Phase diagram of a graphene bilayer in the zero-energy Landau level

Knothe, Angelika; Jolicœur, Thierry

doi:10.1103/physrevb.94.235149

Cited by 13 publications

(28 citation statements)

References 52 publications

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“…11,13; (6) a partial orbitally polarized (POP) state; and finally (7) a more exotic "Broken U(1)×U(1)" state, which supports non-trivial coherence among different combinations of the single-particle states in the spin-valley manifold such that two different U(1) symmetries are spontaneously broken. This contrasts with the other coherent states that we find (which have been discussed in earlier literature as well [11][12][13][14]21 ) -the CAF, KEK, and SVE -which represent families of states with a single spontaneously broken U(1) symmetry.…”

Section: Introductioncontrasting

confidence: 93%

“…Effects of the filled Dirac sea [15][16][17][18] are assumed to be absorbed into renormalizations of the couplings of the effective Hamiltonian 20,21 . We incorporate two aspects distinct from previous work [12][13][14]21 : (i) We include the effect of the trigonal warping t 3 (an interlayer hopping term allowed by the lattice symmetries) nonperturbatively in the one-body states of the low-energy manifold that form our basis.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

“…Projection of the long-range Coulomb interaction into this 8-fold manifold yields an effective Hamiltonian with a layer-polarized state at large D ⊥ and a ferromagnetic state at small D ⊥ , with a first order transition separating them 9,10 . Distinguishing intraand inter-layer Coulomb interactions, as well as inclusion of particle-hole symmetry-breaking terms, leads to the appearance of a state spontaneously breaking a U(1) symmetry [11][12][13][14] .…”

Section: Introductionmentioning

confidence: 99%

“…In large magnetic fields this term has a very small effect 3 . In consequence, this term has previously been either neglected 11,12,14,21 or taken into account only perturbatively 13 . We find, however, that for experimentally relevant values of B ⊥ the nonperturbative effect of the t 3 term is crucial to stabilizing hitherto unknown broken symmetry states.…”

Section: Introductionmentioning

confidence: 99%

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Spin-valley coherent phases of the ν=0 quantum Hall state in bilayer graphene

2017

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Bilayer graphene (BLG) offers a rich platform for broken symmetry states stabilized by interactions. In this work we study the phase diagram of BLG in the quantum Hall regime at filling factor ν = 0 within the Hartree-Fock approximation. In the simplest non-interacting situation this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer-polarized, canted antiferromagnetic, Kekulé, a "spin-valley entangled" state, and a "broken U(1) × U(1)" phase. This last state involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias D and perpendicular magnetic field B ⊥ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed.

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Section: Introductioncontrasting

confidence: 93%

Section: Conclusion and Open Questionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin-valley coherent phases of the ν=0 quantum Hall state in bilayer graphene

2017

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“…In bilayer graphene, a LL diagram that provides a basis to interpret and reconcile the large amount of experimental findings to date has yet to emerge. Predictions of tight-binding models with Hartree-Fock approximations [2,14,[27][28][29][30] are not able to fully account for experimental observations [16].…”

Section: Introductionmentioning

confidence: 99%

Effective Landau Level Diagram of Bilayer Graphene

Tupikov

Watanabe

et al. 2018

Phys. Rev. Lett.

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The E = 0 octet of bilayer graphene in the filling factor range of -4 <  < 4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.2 Bilayer graphene provides a fascinating platform to explore potentially new phenomena in the quantum Hall regime of a two-dimensional electron gas (2DEG). The existence of two spins, two valley indices K and Kʹ, and two isospins corresponding to the n = 0 and 1 orbital wave functions results in an eight-fold degeneracy of the singleparticle E = 0 Landau level (LL) in a perpendicular magnetic field B [1,2]. This SU (8) phase space provides ample opportunities for the emergence of broken-symmetry manybody ground states [3][4][5][6][7][8][9][10][11][12][13][14][15]. The application of a transverse electric field E drives valley polarization through their respective occupancy of the two constituent layers [1,2]. Coulomb exchange interactions, on the other hand, enhance spin ordering and promote isospin doublets [11,15,16]. As a result of these intricate competitions, the E = 0 octet of bilayer graphene (integer filling factor range -4 <  < 4) exhibits a far richer phase diagram than their semiconductor counterparts. Experiments have uncovered 4, 3, 2, 1 coincidence points for filing factors = 0, ±1, ±2 and ±3 respectively, where the crossing of two LLs leads to the closing of the gap and signals the phase transition of the ground state from one order to another [13,[15][16][17][18]. Their appearance provides key information to the energetics of the LLs and the nature of the ground states involved. Indeed, coincidence studies on semiconducting 2DEGs are used to probe the magnetization of quantum Hall states [19] and measure the many-body enhanced spin susceptibility [20]. In bilayer graphene, the valley and isospin degrees of freedom increase the number of potential many-body coherent ground states. Furthermore, the impact of actively controlling these degrees of freedom became evident in the recent observations of fractional and even-denominator fractional quantum Hall effects [17,[21][22][23][24][25].A good starting point of exploring this rich landscape would be a single-particle, or single-particlelike LL diagram, upon which interaction effects can be elucidated perturbatively. Indeed, even in the inherently strongly interacting fractional quantum Hall effect, effective single-particle models, e.g. the composite fermion model [26], can capture the bulk of the interaction effects and provide conceptually simple and elegant ways to understand complex many-body phenomena. In bilayer graphene, a LL ...

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Fractional Quantum Hall Effect in Graphene, a Topological Approach

Jacak

2019

Handbook of Graphene

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Phase diagram of a graphene bilayer in the zero-energy Landau level

Cited by 13 publications

References 52 publications

Spin-valley coherent phases of the ν=0 quantum Hall state in bilayer graphene

Spin-valley coherent phases of the ν=0 quantum Hall state in bilayer graphene

Effective Landau Level Diagram of Bilayer Graphene

Fractional Quantum Hall Effect in Graphene, a Topological Approach

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