• 文献标题:   Hall viscosity and nonlocal conductivity of gapped graphene
  • 文献类型:   Article
  • 作  者:   SHERAFATI M, VIGNALE G
  • 作者关键词:  
  • 出版物名称:   PHYSICAL REVIEW B
  • ISSN:   2469-9950 EI 2469-9969
  • 通讯作者地址:   Univ Missouri
  • 被引频次:   1
  • DOI:   10.1103/PhysRevB.100.115421
  • 出版年:   2019

▎ 摘  要

We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector q) Hall conductivity of "gapped graphene" (a nontopological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosities and conductivity up to q(2) at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graphene, the derivation reveals a significant difference between the two systems. First of all, both the Hall viscosity and the Hall conductivity vanish when the Fermi level lies in the gap that separates the lowest Landau level in the conduction band from the highest Landau level in the valence band. It is only when the Fermi level is not in the gap that the familiar formulas of gapless graphene are recovered. Second, in the case of gapped graphene, it is not possible (at least, within our present approach) to define a single-valley Hall viscosity: this quantity diverges with a strength proportional to the magnitude of the gap. It is only when both valleys are included that the diverging terms, having opposite signs in the two valleys, cancel out, and the familiar result is recovered. In contrast to this, the nonlocal Hall conductivity is finite in each valley. These results indicate that the Hoyos-Son formula [Phys. Rev. Lett. 108, 066805 (2012)] connecting the Hall viscosity to the coefficient of q(2) in the small-q expansion of the q-dependent Hall conductivity cannot be applied to each valley, but only to the system as a whole. The problem of defining a "valley Hall viscosity" remains open.