excitement in the
physics community due to their unique electronic properties [2]. The intrinsic
physics of these materials, however, is partially masked by disorder, which can
arise from various sources such as ripples [3] or charged impurities [4].
Recent improvements in quality have been achieved by suspending graphene flakes
[5,6], yielding samples with very high mobilities and little charge
inhomogeneity. Here we report the fabrication of suspended bilayer graphene
devices with very little disorder. We observe fully developed quantized Hall
states at magnetic fields of 0.2 T, as well as broken symmetry states at
intermediate filling factors , , and . The
devices exhibit extremely high resistance in the state that grows
with magnetic field and scales as magnetic field divided by temperature. This
resistance is predominantly affected by the perpendicular component of the
applied field, indicating that the broken symmetry states arise from many-body
interactions.Comment: 23 pages, including 4 figures and supplementary information; accepted
to Nature Physic
Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene
We study the realization in a model of graphene of the phenomenon whereby the
tendency of gauge-field mediated interactions to break chiral symmetry
spontaneously is greatly enhanced in an external magnetic field. We prove that,
in the weak coupling limit, and where the electron-electron interaction
satisfies certain mild conditions, the ground state of charge neutral graphene
in an external magnetic field is a quantum Hall ferromagnet which spontaneously
breaks the emergent U(4) symmetry to U(2)XU(2).
We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet
order parameter is given exactly by the leading order in perturbation theory.
On the other hand, the chiral condensate which is the order parameter for
chiral symmetry breaking generically obtains contributions at all orders. We
compute the leading correction to the chiral condensate. We argue that the
ensuing fermion spectrum resembles that of massive fermions with a vanishing
U(4)-valued chemical potential. We discuss the realization of parity and charge
conjugation symmetries and argue that, in the context of our model, the charge
neutral quantum Hall state in graphene is a bulk insulator, with vanishing
longitudinal conductivity due to a charge gap and Hall conductivity vanishing
due to a residual discrete particle-hole symmetry.Comment: 35 page
Observation of the Fractional Quantum Hall Effect in Graphene
When electrons are confined in two dimensions and subjected to strong
magnetic fields, the Coulomb interactions between them become dominant and can
lead to novel states of matter such as fractional quantum Hall liquids. In
these liquids electrons linked to magnetic flux quanta form complex composite
quasipartices, which are manifested in the quantization of the Hall
conductivity as rational fractions of the conductance quantum. The recent
experimental discovery of an anomalous integer quantum Hall effect in graphene
has opened up a new avenue in the study of correlated 2D electronic systems, in
which the interacting electron wavefunctions are those of massless chiral
fermions. However, due to the prevailing disorder, graphene has thus far
exhibited only weak signatures of correlated electron phenomena, despite
concerted experimental efforts and intense theoretical interest. Here, we
report the observation of the fractional quantum Hall effect in ultraclean
suspended graphene, supporting the existence of strongly correlated electron
states in the presence of a magnetic field. In addition, at low carrier density
graphene becomes an insulator with an energy gap tunable by magnetic field.
These newly discovered quantum states offer the opportunity to study a new
state of matter of strongly correlated Dirac fermions in the presence of large
magnetic fields
Higher-order renormalization of graphene many-body theory
We study the many-body theory of graphene Dirac quasiparticles interacting
via the long-range Coulomb potential, taking as a starting point the ladder
approximation to different vertex functions. We test in this way the low-energy
behavior of the electron system beyond the simple logarithmic dependence of
electronic correlators on the high-energy cutoff, which is characteristic of
the large-N approximation. We show that the graphene many-body theory is
perfectly renormalizable in the ladder approximation, as all higher powers in
the cutoff dependence can be absorbed into the redefinition of a finite number
of parameters (namely, the Fermi velocity and the weight of the fields) that
remain free of infrared divergences even at the charge neutrality point. We
illustrate this fact in the case of the vertex for the current density, where a
complete cancellation between the cutoff dependences of vertex and electron
self-energy corrections becomes crucial for the preservation of the gauge
invariance of the theory. The other potentially divergent vertex corresponds to
the staggered (sublattice odd) charge density, which is made cutoff independent
by a redefinition in the scale of the density operator. This allows to compute
a well-defined, scale invariant anomalous dimension to all orders in the ladder
series, which becomes singular at a value of the interaction strength marking
the onset of chiral symmetry breaking (and gap opening) in the Dirac field
theory. The critical coupling we obtain in this way matches with great accuracy
the value found with a quite different method, based on the resolution of the
gap equation, thus reassuring the predictability of our renormalization
approach.Comment: 27 pages, 7 figures, references adde
Multicomponent fractional quantum Hall effect in graphene
We report observation of the fractional quantum Hall effect (FQHE) in high
mobility multi-terminal graphene devices, fabricated on a single crystal boron
nitride substrate. We observe an unexpected hierarchy in the emergent FQHE
states that may be explained by strongly interacting composite Fermions with
full SU(4) symmetric underlying degrees of freedom. The FQHE gaps are measured
from temperature dependent transport to be up 10 times larger than in any other
semiconductor system. The remarkable strength and unusual hierarcy of the FQHE
described here provides a unique opportunity to probe correlated behavior in
the presence of expanded quantum degrees of freedom.Comment: 5 pages, 3 figure
Dirac cones reshaped by interaction effects in suspended graphene
We report measurements of the cyclotron mass in graphene for carrier
concentrations n varying over three orders of magnitude. In contrast to the
single-particle picture, the real spectrum of graphene is profoundly nonlinear
so that the Fermi velocity describing the spectral slope reaches ~3x10^6 m/s at
n <10^10 cm^-2, three times the value commonly used for graphene. The observed
changes are attributed to electron-electron interaction that renormalizes the
Dirac spectrum because of weak screening. Our experiments also put an upper
limit of ~0.1 meV on the possible gap in graphene
Spin and valley quantum Hall ferromagnetism in graphene
In a graphene Landau level (LL), strong Coulomb interactions and the fourfold
spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At
partial filling, exchange interactions can spontaneously break this symmetry,
manifesting as additional integer quantum Hall plateaus outside the normal
sequence. Here we report the observation of a large number of these quantum
Hall isospin ferromagnetic (QHIFM) states, which we classify according to their
real spin structure using temperature-dependent tilted field magnetotransport.
The large measured activation gaps confirm the Coulomb origin of the broken
symmetry states, but the order is strongly dependent on LL index. In the high
energy LLs, the Zeeman effect is the dominant aligning field, leading to real
spin ferromagnets with Skyrmionic excitations at half filling, whereas in the
`relativistic' zero energy LL, lattice scale anisotropies drive the system to a
spin unpolarized state, likely a charge- or spin-density wave.Comment: Supplementary information available at http://pico.phys.columbia.ed
Properties of Graphene: A Theoretical Perspective
In this review, we provide an in-depth description of the physics of
monolayer and bilayer graphene from a theorist's perspective. We discuss the
physical properties of graphene in an external magnetic field, reflecting the
chiral nature of the quasiparticles near the Dirac point with a Landau level at
zero energy. We address the unique integer quantum Hall effects, the role of
electron correlations, and the recent observation of the fractional quantum
Hall effect in the monolayer graphene. The quantum Hall effect in bilayer
graphene is fundamentally different from that of a monolayer, reflecting the
unique band structure of this system. The theory of transport in the absence of
an external magnetic field is discussed in detail, along with the role of
disorder studied in various theoretical models. We highlight the differences
and similarities between monolayer and bilayer graphene, and focus on
thermodynamic properties such as the compressibility, the plasmon spectra, the
weak localization correction, quantum Hall effect, and optical properties.
Confinement of electrons in graphene is nontrivial due to Klein tunneling. We
review various theoretical and experimental studies of quantum confined
structures made from graphene. The band structure of graphene nanoribbons and
the role of the sublattice symmetry, edge geometry and the size of the
nanoribbon on the electronic and magnetic properties are very active areas of
research, and a detailed review of these topics is presented. Also, the effects
of substrate interactions, adsorbed atoms, lattice defects and doping on the
band structure of finite-sized graphene systems are discussed. We also include
a brief description of graphane -- gapped material obtained from graphene by
attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic