Speaker: Prof. Kartiek Agarwal

Title: Majorana Zero Modes in Finite Superconductors

Host: Chunhui Du

Abstract: Majorana Zero Modes (MZMs) are non-Abelian excitations central to topological quantum computing, offering the tantalizing prospect of quantum hardware that is inherently robust to noise. In this talk, I will explore how MZMs can emerge in finite topological superconductors, where the usual assumption of U(1) symmetry breaking—underlying their mean-field description—no longer holds. I will present evidence for MZMs in two classes of number-conserving one-dimensional models: one with long-range interactions and one without, using numerical and analytical arguments. We show how it is possible to construct both Cooper pair and MZM operators in this setting, and how these can be extracted from numerical simulation or experiment solely from number-conserving correlators. I will also discuss how hallmark features such as single-particle edge tunneling and robustness to certain perturbations persist in this setting, while highlighting new challenges to conventional wisdom on the topological robustness of MZM braiding.