Direct measurement of ferroelectric polarization in a tunable semimetal

Abstract

Ferroelectricity, the electrostatic counterpart to ferromagnetism, has long been thought to be incompatible with metallicity due to screening of electric dipoles and external electric fields by itinerant charges. Recent measurements, however, demonstrated signatures of ferroelectric switching in the electrical conductance of bilayers and trilayers of WTe₂, a semimetallic transition metal dichalcogenide with broken inversion symmetry. An especially promising aspect of this system is that the density of electrons and holes can be continuously tuned by an external gate voltage. This degree of freedom enables measurement of the spontaneous polarization as free carriers are added to the system. Here we employ capacitive sensing in dual-gated mesoscopic devices of bilayer WTe₂ to directly measure the spontaneous polarization in the metallic state and quantify the effect of free carriers on the polarization in the conduction and valence bands, separately. We compare our results to a low-energy model for the electronic bands and identify the layer-polarized states that contribute to transport and polarization simultaneously. Bilayer WTe₂ is thus shown to be a fully tunable ferroelectric metal and an ideal platform for exploring polar ordering, ferroelectric transitions, and applications in the presence of free carriers.

Fig. 1. Fabrication and measurement of the bilayer capacitance device.

a Schematic of our lithography-free encapsulation and contact method, using a boron nitride (BN) crystal previously prepared with through-hole Au contacts to pick up and transfer WTe₂ on to another BN dielectric layer with a graphite bottom gate below. Top gate and leads to the through-hole contacts and bottom gate are patterned after fully encapsulating the WTe₂. b Measurement schematic showing the measurable capacitances: C_t, between the top gate and WTe₂, and C_b, between the bottom gate and WTe₂. C_i is the interlayer capacitance across the bilayer. c Measured top capacitance, C_t, as a function of carrier density, n₀, at zero and finite electric field, E_⊥. d Side-view structure of bilayer WTe₂ in two stable configurations, each showing the net polarization state along c-axis (P). The two states are related equivalently by a mirror operation along the c-axis (${\mathcal{M}}_c$) or by lateral translation between the layers along the b-axis of 0.72 Å^,, or ~11% of the unit cell. The ⋆ symbol labels a Te atom before and after the mirror operation (black) and translation (red) as a visual guide. The mirror/translation equivalence allows a subtle shift between the layers to switch the structure between polarization states. e Top-view structure showing the only invariant symmetry of the crystal, mirror reflection along the a-axis (${\mathcal{M}}_a$).

Fig. 2. Hysteresis in the electric field response for electrons and holes.

a Forward and b backward scans of the top capacitance C_t as a function of electric field, E_⊥, for a range of carrier densities, n₀. c Capacitance traces measured along the dashed lines in a, b (beginning at the ⋆ symbol in each case) displaying a smooth background as well as sudden jumps at electric field values that depend on the sweep direction. d Difference between the traces in c. e Compilation of differences between forward and backward scans in a, b for an extended range of carrier densities, showing the change in sign of the switching from electrons to holes and the gradual density dependence of the switching behavior.

Fig. 3. Layer-polarized bands yield distinct capacitance branches for each polarization state.

a Schematic low-energy bands showing layer-polarized valleys (orange and purple) in the P⁺ state, for small electron density and E_⊥ = 0. In the P⁻ state, the colors and layer polarization would be interchanged. Each pair of valleys is centered around a point along Γ–X, labeled Q. Band parameters are exaggerated to emphasize separation of valleys. b Representative calculated layer densities, c compressibilities, and d polarization $\propto n_1^{\pm }-n_2^{\pm }$ in each polarization state, ±, from n₀ ≈ 0. e Computed top capacitances, $C_{\mathrm{t}}^{+}$ and $C_{\mathrm{t}}^{-}$ in the P⁺ and P⁻ states, respectively, for the listed densities versus electric field, with colored symbols indicating the hysteretic path observed in experiment, while gray symbols denote portions of each capacitance branch that are inaccessible in experiment due to switching behavior (switching fields are not computed in the model; solid vertical lines are shown extending from experimental switching fields in f to reflect the loop observed in the experiment). Capacitance is calculated using computed layer densities, potentials, and compressibilities to evaluate Eq. (11a). f Measured top capacitance hysteresis loops for matching electron and hole densities in e.

Fig. 4. Ferroelectric polarization in the presence of free carriers.

a Measured density dependence of $\mathrm{\Delta }{C}_{\mathrm{t}}\equiv C_{\mathrm{t}}^{+}-C_{\mathrm{t}}^{-}$ at E_⊥ = 0. b Change in measured spontaneous polarization calculated by integration, ΔP_s ∝ ∫ΔC_tdn₀. Left axis provides 2D polarization units while the right scale is given in terms of charge separation between the layers, Δp_s = ΔP_s/d_i for WTe₂ interlayer separation, d_i = 0.7 nm. Background shading follows the magnitude of ΔP_s, illustrating distinct regions of ferroelectric (FE) behavior. c Computed ΔC_t and d ΔP_s based on model Hamiltonian for bilayer WTe₂, with inset in d showing computed ΔP_s for an extended density range (with identical units). ΔP_s is computed by two different methods: “Exact” using Eq. (18), and “Approx.” using Eq. (33).