Excitonic effects in two-dimensional massless Dirac fermions

Wang, Jianhui; Fertig, H. A.; Murthy, Ganpathy; Brey, L.

doi:10.1103/physrevb.83.035404

Cited by 26 publications

(29 citation statements)

References 39 publications

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“…For example, a modulated superlattice potential yields a Landau level spectrum 27 , for which σ may have behavior reminiscent of edge state transport 50 . It is also interesting to speculate that for isotropic superlattice potentials, one may sufficiently slow the electron velocity so that electron-electron interaction effects become important 51,52 . We leave these questions as well as the possible effect of temperature and disorder for future research.…”

Section: Discussionmentioning

confidence: 99%

Transport in superlattices on single-layer graphene

et al. 2011

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We study transport in undoped graphene in the presence of a superlattice potential both within a simple continuum model and using numerical tight-binding calculations. The continuum model demonstrates that the conductivity of the system is primarily impacted by the velocity anisotropy that the Dirac points of graphene develop due to the potential. For one-dimensional superlattice potentials, new Dirac points may be generated, and the resulting conductivities can be approximately described by the anisotropic conductivities associated with each Dirac point. Tight-binding calculations demonstrate that this simple model is quantitatively correct for a single Dirac point, and that it works qualitatively when there are multiple Dirac points. Remarkably, for a two-dimensional potential which may be very strong but introduces no anisotropy in the Dirac point, the conductivity of the system remains essentially the same as when no external potential is presentFunding for the work described here was provided by MICINN-Spain via Grants No. FIS2009-08744 (L.B.) and No. FIS2008-04209 (P.B. and A.L.Y.), and by the NSF through Grant No. DMR-1005035 (H.A.F.

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Section: Discussionmentioning

confidence: 99%

Transport in superlattices on single-layer graphene

et al. 2011

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“…To specify whether suspended graphene has a semimetallic or insulating ground state, one needs to calculate the critical value α c and then compares it with α ≈ 2.2. The value of α c has been evaluated by means of several different methods, including Dyson-Schwinger (DS) equation [65,[70][71][72][73][74][75][76][77][78][79][80][81][82][83], Bethe-Salpeter (BS) equation [84][85][86], RG approach [86][87][88][89], Monte Carlo simulations [90][91][92][93][94][95][96][97], and some other methods [98,99]. Drut and Lähde claimed that α c ≈ 1.1 in a 2D Dirac fermion system [90,91], which indicates that graphene placed on SiO 2 substrate is semimetallic but suspended graphene is insulating at zero temperature.…”

Section: Introductionmentioning

confidence: 99%

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Wang¹,

Liu²,

Zhang³

2017

Phys. Rev. B

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A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO2/VO2 nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

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“…Pair formation has also been studied in gapped graphene [33,34,35,24] and the two body problem was considered in bilayer graphene quantum dots [36]. Excitonic effects in Dirac materials have been studied using a variety of approaches such as the Bethe-Salpeter method [37] as well as the twobody tight-binding matrix Hamiltonian [35,38,39,29], we shall employ the later method.…”

Section: Introductionmentioning

confidence: 99%