Dynamics in the quantum Hall effect and the phase diagram of graphene

Gorbar, É. V.; Gusynin, V. P.; Miransky, V. A.; Shovkovy, Igor

doi:10.1103/physrevb.78.085437

Cited by 58 publications

(131 citation statements)

References 64 publications

Supporting

Mentioning

126

Contrasting

Order By: Relevance

“…This establishes a one-to-one correspondence between the states (38) and the elements of the Grassmannian manifold Gr(2, 4), known as the Plücker embedding in mathematical literature 48 ; the constraint (36) is called the Plücker relation. The parametrization of the occupied subspaces, generated by χ a,b , and therefore of the Grassmannian Gr(2, 4), is efficiently realized by the matrix…”

Section: A Basic Concept and Exact Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Phase diagram for theν=0quantum Hall state in monolayer graphene

2012

View full text Add to dashboard Cite

The ν = 0 quantum Hall state in a defect-free graphene sample is studied within the framework of quantum Hall ferromagnetism. We perform a systematic analysis of the "isospin" anisotropies, which arise from the valley and sublattice asymmetric short-range electron-electron (e-e) and electron-phonon (e-ph) interactions. The phase diagram, obtained in the presence of generic isospin anisotropy and the Zeeman effect, consists of four phases characterized by the following orders: spinpolarized ferromagnetic, canted antiferromagnetic, charge density wave, and Kekulé distortion. We take into account the Landau level mixing effects and show that they result in the key renormalizations of parameters. First, the absolute values of the anisotropy energies become greatly enhanced and can significantly exceed the Zeeman energy. Second, the signs of the anisotropy energies due to e-e interactions can change upon renormalization. A crucial consequence of the latter is that the short-range e-e interactions alone could favor any state on the phase diagram, depending on the details of interactions at the lattice scale. On the other hand, the leading e-ph interactions always favor the Kekulé distortion order. The possibility of inducing phase transitions by tilting the magnetic field is discussed.

show abstract

Section: A Basic Concept and Exact Resultsmentioning

confidence: 99%

“…A lot of theoretical activity has been devoted [20][21][22][23][24][25][27][28][29][30][31][32][34][35][36][37][38] to the properties of the ν = 0 quantum Hall state in graphene (see also Refs. 39,40 for reviews).…”

Section: Introductionmentioning

confidence: 99%

Phase diagram for theν=0quantum Hall state in monolayer graphene

2012

View full text Add to dashboard Cite

show abstract

“…[3][4][5][6][7][8][9][10][11][12][13] Recently, bilayer graphene is found to show an anomalous behavior in its spectral and transport properties, which has attracted much experimental and theoretical interest. Theoretical studies 4,5 show that interlayer coupling modifies the intralayer relativistic spectrum to yield a quasiparticle spectrum with a parabolic energy dispersion, which implies that the quasiparticles in bilayer graphene cannot be treated as massless but have a finite mass.…”

Section: Introductionmentioning

confidence: 99%

Quantum Hall effect in bilayer graphene: Disorder effect and quantum phase transition

Sheng

Shen

et al. 2009

Phys. Rev. B

View full text Add to dashboard Cite

We numerically study the quantum Hall effect ͑QHE͒ in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with nonquantized Hall Effect. The Hall conductivity around the band center ͑Dirac point͒ shows an anomalous quantization proportional to the valley degeneracy, but the = 0 plateau is markedly absent, which is in agreement with experimental observation. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering, which is separated by a small critical region in between near the Dirac point. The longitudinal conductance around the Dirac point is shown to be nearly a constant in a range of disorder strength, until the last two QHE plateaus completely collapse.

show abstract

“…At the microscopic level, the excitonic condensates corresponds to a charge density wave (CDW), or a valley polarized CDW. Symmetry arguments, as well as direct effective model studies 40,41 suggest that the order parameters associated with the MC and QHF scenarios necessarily coexist. Also, in principle, these two could reproduce all integer QH plateaus observed experimentally in strong magnetic fields.…”

mentioning

confidence: 99%

“…The corresponding order parameters are excitonic (particle-hole) condensates responsible for the generation of the Dirac and/or Haldane masses of quasiparticles 6,[36][37][38][39][40][41][42][43] . At the microscopic level, the excitonic condensates corresponds to a charge density wave (CDW), or a valley polarized CDW.…”

mentioning

confidence: 99%

Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

Shovkovy

Xia

2016

Phys. Rev. B

View full text Add to dashboard Cite

By making use of the generalized Landau-level representation (GLLR) for the quasiparticle propagator, we study the effect of screening on the properties of the quantum Hall states with integer filling factors in graphene. The analysis is performed in the low-energy Dirac model in the meanfield approximation, in which the long-range Coulomb interaction is modified by the one-loop static screening effects in the presence of a background magnetic field. By utilizing a rather general ansatz for the propagator, in which all dynamical parameters are running functions of the Landau-level index n, we derive a self-consistent set of the Schwinger-Dyson (gap) equations and solve them numerically. The explicit solutions demonstrate that static screening leads to a substantial suppression of the gap parameters in the quantum Hall states with a broken U (4) flavor symmetry. The temperature dependence of the energy gaps is also studied. The corresponding results mimic well the temperature dependence of the activation energies measured in experiment. It is also argued that, in principle, the Landau-level running of the quasiparticle dynamical parameters could be measured via optical studies of the integer quantum Hall states.

show abstract

Dynamics in the quantum Hall effect and the phase diagram of graphene

Cited by 58 publications

References 64 publications

Phase diagram for theν=0quantum Hall state in monolayer graphene

Phase diagram for theν=0quantum Hall state in monolayer graphene

Quantum Hall effect in bilayer graphene: Disorder effect and quantum phase transition

Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

Contact Info

Product

Resources

About