Research Article

The role of electron-electron interactions in two-dimensional Dirac fermions

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Science  10 Aug 2018:
Vol. 361, Issue 6402, pp. 570-574
DOI: 10.1126/science.aao2934

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Computers tease out interaction effects

Although graphene is often thought of as a material in which electron-electron interactions are negligible, some of its properties cannot be explained by such a simple picture. Tang et al. undertook comprehensive quantum Monte Carlo numerical calculations that consider both long-range and contact interactions in systems that, like graphene, have two-dimensional (2D) Dirac electrons. Different 2D Dirac materials systems, such as topological insulators and graphene on various substrates, reside in different parts of the resulting phase diagram.

Science, this issue p. 570


The role of electron-electron interactions in two-dimensional Dirac fermion systems remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator and a semimetallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. We predict that experimental realizations of Dirac fermions span this crossover and that this determines whether the Fermi velocity is increased or decreased by interactions. We explain several long-standing mysteries, including why the observed Fermi velocity in graphene is consistently about 20% larger than values obtained from ab initio calculations and why graphene on different substrates shows different behaviors.

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