Ab initio study of Proximity-Induced Superconductivity in PbTe/Pb heterostructures

TL;DR

This work presents a first-principles study of proximity-induced superconductivity in PbTe/Pb heterostructures using a unified Kohn–Sham DFT and Bogoliubov–de Gennes framework (SIESTA-BdG). It reveals strong PbTe–Pb hybridization that metallizes the interface and a significant Schottky barrier, posing challenges for achieving the energy alignment needed for Majorana modes. In the superconducting state, a proximity-induced gap appears on the PbTe side with an intermediate coupling and an anisotropic pairing potential, while the Pb side exhibits a poisoned gap; the anomalous density is notably anisotropic and decays into PbTe over about $\eta \approx 14$ Å. The results are robust to strain and electric fields, offering insights into the design and tunability of PbTe/Pb-based devices for Majorana applications and other proximity-driven phenomena.

Abstract

Semiconductor-superconductor hybrid devices have been proposed as promising platforms for detecting and analyzing Majorana zero modes, which find applications in topological quantum computing. In this work, we solve the Kohn-Sham Density Functional Theory and Bogoliubov-de Gennes equations to describe the normal and superconducting properties of a PbTe/Pb heterostructure. We resolve a proximity-induced superconducting gap on the PbTe side. The hybridization between PbTe and Pb causes the emergence of a soft Bardeen-Cooper-Schrieffer-like superconducting gap. We compute the anomalous charge density in real space, estimating its decay length and showing that the pairing potential is anisotropic, which is a necessary condition for unconventional superconductivity. Contrary to the models that predict Majorana zero modes in these interfaces, we find a significantly large Schottky barrier in the normal state preventing the emergence of zero modes. Our findings strengthen the understanding of the physics governing PbTe/Pb hybrid devices and their viability for Majorana zero modes applications.

Figures (13)

• Figure 1: (a) Side view of the relaxed (4, -5) PbTe/Pb interface stacked along the [001] direction. (b) Average electrostatic potential $\Delta V_{ave}$ across the interface, including a schematic of the energy alignment between a semiconductor and a normal metal. (c) Schematic band alignment at the interface between a semiconductor and a superconductor.
• Figure 2: (a) PbTe/Pb normal state band structure. The bands cross the Fermi level, resulting in a metallic heterostructure. (b) Normal state bands with the coupling between the PbTe and Pb sides of the heterostructure set to zero. The color intensity represents the contribution from the PbTe orbitals.
• Figure 3: PbTe/Pb normal state DOS for different (a) strain and (b) applied electric field across the interface, represented with different colors.
• Figure 4: (a) Superconducting DOS (SC--DOS, $\rho(\varepsilon)$, black continuous line) and anomalous DOS (ADOS, $\chi(\varepsilon)$, dashed green line) for the (4, -5) PbTe/Pb HS, with coherence peaks at $\pm \Delta/2 \sim \pm 1$ eV. The dashed black line indicates zero DOS. SC--DOS projected on individual (b) PbTe and (c) Pb layers, and (d) for the PbTe/Pb HS for diffrent strain values.
• Figure 5: (a) Anomalous density of states $\chi(\mathbf{r})$ along the z-axis in real space. Vertical dashed lines represent the layer position in the PbTe (olive) and Pb (black) regions of the heterostructure. (b) 3D visualization of the anomalous DOS near the interface region. We set the isosurface level to a fixed value ($1.7\times10^{-7}$ 1/Bohr$^3$), which indicate regions where $\chi(\mathbf{r})$ is constant. To enhance visualization, the isosurface on the PbTe side of the heterostructure (blue) is set to a value 10 times smaller than the Pb side (red).