Session Y44: Exotic Majorana Physics and Beyond

Solid state realizations of Sachdev-Ye-Kitaev models

An intriguing connection, pointed out by Kitaev in 2015, exists between a simple model of Majorana fermions with random all-to-all interactions – the Sachdev-Ye-Kitaev (SYK) model – and the horizons of extremal black holes in two-dimensional anti-de Sitter space. This connection furnishes a rare example of holographic duality between a solvable quantum-mechanical model and Einstein gravity. It also opens up a possibility to study quantum black holes, realized holographically in a quantum mechanical model, in a tabletop experiment. In this talk I will review some of these developments and describe the recent efforts to bring the family of SYK models closer to experimental reality. The proposed experimental realizations employ both complex and Majorana fermions in various atomic and solid state systems. These include some of the standard platforms for Majorana zero modes (proximitized quantum wires and topological insulator - superconductor interfaces) as well as electrons in the lowest Landau level in a graphene flake with an irregular boundary.   

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. I will discuss a potential solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. Random matrix theory and numerics show that this setup indeed emulates the SYK model (with certain corrections). Tunneling measurements provide an appealing first experimental test of this scenario.   

Majorana Multiplexing

TBD   

Quantum Engineering of Majorana Fermions

The experimental observation of Majorana states in topological superconductors represents a major breakthrough in realizing their applications in topological quantum computing. This has stimulated the search for new possibilities to engineer Majorana states at the nanoscale, in particular using magnetic-superconducting hybrid (MSH) structures in which islands of magnetic adatoms are placed on the surface of s-wave superconductors.

In this talk, I provide several examples for the quantum engineering of Majorana fermions in MSH systems [1,2]. First, I will report the results of a theory-experiment collaboration demonstrating the ability to tune between a topological phase exhibiting chiral Majorana edge modes and a trivial phase in Fe-Re MSH structures using interface engineering [1]. Second, I will show that one can create a topological switch in MSH systems by imprinting magnetic skyrmions, allowing one to write and delete topological phases. Similarly, it is possible to engineer chiral Majorana states of arbitrary shape through the creation of magnetic domain walls. Third, I show that it is possible to continuously tune MSH systems between 2D and 1D topological phases using atomic manipulation, and thus to change the character of the associated Majorana modes. Finally, I will demonstrate that Josephson scanning tunneling spectroscopy is a crucial tool in identifying topological phases [3].

[1] Atomic-Scale Interface Engineering of Majorana Edge Modes in a 2D Magnet-Superconductor Hybrid System, A. Palacio-Morales, E. Mascot, S. Cocklin, H. Kim, S. Rachel, D. K. Morr and R. Wiesendanger, arXiv:1809.04503
[2] Quantized charge transport in chiral Majorana edge modes, S. Rachel, E. Mascot, S. Cocklin, M. Vojta, and D.K. Morr, Phys. Rev. B 96, 195162 (2017).
[3] M. Graham and D.K. Morr, Phys. Rev. B 96, 184501 (2017)   

The Majorana-Hubbard Model

When a vortex lattice forms in a superconducting layer on a topological insulator a Majorana fermion is predicted to appear in each vortex core. Hopping and interaction terms between the Majorana fermions lead to a novel generalization of the Hubbard model. Furthermore, the hopping amplitude is predicted to vanish at a special value of the chemical potential in the topological insulator, allowing the phase diagram to be studied as a function of the ratio of interaction strength to hopping amplitude. I will present results on the interesting phase diagrams, which includes supersymmetric critical points, in both one and two dimensions.