Anomalous thermodynamic properties of the electron accumulation layer in SrTiO3

Due to the nonlinear dielectric response within SrTiO3 (STO), an accumulation layer created by positive charges at the surface of the STO sample (x=0) has an electron density profile n(x) that slowly decays as 1/x12/7. Here we show that the long tail of n(x) causes the magnetization and the specific heat of the accumulation layer to diverge at large x. We explore the truncation of the tail by the finite sample width W, the transition from the nonlinear to linear dielectric response with dielectric constant κ, and the use of a back gate with a negative voltage -V. We find that both the magnetization and specific heat are anomalously large and obey nontrivial power law dependences on W, κ, or V. We conclude with a discussion of how the capacitance as a function of the back gate voltage may be used to study the shape of the n(x) tail in thin samples.