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HL: Fachverband Halbleiterphysik

HL 20: Poster I

HL 20.2: Poster

Dienstag, 10. März 2026, 18:00–20:00, P1

Tensor network methods for electron-hole complex in nanoplatelets — •Bruno Hausmann and Marten Richter — Institut für Physik und Astronomie, Technische Universität Berlin, Germany

Nanoplatelets are colloidally grown, atomically thin, rectangular semiconductor nanostructures. Excitons in nanoplatelets are solutions of a four-dimensional Schrödinger equation. This is especially true as the structure is in between the weak and strong confinement regimes. Solving this equation is computationally expensive compared to the typical two-dimensional Wannier equation under weak confinement. Going beyond excitons to trions and biexcitons, the memory size of the discretized wavefunctions grows exponentially with the particle number. Tensor network methods have successfully been applied to solve high-dimensional eigenvalue problems. Here we adapt them to the eigenvalue equation for excitons and trions by decomposing the real-space wavefunctions into quantics tensor trains (QTT). Operators that transform the indices, e.g. shift operators in finite differences, become binary circuits, e.g. an addition network. We were able to compute ground and excited states together with their energies for platelet dimensions between strong and weak confinement with a resolution (up to 2048 grid points per dimension) infeasible to implement without tensor networks. For illustration, eigenenergies, oscillator strengths, and various wavefunction projections were calculated.

Keywords: Tensor Networks; Electron-Hole Complexes; Nanoplatelets