  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
noninvasively image the electrostatic landscape and local mechanical response
in the prototypical LaAlO3/SrTiO3 system with unprecedented sensitivity. Our
measurements reveal that on microscopic scales SrTiO3 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/SrTiO3 interface.
