Two-dimensional helical superconductivity and gapless superconducting edge modes in the 1T$^\prime$-WS$_2$/2H-WS$_2$ heterophase bilayer

Abstract

We propose a material platform comprised of transition metal dichalcogenide (TMDC) heterostructures to realize the two-dimensional (2D) helical superconductivity with an intrinsic gap. By van der Waals stacking a 2D superconductor (1T$^\prime$-WS$_2$ with inversion symmetry) on top of a 2D topological insulator (2H-WS$_2$ with mirror symmetry), the resulting TMDC bilayer exhibits Rashba superconductivity. Under an external in-plane magnetic field, the system can host finite-momentum Cooper pairing, evidenced by the divergence in the particle-particle susceptibility of a $k\cdot p$ Hamiltonian fitted to the \textit{ab initio} theory band structure. The resulting 2D helical superconducting phase can induce superconductivity in the edge states with its spatially varying order parameter. By varying the strength of the in-plane magnetic field, we demonstrate that the helical edge state can undergo a phase transition to a one-dimensional gapless phase with narrow Fermi segments corresponding to zero-energy Bogoliubov quasi-particles. The controllable one-dimensional gapless phase serves as a clear experimental fingerprint of 2D helical superconductivity. The proposed 2D TMDC heterostructure is promising for intrinsic nonreciprocal superconducting transport and the development of Majorana-based quantum devices.

Figures (4)

• Figure 1: Schematic of bulk FF-like states in a 2D helical superconductor under an external field. The external field can induce the transition of the superconducting edge modes from a gapped phase to a gapless phase.
• Figure 2: (a) Top and (b) side views of the 1T$^\prime$-WS$_2$/2H-WS$_2$ heterophase bilayer. Gray and yellow spheres indicate W and S atoms, respectively. The green rectangle (purple diamond) corresponds to the unit cell of the 1T$^\prime$ (2H) phase. (c) Band structure of the heterophase bilayer, where green(purple) indicates the weight in the 1T$^\prime$(2H) layer. (d) Low energy band structure (with SOC) near $\Gamma$. Blue dashed lines indicate the bands without SOC. (e) The Brillouin zone of the 2H phase (purple) and 1T$^\prime$ phase (green). (f) Spin projection ($S_x$) of HPB Fermi pockets within the dashed rectangle. Red and blue indicate spin projection to $\pm$ x respectively.
• Figure 3: Intraband contributions of the particle-particle susceptibility (a) $\Pi_{++}$ and (b) $\Pi_{--}$ evaluated at different Zeeman energies at temperature $\beta=1/0.0001$. Insets show the Fermi pocket pairing at $E_z=1$ meV. (c) Position and (d) peak height of the highest logarithmic divergence in the particle-particle susceptibility as a function of $E_z$ at $\eta=10^{-7}$.
• Figure 4: (a) Phase diagram of the superconducting helical edge states in the WS$_2$ HPB ribbon. GG: gapped superconducting on both edges; GL: one edge gapless; LL: both edges gapless. Red line represents $q \propto B$ with phase transition points $\mathit{\Theta_{1,2}}$ corresponding to critical Zeeman energies $E_{z1,z2}$. (b) The Bogoliubov quasiparticle band structures of two edges (left and right) at the first critical phase transition point (black solid line) near the Fermi wavevector $k_F+\Delta k$. Blue and green dashed lines indicate the 1.5$\times$ and 0.5$\times$ the critical $B$ field, corresponding to the GL and GG phase respectively. The Fermi velocity $v_F\approx 0.1$ eV$\cdot$Å is used.