Two-dimensional Topological Ferroelectric Metal with Giant Shift Current

Abstract

The pursuit for "ferroelectric metal" which combines seemingly incompatible spontaneous electric polarization and metallicity, has been assiduously ongoing but remains elusive. Unlike traditional ferroelectrics with a wide band gap, ferroelectric (FE) metals can naturally incorporate nontrivial band topology near the Fermi level, endowing them with additional exotic properties. Here, we show first-principles evidence that the metallic PtBi2 monolayer is an intrinsic two-dimensional (2D) topological FE metal, characterized by out-of-plane polarization and a moderate switching barrier. Moreover, it exhibits a topologically nontrivial electronic structure with Z2 invariant equal to 1, leading to a significant FE bulk photovoltaic effect. A slight strain can further enhance this effect to a remarkable level, which far surpass that of previously reported 2D/3D FE materials. Our work provides an important step towards realizing intrinsic monolayer topological FE metals and paves a promising way for future nonlinear optical devices.

Figures (5)

• Figure 1: (a) Crystal structure of bulk t-PtBi2. Pt and Bi atoms are labeled with gray and purple colors, respectively, and $d_0$ denotes the equilibrium interlayer spacing in the bulk state. (b) Calculated exfoliation energy versus separation distance in comparison with graphite and Ca2N. (c) Top and side views of monolayer PtBi2, with a thickness of $L = 4.06~\text{\AA}$.
• Figure 2: (a) Ferroelectric switching pathway of PtBi2. (b) Phonon dispersion of FE state and NP state, where the soft modes in NP state are labeled by $B_{1u}$ and $B_{2u}$. (c) Energy landscapes as a function of ($B_{1u}$, $B_{2u}$) by freezing the modes with step-changed amplitude. (d) Top and side view of the NP structures together with the eigen-mode $B_{1u}$ marked by red and blue arrows in the left shaded area. An isosurface of the difference in charge densities of FE states (FE1 and FE2) with NP state are shown in the right panel, where light blue and yellow color denotes electron depletion and accumulation, respectively.
• Figure 3: (a) Band structure of monolayer PtBi2 without and with SOC, depicted in blue and red colors, respectively. (b) Evolution of WCCs for PtBi2 monolayer in the $k_z = 0$ plane, which indicates its topological invariant $\mathbb{Z}_2 = 1$.
• Figure 4: (a) Shift-current conductivity $\sigma_{xx}^x$, (b) JDOS, (c) the absorptive part of the dielectric function $\Im\epsilon_{xx}$ and (d) aggregate shift vector $\bar{R}^{x;x}$ as a function of the photon energy under different biaxial tensile strain.
• Figure 5: (a) Shift-current conductivity $\sigma_{xx}^x$ as a function of Fermi level and photon energy under 4% biaxial strain, with the pentagram highlighting the maximum value. (b) A comparison of maximum shift current and corresponding photon energy in PtBi2 with other widely studied 2D/3D ferroelectric materials MX_scd1t_mos2_scNbOCl2_scCsGeI3_scRappePRL.