Fig. 1.

Electron tunnelling through a flexoelectrically polarised ultrathin barrier. a Schematic of the experimental setup, illustrating flexoelectric polarisation (blue arrow) generated by the atomic force microscope (AFM) tip pressing the surface of ultrathin SrTiO₃ (STO). b Simulated transverse strain u₁₁ in a nine unit cell-thick (i.e. 3.5 nm-thick) STO under a representative tip loading force of 5 μN. Along the central line, u₁₁ varies by ~0.5% within ∆x₃ = 0.5 nm, yielding ∂u₁₁/∂x₃ ~ 10⁷ m⁻¹. c Polarisation profile, obtained by phase-field simulation, for the strain profile in b. Arrows denote the polarisation direction. In the tip-contact region, the polarisation along the x₃ direction was around 0.17 C m⁻² on average. Note that when neglecting flexoelectricity (i.e. f = 0), our simulation does not produce any polarisation in STO, which again confirms the flexoelectricity-based origin of our observation. Source data are provided as a Source Data file