Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene

Côté, R.; Rondeau, Maxime; Gagnon, A.-M.; Barlas, Yafis

doi:10.1103/physrevb.86.125422

Cited by 15 publications

(18 citation statements)

References 35 publications

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“…Previously, similar linear scaling orbital splitting with Δ ≈ 0.1 meV/T was observed in the lowest LL of the ABC TLG by transport measurements [16]. In the ABC-stacked TLG, the existence of a next-nearest interlayer hopping 4  is expected to lift the orbital degeneracy of the lowest LL and the orbital splitting in magnetic field can be expressed as, is the magnetic length [42]. Therefore, the orbital splitting should increase linearly with magnetic fields.…”

supporting

confidence: 61%

High-Magnetic-Field Tunneling Spectra of ABC -Stacked Trilayer Graphene on Graphite

Yin

Shi

et al. 2019

Phys. Rev. Lett.

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ABC-stacked trilayer graphene (TLG) are predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat-band structures near the charge neutrality point (CNP). Here, using high magnetic field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG. We observe an approximately linear magneticfield-scaling of the valley splitting and orbital splitting in the ABC-stacked TLG. Our experiment indicates that the valley splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the orbital splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlation effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields.

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supporting

confidence: 61%

High-Magnetic-Field Tunneling Spectra of ABC -Stacked Trilayer Graphene on Graphite

Yin

Shi

et al. 2019

Phys. Rev. Lett.

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“…As in our previous work, we use the MFT to deal with the interactions between the electrons [10,18]. By the MFT, the 'free energy' functional Φ is approximated as shown in Fig.…”

Section: Mft For Interacting Dirac Fermions In Graphenementioning

confidence: 99%

Orbital magnetization of interacting Dirac fermions in graphene

Yan

Ting

2017

Phys. Rev. B

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We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with respect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interacting Dirac fermions in graphene. The charge and spin orderings and the exchange interactions between all the Landau levels are taken into account by the mean-field theory. The results for the orbital magnetization of interacting Dirac fermions are compared with that of noninteracting cases.PACS numbers: 75.25. Dk,75.70.Ak,73.22.Pr I. INTRDUCTIONThe study of the properties of interacting Dirac (or Weyl) fermions in (topological) semimetals under a magnetic field is a fundamental subject of the condensed matter physics [1,2]. One of the physical themes is to investigate the orbital magnetization (OM) of the Dirac fermions (DFs) with Coulomb interactions. The OM of an electron system is usually defined as [3]where Ω = Ω(T, µ, B), as a function of the temperature T and the chemical potential µ and the magnetic field B, is the thermal dynamic potential. Equation (1) is equivalent to a statistical average of the OM operator [4]. However, for Dirac (or Weyl) fermions, Eq. (1) is ill defined because the occupation of the Landau levels in the lower band leads to divergence of Ω and thereby M . For noninteracting DFs in graphene, Ω can be evaluated with a special method [5][6][7][8] by which the field B dependent part of Ω is separated out. The effects of finite-temperature occupations and the impurity broadening of the Landau levels on the OM of the noninteracting DFs have been studied [7][8][9]. Nonetheless, for interacting DFs, it is not easy to separate the B-dependent part of Ω from that of the independent part. Study of the OM of Dirac fermions with Coulomb interactions is lacking. How to calculate the OM of interacting DFs is still an open question. In this paper, we are developing a general approach for solving this problem and use it to calculate the OM of interacting Dirac fermions in graphene. II. FORMALISMThe electrons in graphene are moving on a honeycomb lattice of carbon atoms. The Hamiltonian of the electrons with a neutralizing background iswhere c † is (c is ) creates (annihilates) an electron of spin s in site i, ij sums over the nearest-neighbor (NN) sites, t ≈ 3 eV is the NN hopping energy, δn is = n is − n s is the number deviation of electrons of spin s at site i from the average occupation n s , and U and v ij are the Coulomb interactions between electrons. In real space, v ij = v(r ij ) with r ij the distance between sites i and j is given bywhere q 0 is a parameter taking into account the wavefunction spreading effect in the short-range interactions between electrons. Here we take q 0 = 0.5/a 0 with a 0 ≈ 2.46 A as the lattice constant of graphene. For carrier concentration close to the charge neutrality...

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“…In order to treat the single-layer, bilayer graphene [34] and chiral multilayer graphene (neglecting the trigonal warping effects) with 2 N layers [35][36][37][38] simultaneously we start from the Hamiltonian given in a unified form as …”

Section: Exact Calculation Of Dos and Capacitance In Chiral Multilayementioning

confidence: 99%

Quantum oscillations as the tool for study of new functional materials (Review Article)

Gusynin

Локтев

Luk’yanchuk

et al. 2014

Low Temperature Physics

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We present an overview of our recent results on quantum magnetic oscillations in new functional materials. We begin with the Lifshitz and Kosevich approach for quasi-2D layered materials and obtain general formulas for the oscillatory parts of the grand thermodynamic potential and magnetization. Then we consider the oscillations of the Nernst-Ettingshausen coefficient which consists of thermal and magnetization parts. The difference between normal and Dirac carriers is also discussed. To conclude we consider a model for multilayer graphene which allows to calculate exactly the Berry phase which remains undetermined in the Lifshitz-Kosevich approach. The magnetic oscillations of the density of states and capacitance for different number of the carbon layers are described.

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Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene

Cited by 15 publications

References 35 publications

High-Magnetic-Field Tunneling Spectra of ABC -Stacked Trilayer Graphene on Graphite

High-Magnetic-Field Tunneling Spectra of ABC -Stacked Trilayer Graphene on Graphite

Orbital magnetization of interacting Dirac fermions in graphene

Quantum oscillations as the tool for study of new functional materials (Review Article)

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