Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
arXiv:2408.16499 · doi:10.1103/PhysRevB.111.014501
Abstract
Competition between magnetism and superconductivity can lead to unconventional and topological superconductivity. However, the experimental confirmation of the presence of Majorana edge states and unconventional pairing currently poses a major challenge. Here we consider a two-dimensional lattice model for a superconductor with spin-orbit coupling and exchange coupling to randomly distributed magnetic impurities. Depending on parameters of the model, this system may display topologically trivial or nontrivial edge states. We map out the phase diagram by computing the Bott index, a topological invariant defined in real space. We then use machine learning (ML) algorithms to predict the Bott index from the local density of states (LDOS) at zero energy, obtaining high-accuracy results. We also train ML models to predict the amplitude of odd-frequency pairing in the anomalous Green's function at zero energy. Once the ML models are trained using the LDOS, which is experimentally accessible via scanning tunneling spectroscopy, our method could be applied to predict the number of Majorana edge states and to estimate the magnitude of odd-frequency pairing in real materials.
11 pages, 9 figures
References in corpus (22)
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- Learning phase transitions by confusion
- Provably efficient machine learning for quantum many-body problems
- Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
- Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
- Evidence of topological Shiba bands in artificial spin chains on superconductors
- Theory of Majorana zero modes in unconventional superconductors
- Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
- Non-Majorana modes in diluted spin chains proximitized to a superconductor
- Improved machine learning algorithm for predicting ground state properties
- Identifying Topological Phase Transitions in Experiments Using Manifold Learning
- Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
- Structural and electronic properties of realistic two-dimensional amorphous topological insulators
- Odd-frequency Cooper pair amplitude around a vortex core in a chiral p-wave superconductor in the quantum limit
- Machine Learning Microscopic Form of Nematic Order in twisted double-bilayer graphene
- A supervised learning algorithm for interacting topological insulators based on local curvature
- Odd-frequency superconductivity in dilute magnetic superconductors
- Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
- An odd-frequency Cooper pair around a magnetic impurity
- Deep Learning Hamiltonians from Disordered Image Data in Quantum Materials
- Renormalization-group-inspired neural networks for computing topological invariants
- Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder