Type-II Weyl cone transitions in driven semimetals

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Type-II Weyl cone transitions in driven semimetals

Ching-Kit Chan, Yun-Tak Oh, Jung Hoon Han, and Patrick A. Lee

Phys. Rev. B 94, 121106(R) – Published 7 September 2016

Abstract

Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocketlike Fermi surfaces, can be induced in driven Dirac semimetals and line node semimetals. Under a circularly polarized drive, both semimetal systems immediately generate Weyl node pairs whose types can be further controlled by the driving amplitude and direction. The resultant phase diagrams demonstrate experimental feasibilities.

Received 22 May 2016
Revised 23 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.121106

Physics Subject Headings (PhySH)

Weyl fermions

Dirac semimetal Weyl semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ching-Kit Chan¹, Yun-Tak Oh², Jung Hoon Han², and Patrick A. Lee¹

¹Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Physics, Sungkyunkwan University, Suwon 16419, Korea

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Issue

Vol. 94, Iss. 12 — 15 September 2016

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Figure 1
Schematics of driven semimetals. ( $a_{1}$ ) Dispersion of an undriven DSM with two pairs of Dirac nodes. The energy gap at $\vec{k} = 0$ is parametrized by $| m_{0} |$ . ( $a_{2}$ ) Phase diagram of the undriven DSM. The type-I and type-II phases are determined only by a microscopic parameter $| c_{z} / m_{z} |$ [Eq. (1)]. ( $a_{3}$ ), ( $a_{4}$ ) Driven DSMs. Green arrows denote driving directions. ( $a_{3}$ ) A $k_{z}$ -drive splits the Dirac nodes into pairs of Weyl nodes along $k_{z}$ , but cannot change the type of the cone. ( $a_{4}$ ) Driving along $k_{x}$ moves the nodes away from the $k_{z}$ axis and can induce a type-II Weyl transition. The tilting axis is related to the chirality. The circles show top views of the cones and the shaded regions mark the electron pockets. ( $b_{1}$ ) Undriven LNSM with a nodal ring. The dispersion in the $k_{x} - k_{z}$ plane can be generated by rotating that of ( $a_{1}$ ). An external drive gaps out the nodal line and creates a Weyl pair along the drive. Depending on model parameters, the photoinduced Weyl cone can belong to type I ( $b_{2}$ ) or type II ( $b_{3}$ ).
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Figure 2
Phases and phase diagrams of driven DSMs. (a) Undriven type-I Dirac dispersion. (b) Dispersion when driven along $k_{x}$ . Left panel: the Dirac node is split into a type-II Weyl pair with electron and hole pockets. Only the $χ = 1$ nodes are shown. The $χ = - 1$ counterparts can be obtained by reversing the $k_{x}$ axis. Right panel: zoom-in dispersion in the vicinity of one of the split nodes. (c) Phase diagram of the driven DSM showing the photoinduced type-II Weyl phase ( $A$ in units of $Å^{- 1}$ ). The false color scale gives the maximum tilting ratio $| T / U |$ in the type-II phase and the phase boundary happens at $max (| T / U |) = 1$ . In (a)–(c) $- m_{0} = 0.5 eV$ and $- Δ c = 1$ , where in (a) and (b) $c_{z} / | m_{z} | = 0.8$ . The mass and anisotropy are important to induce the type-II phase. (d) Shrinking of the type-II region as we reduce $- m_{0}$ (dashed blue, from $0.5 eV$ to $0.37, 0.23, 0.1 eV$ ) and $- Δ c$ (dot-dashed red, from 1 to 0.8,0.5,0), respectively. Common parameters: $v_{x} = v_{y} = 2.5 eV Å, m_{x, y, z} = - 10 eV Å^{2}, c_{x} = c_{y}, ω = 0.1 eV$ , and $χ = ξ = 1$ .
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Figure 3
Phase diagrams of driven LNSMs using a realistic and small mass $- m_{0} = 0.1 eV$ . The induced type-II phase region is much larger. (a) Phase diagram at a fixed driving angle $θ_{A} = π / 4$ . The corresponding phase boundary for the DSM case is marked by the dashed line for comparison. (b) Phase diagram at fixed $c_{z} / | m_{z} | = 0.8$ . Different from the DSM case, the type-II phase can occur even for small driving amplitudes in LNSMs. The requirements on the mass and drive to photoinduce a type-II phase in LNSMs are much relaxed. Common parameters: $v_{y} = 2.5 eV Å, m_{x, y, z} = - 10 eV Å^{2}, c_{x} = c_{y}, ω = 0.1 eV, ξ = 1$ , and $- Δ c = 1$ .
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