Speaker
Description
We present a versatile framework for constructing effective models of superconducting (SC) heterostructures described by the generalized SC Anderson Impurity Model (SC-AIM) with multiple impurities and leads. Our method, Chain Expansion (ChE), maps superconducting leads onto finite one-dimensional chains, enabling efficient simulations while retaining essential physical properties. The mapping can be tailored to optimally capture either low-energy physics or the full-bandwidth tunneling self-energy.
We derive simple analytical expressions to generate chains suited for different computational tasks, including ground state analysis and real-time evolution. Benchmarking against Numerical Renormalization Group (NRG) results, we demonstrate that ChE-based models exhibit excellent agreement with full SC-AIM solutions across a broad parameter space—even when using short chains amenable to Exact Diagonalization (ED). Accuracy systematically improves with chain length, and longer chains remain tractable due to the method’s one-dimensional structure, which is compatible with Density Matrix Renormalization Group (DMRG) techniques. Time dynamics computed using ChE align well with non-equilibrium Green’s function approaches.
After validating ChE on benchmark systems, we explore complex setups involving multiple quantum dots in serial and parallel configurations. We analyze their tunability, intricate phase diagrams, and the role of parity in shaping Andreev bound states (ABS) and supercurrent behavior.
