Weyl Semimetal in a Topological Insulator Multilayer

Weyl Semimetal in a Topological Insulator Multilayer

September 20, 2011 | A.A. Burkov1,2 and Leon Balents2
This paper proposes a simple realization of a three-dimensional (3D) Weyl semimetal phase using a multilayer structure composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary insulator spacer layers. The system exhibits a Weyl semimetal phase with only two Dirac nodes of opposite chirality, separated in momentum space. This phase is an intermediate state between an ordinary insulator and a 3D quantum anomalous Hall (QAH) insulator. The Weyl semimetal has a finite anomalous Hall conductivity and topologically protected edge states. The structure consists of alternating layers of a 3D TI, such as Bi₂Se₃, and an ordinary insulator. The Hamiltonian for this heterostructure is derived, and the band structure is analyzed. When the spin splitting is absent, the system has a fully gapped band structure, but when spin splitting is introduced, Dirac nodes appear. These nodes are separated in momentum space, leading to a stable Weyl semimetal phase. The Weyl semimetal is characterized by a nonzero anomalous Hall conductivity, proportional to the separation of the Dirac nodes, and topologically protected chiral edge states. The Hall conductivity is calculated using the Kubo formula, showing a finite DC conductivity at zero temperature, with Drude weight vanishing as T². This indicates that the Weyl semimetal is an unusual metallic phase, not an insulator, with nonzero anomalous Hall conductivity and topologically protected edge states. The results suggest that the Weyl semimetal has Fermi arcs, which are surface states corresponding to the 2D quantum Hall states. The edge states are localized to the surface and are distinct from ordinary quantum Hall edge states, as they exist in a finite subset of the edge Brillouin zone. The paper concludes that the proposed Weyl semimetal is a simple realization of the 3D Weyl semimetal phase, with only two Dirac nodes, and is characterized by a finite anomalous Hall conductivity and topologically protected edge states. Open questions include the influence of Coulomb interactions on the properties of Weyl semimetals, particularly their transport properties.This paper proposes a simple realization of a three-dimensional (3D) Weyl semimetal phase using a multilayer structure composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary insulator spacer layers. The system exhibits a Weyl semimetal phase with only two Dirac nodes of opposite chirality, separated in momentum space. This phase is an intermediate state between an ordinary insulator and a 3D quantum anomalous Hall (QAH) insulator. The Weyl semimetal has a finite anomalous Hall conductivity and topologically protected edge states. The structure consists of alternating layers of a 3D TI, such as Bi₂Se₃, and an ordinary insulator. The Hamiltonian for this heterostructure is derived, and the band structure is analyzed. When the spin splitting is absent, the system has a fully gapped band structure, but when spin splitting is introduced, Dirac nodes appear. These nodes are separated in momentum space, leading to a stable Weyl semimetal phase. The Weyl semimetal is characterized by a nonzero anomalous Hall conductivity, proportional to the separation of the Dirac nodes, and topologically protected chiral edge states. The Hall conductivity is calculated using the Kubo formula, showing a finite DC conductivity at zero temperature, with Drude weight vanishing as T². This indicates that the Weyl semimetal is an unusual metallic phase, not an insulator, with nonzero anomalous Hall conductivity and topologically protected edge states. The results suggest that the Weyl semimetal has Fermi arcs, which are surface states corresponding to the 2D quantum Hall states. The edge states are localized to the surface and are distinct from ordinary quantum Hall edge states, as they exist in a finite subset of the edge Brillouin zone. The paper concludes that the proposed Weyl semimetal is a simple realization of the 3D Weyl semimetal phase, with only two Dirac nodes, and is characterized by a finite anomalous Hall conductivity and topologically protected edge states. Open questions include the influence of Coulomb interactions on the properties of Weyl semimetals, particularly their transport properties.
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