Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene (original) (raw)
Related papers
Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation
2015
Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works make theoretical analysis of such systems extremely relevant. In this paper we describe a methodology for investigating the possibility of realizing specific fractional quantum Hall states in bilayer graphene taking into account polarization effects and virtual interband transitions. We apply this methodology to explore the possibility of realizing the Moore-Read Pfaffian state in bilayer graphene. Contents D. Additional data on the Moore-Read Pfaffian state stability References
Science (New York, N.Y.), 2014
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. Here, we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = -2, -1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.
Physical Review B, 2018
Incompressible even denominator fractional quantum Hall states at fillings ν = ± 1 2 and ν = ± 1 4 have been recently observed in monolayer graphene. We use a Chern-Simons description of multicomponent fractional quantum Hall states in graphene to investigate the properties of these states and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as ν = 1/3, 2/5, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublattice or chiral symmetry breaking orders (such as charge-density-wave and antiferromagnetism) of composite Dirac fermions, a phenomenon unifying integer and fractional quantum Hall physics for relativistic fermions. We also discuss possible experimental probes that can narrow down the candidate broken symmetry phases for the fractional quantum Hall states in the zeroth Landau level of monolayer graphene.
Importance of interband transitions for the fractional quantum Hall effect in bilayer graphene
Physical Review B, 2012
Several recent works have proposed that electron-electron interactions in bilayer graphene can be tuned with the help of external parameters, making it possible to stabilize different fractional quantum Hall states. In these prior works, phase diagrams were calculated based on a single Landau level approximation. We go beyond this approximation and investigate the influence of polarization effects and virtual interband transitions on the stability of fractional quantum Hall states in bilayer graphene. We find that for realistic values of the dielectric constant, the phase diagram is strongly modified by these effects. We illustrate this by evaluating the region of stability of the Pfaffian state.
Observation of the fractional quantum Hall effect in graphene
Nature, 2009
When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid 1, 2 . In this strong quantum regime, ...
The total energy of interacting Dirac electrons in the lowest Landau level is found, within the same many-body theoretical framework, to exhibit jointly strong cusps at angular momenta corresponding to quantum Hall fractions and an insulating energy gap (that increases with the magnetic field) at the Dirac point. The model employs single-particle basis functions obeying the infinite-mass boundary condition at the sample edge, and initial volume-type states transform into edge-type states with increasing field. A single-ring rotating-Wigner-molecule correlated many-body state forms as a result of the interelectron repulsion. These results are contrasted with those corresponding to a boundless graphene sheet and a two-dimensional electron gas in semiconductor heterostructures.
Physical Review B, 2010
Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (ν = 1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing, at all sizes, mixed equal-weight bulk and edge components. The consequent depletion of the bulk electron density attenuates the fractional-quantum-Hall-effect excitation energies and the edge charge accumulation results in a gap in the many-body spectrum.
Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010
Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p–n–p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained ...
Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
Nature, 2009
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers' two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field 1,2. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue 3. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence 4-9. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements 10. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.