Local electrostatic imaging of striped domain order in LaAlO ₃/SrTiO₃

The emerging field of complex oxide interfaces is generically built on one of the most celebrated substrates - strontium titanate (SrTiO₃). This material hosts a range of phenomena, including ferroelasticity, incipient ferroelectricity, and most puzzlingly, contested giant piezoelectricity. Although these properties may markedly influence the oxide interfaces, especially on microscopic length scales, the lack of local probes capable of studying such buried systems has left their effects largely unexplored. Here we use a scanning charge detector - a nanotube single-electron transistor - to non-invasively image the electrostatic landscape and local mechanical response in the prototypical LaAlO₃/SrTiO₃ system with unprecedented sensitivity. Our measurements reveal that on microscopic scales SrTiO 3 exhibits large anomalous piezoelectricity with curious spatial dependence. Through electrostatic imaging we unravel the microscopic origin for this extrinsic piezoelectricity, demonstrating its direct, quantitative connection to the motion of locally ordered tetragonal domains under applied gate voltage. These domains create striped potential modulations that can markedly influence the two-dimensional electron system at the conducting interface. Our results have broad implications to all complex oxide interfaces built on SrTiO₃ and demonstrate the importance of microscopic structure to the physics of electrons at the LaAlO₃ /SrTiO ₃ interface.