# Universality of Electron Mobility in LaAlO$_3$/SrTiO$_3$ and bulk SrTiO$_3$

## TL;DR

This paper derives a simple relation between electron density and mobility in LAO/STO interfaces, showing they behave similarly to bulk STO, and suggests revisiting the polar catastrophe model due to unexpected mobility behavior.

## Contribution

It introduces a new expression linking 3D and sheet electron densities and compares interface mobility with bulk STO, challenging existing polar catastrophe assumptions.

## Key findings

- Mobility depends on 3D electron density similarly in LAO/STO and bulk STO.
- In LAO/STO, mobility remains high despite expectations, indicating a need to revisit the polar catastrophe model.
- The derived relation explains the mobility behavior across different doping regimes.

## Abstract

Metallic LaAlO$_3$/SrTiO$_3$ (LAO/STO) interfaces attract enormous attention, but the relationship between the electron mobility and the sheet electron density, $n_s$, is poorly understood. Here we derive a simple expression for the three-dimensional electron density near the interface, $n_{3D}$, as a function of $n_s$ and find that the mobility for LAO/STO-based interfaces depends on $n_{3D}$ in the same way as it does for bulk doped STO. It is known that undoped bulk STO is strongly compensated with $N \simeq 5 \times 10^{18}~\rm{cm^{-3}}$ background donors and acceptors. In intentionally doped bulk STO with a concentration of electrons $n_{3D} < N$ background impurities determine the electron scattering. Thus, when $n_{3D} < N$ it is natural to see in LAO/STO the same mobility as in the bulk. On the other hand, in the bulk samples with $n_{3D} > N$ the mobility collapses because scattering happens on $n_{3D}$ intentionally introduced donors. For LAO/STO the polar catastrophe which provides electrons is not supposed to provide equal number of random donors and thus the mobility should be larger. The fact that the mobility is still the same implies that for the LAO/STO the polar catastrophe model should be revisited.