Topological superconductivity of a two-dimensional electron gas at the (001) LaAlO\textsubscript{3}/SrTiO\textsubscript{3} interface

Abstract

We investigate the emergence of topological superconductivity and Majorana zero modes in the two-dimensional electron gas formed at the LaAlO$_3$/SrTiO$_3$ (001) interface. Using a realistic multiband tight binding model that incorporates the $t_{2g}$ orbital structure together with atomic and Rashba spin-orbit couplings, we determine the topological phase diagrams for both fully two-dimensional and quasi-one-dimensional geometries. In the two-dimensional limit, we show that a finite out-of-plane magnetic-field component is required to drive a topological phase transition. In this case, the critical field is strongly band dependent, and for higher-lying bands, it is controlled by the interplay of spin and orbital Zeeman effects, as well as atomic spin-orbit coupling. Although a purely in-plane field is insufficient to induce the topological transition in a full 2D system, we demonstrate that a lateral confinement relaxes this constraint. In this case, the character of the edge modes depends sensitively on the field orientation, with out-of-plane fields producing conventional counterpropagating chiral modes and transverse in-plane fields giving rise to co-propagating antichiral modes. Finally, Majorana zero modes in LAO/STO nanowires with varying widths are analyzed. We demonstrate that subbands predominantly composed of $d_{yz/xz}$ orbitals exhibit exceptionally long localization lengths, which may preclude the observation of Majorana bound states in nanowires of typical experimental dimensions.

Figures (12)

• Figure 1: (a) Dispersion relation $E(k_x, k_y=0)$ for the LAO/STO 2DEG. The horizontal dashed lines indicate the helical band minima, denoted by $\mu_l$ with $l = 1,2,3$, which are used as reference chemical potentials for determining the corresponding topological phase diagram. (b) Enlarged view of panel (a), highlighting the spin splitting of the band induced by SO coupling. In both panels, the contributions of the $d_{xy}$, $d_{xz}$, and $d_{yz}$ orbitals are represented using the RGB color scheme, such that the resulting color reflects their relative mixture.
• Figure 2: Chern number as a function of the chemical potential $\mu$ and the out-of-plane magnetic field $B_z$, evaluated in the vicinity of the bottom of the helical bands denoted as $\mu_l$ with $l = 1,2,3$ in Fig. \ref{['fig:disp_NM']}(a).
• Figure 3: Dispersion relations of the superconducting LAO/STO 2DEG determined along the $k_x$ direction for (a-c) $\mu_{1}$, (d-f) $\mu_{2}$, and (g-i) $\mu_{3}$. In each row, the subsequent panels present the results for three distinct values of the magnetic field $B_z$: $B_z = 0$, $B^c_z$ corresponding to the critical field at $\mu=\mu_l$, and $B_z>B^c_z$. Critical field values are presented in Tab. \ref{['tab1']}. As in Fig. \ref{['fig:disp_NM']}(a), the contributions of the $d_{xy}$ , $d_{xz}$ , and $d_{yz}$ orbitals are represented using the RGB color scheme.
• Figure 4: Chern number as a function of the in-plane and out-of-plane magnetic field components $(B_y,B_z)$, evaluated for $\mu_l$ with $l = 1, 2, 3$ marked in Fig. \ref{['fig:disp_NM']}(a).
• Figure 5: The Wannier center flow as $\theta$ along $k_x$ for individual bands (black) and the sum over them (magenta) proportional to the electronic polarization. Results for the chosen chemical potentials (a-c) $\mu_{1}$, (d-f) $\mu_{2}$ and (g-i) $\mu_{3}$ and the magnetic field (a,d,g) $B_z = -1\ \mathrm{T}$, (b,e,h) $B_z=0$, and (c,f,i) $B_z=1\ \mathrm{T}$.