The LaAlO₃-SrTiO₃ (LAO-STO) heterostructure is known to host an electron gas of two-dimensional character (2DEG) at its interface. There is evidence of an enhancement in the measured differential capacitance of top-gated LAO-STO [1,2], in excess of the geometric capacitance. In this work, we present a phenomenological model that features a coupling between charge (in 2DEG) and structural distortion (in surface layers of STO), and calculate the modification of differential capacitance due to this term. We classify the phases of single-domain STO coupled to 2DEG charge, account for the contribution from ferroelastic domain boundaries, and make connections with data available from experiments.

[1] L. Li, C. Richter, S. Paetel, T. Kopp, J. Mannhart, and R. C. Ashoori, Science 332(6031), 825 (2011).

[2] F. Bi, M. Huang, C.-W. Bark, S. Ryu, S. Lee, C.-B. Eom, P. Irvin, and J. Levy, J. Appl. Phys. 119, 025309 (2016).