QuantumSpark

The TopoEliashberg project introduces a computational framework designed to discover advanced quantum materials that host Majorana phases. These phases are critical for future quantum computing technologies. By combining advanced simulations of crystal structures, magnetic properties, and electron-phonon interactions, the framework maps out how superconductivity behaves at the atomic level in complex layered materials. Specifically, it investigates stacks of altermagnets, polar control interfaces, and superconductors to see if their topological properties can be electrically switched on and off. The overall goal is to provide a rigorous roadmap for predicting robust quantum states using realistic, material-specific data rather than simplified theoretical models.

The manuscript outlines a detailed methodology for predicting topological superconductivity using first-principles calculations. It links Quantum ESPRESSO, Wannier90, and EPW to generate a realistic, band and momentum dependent pairing gap $\Delta_{n}(k,T)$ that is explicitly transferred into an orbital-spin Wannier pairing matrix $\Delta_{\alpha\beta}(k,T)$ . A central theoretical construct is the Bogoliubov-de Gennes Hamiltonian, represented as follows:

H_{BdG}(k)=\begin{pmatrix}H_{W}(k)-\mu&\hat{\Delta}(k,T)\\\hat{\Delta}^{\dagger}(k,T)&-H_{W}^{T}(-k)+\mu\end{pmatrix}

For two-dimensional class-D phases, the topological invariant is the Chern number, calculated across negative-energy bands:

\mathcal{C}_{BdG}=\frac{1}{2\pi}\sum_{E_{m}<0}\int_{BZ}\Omega_{m,z}^{BdG}(k)d^{2}k

A nonzero Chern number in a gapped bulk indicates the presence of chiral Majorana boundary modes. The experimental robustness of these boundary states heavily depends on the topological minigap $E_{top}=\min_{k,m}\vert{}E_{m}^{BdG}(k)\vert{}$ , which must be large enough to overcome disorder and thermal fluctuations. The proposed material architecture integrates an altermagnetic layer for compensated momentum-dependent spin splitting, a sliding ferroelectric interface for switchable inversion breaking, and a two-dimensional superconductor. By evaluating these realistic physical interactions, the framework seeks to establish nonvolatile electrical switching of the topological invariant, aiming for outcomes like $\mathcal{C}_{BdG}(+P_{0})=-\mathcal{C}_{BdG}(-P_{0})$ .

TopoEliashberg

Lead Researchers

Manuscripts & Data