The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

Menezes, N.; Alves, Van Sérgio; Smith, C. Morais

doi:10.1140/epjb/e2016-70606-4

Cited by 18 publications

(19 citation statements)

References 27 publications

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“…At this high temperature, the spin ordering vanishes but the LLs of the DFs are strongly changed by the interactions through the self-energy Σ 1 . Σ 1 gives rise to an enhancement of the velocity [33][34][35] enhancement of the velocity, the OM of the interacting DFs is stronger than that of the free DFs. For finite doping at very small B and T = 0, there are rapid de Haas-van Alphen oscillations similarly as that indicated in Sec.…”

Section: Orbital Magnetizationmentioning

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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Section: Orbital Magnetizationmentioning

confidence: 99%

Orbital magnetization of interacting Dirac fermions in graphene

Yan

Ting

2017

Phys. Rev. B

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“…The conventional approach [25][26][27][28][29][30][31][32][33][34][35][36][37] to treat the interaction-induced renormalization of Landau level energies is based on the Hartree-Fock approximation, where the renormalized energy…”

Section: Theoretical Modelmentioning

confidence: 99%

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

Sokolik

Lozovik

2018

Phys. Rev. B

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Renormalization of Landau level energies in graphene in strong magnetic field due to Coulomb interaction is studied theoretically, and calculations are compared with two experiments on carrierdensity dependent scanning tunneling spectroscopy. An approximate preservation of the square-root dependence of the energies of Landau levels on their numbers and magnetic field in the presence of the interaction is examined. Many-body calculations of the renormalized Fermi velocity with the statically screened interaction taken in the random-phase approximation show good agreement with both experiments. The crucial role of the screening in achieving quantitative agreement is found. The main contribution to the observed rapid logarithmic growth of the renormalized Fermi velocity on approach to the charge neutrality point turned out to be caused not by mere exchange interaction effects, but by weakening of the screening at decreasing carrier density. The importance of a self-consistent treatment of the screening is also demonstrated.

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“…Most theoretical models of Coulomb many-body effects in graphene [7][8][9][10][11][12][13][14][15]26] take into account three major contributions to the inter-Landau level transition energies: single-particle exchange self-energies of electron and hole, an excitonic shift due to electron-hole Coulomb attraction (also referred to as a vertex correction) and an electron-hole exchange energy. The latter contribution is principal in calculating dispersions of collective magneto-plasmon excitations [3,[7][8][9][29][30][31][32][33][34], but vanishes for optically excited nearly zero-momentum electron-hole pairs, therefore we will not include it in our calculations.…”

Section: A Exchange Self-energiesmentioning

confidence: 99%

“…The existing theoretical calculations [7][8][9][10][11][12][13]26] of inter-Landau level transitions in graphene were carried out in * Electronic address: lozovik@isan.troitsk.ru the first order in Coulomb interaction, which implies using of the unscreened Coulomb interaction in all matrix elements [28]. This results in the overestimation of manybody effects in comparison with the experimental data, as noted in Refs.…”

Section: Introductionmentioning

confidence: 99%

Many-body effects of Coulomb interaction on Landau levels in graphene

2017

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In strong magnetic fields, massless electrons in graphene populate relativistic Landau levels with the square-root dependence of each level energy on its number and magnetic field. Interactioninduced deviations from this single-particle picture were observed in recent experiments on cyclotron resonance and magneto-Raman scattering. Previous attempts to calculate such deviations theoretically using the unscreened Coulomb interaction resulted in overestimated many-body effects. This work presents many-body calculations of cyclotron and magneto-Raman transitions in single-layer graphene in the presence of Coulomb interaction, which is statically screened in the random-phase approximation. We take into account self-energy and excitonic effects as well as Landau level mixing, and achieve good agreement of our results with the experimental data for graphene on different substrates. Important role of a self-consistent treatment of the screening is found.

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The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

Cited by 18 publications

References 27 publications

Orbital magnetization of interacting Dirac fermions in graphene

Orbital magnetization of interacting Dirac fermions in graphene

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

Many-body effects of Coulomb interaction on Landau levels in graphene

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