Research ArticleCONDENSED MATTER PHYSICS

Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer

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Science Advances  18 Jan 2019:
Vol. 5, no. 1, eaau6120
DOI: 10.1126/sciadv.aau6120

Figures

  • Fig. 1 Band inversion under competition between Coulomb interaction and chiral quantum tunneling.

    (A) Heterobilayers of semiconducting TMDs feature the type II band alignment, where conduction and valence band edges are spin-valley–locked massive Dirac cones from opposite layers. The bandgap Eg in the noninteracting limit can be closed and inverted by an interlayer bias. (B to D) Phases of the bilayer under the competition between Coulomb and interlayer quantum tunneling of the symmetry dictated chiral form (c.f. text). The dominance of Coulomb at positive small Eg leads to ES of spontaneous s-wave interlayer coherence, shown in (D). The dominance of chiral quantum tunneling at negative Eg pins the interlayer coherence in the p-wave channel, where the bilayer is a QSH insulator, shown in (B). (E) Such phase transition occurs nonsimultaneously for spin-up and spin-down species. Between ES and QSH phases, there is a phase of coexistence of ES in spin-down and QAH in spin-up species, as shown in (C).

  • Fig. 2 Phase diagram.

    (A) Phase diagram as a function of bandgap Eg and interlayer dielectric constant ε. (B to G) Examples of the six phases. The quasiparticle energy bands are shown, together with the magnitude |Δ| and phase angle arg(Δ) of the order parameter (see text), over a momentum space region of [− π/8a0, π/8a0] × [− π/8a0, π/8a0] at the two valleys, respectively, with a0 being the lattice constant. The curves atop of |Δ| map show their values along the dashed cut. The QSH and QAH phases have the same p-type arg(Δ) map as in the NI phase. In (C) to (E), the exciton density of the ES is Embedded Image, Embedded Image, and Embedded Image (aB2ε/me2), respectively, and the anisotropic |Δ| corresponds to an in-plane electric dipole of 6.8eÅ, 9.0eÅ, and 8.3eÅ per exciton, in directions denoted by the white arrows.

  • Fig. 3 Topological phase transitions without gap closing.

    (A) Energies of stable solutions of the mean-field Hamiltonian relative to that of the MES state. Inset shows the MES state energy, with the dashed part being the extrapolation. ε = 6, corresponding to the lower gray horizontal line in Fig. 2A. (B) Energies of stable solutions measured from the energy of the ES state. ε = 12, corresponding to the upper gray horizontal line in Fig. 2A. The NI and topologically nontrivial QSH (QAH) ground states are connected, without gap closing, through the ES (MES) ground state with spontaneous symmetry breaking. Inset of (B) plots the electron-hole pair density |vk|2 for two representative NI and QSH states.

  • Fig. 4 Configurable spintronics highways.

    Topological boundaries between NI, QAH, and QSH can be electrically patterned and reconfigured on a bilayer using split top-bottom gate pairs, for wiring protected helical/chiral spin channels. Red and blue colors denote spin-up and spin-down channels, respectively.

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