Strongly interacting Majorana fermions

Abstract

Interesting phases of quantum matter often arise when the constituent particles -- electrons in solids -- interact strongly. Such strongly interacting systems are however quite rare and occur only in extreme environments of low spatial dimension, low temperatures or intense magnetic fields. Here we introduce a new system in which the fundamental electrons interact only weakly but the low energy effective theory is described by strongly interacting Majorana fermions. The system consists of an Abrikosov vortex lattice in the surface of a strong topological insulator and is accessible experimentally using presently available technology. The simplest interactions between the Majorana degrees of freedom exhibit an unusual nonlocal structure that involves four distinct Majorana sites. We formulate simple lattice models with this type of interaction and find exact solutions in certain physically relevant one- and two-dimensional geometries. In other cases we show how our construction allows for the experimental realization of interesting spin models previously only theoretically contemplated.

16 pages, 5 figures. The third version has been accepted for publication in Physical Review B

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Cited by in corpus (60)

• Classification of topological quantum matter with symmetries
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Towards realistic implementations of a Majorana surface code
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Roadmap to Majorana surface codes
• Phase Diagram of the Interacting Majorana Chain Model
• Majorana Fermion Surface Code for Universal Quantum Computation
• Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
• Scalable Majorana vortex modes in iron-based superconductors
• All Majorana Models with Translation Symmetry are Supersymmetric
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Statistical translation invariance protects a topological insulator from interactions
• Majorana bound states in semiconducting nanostructures
• Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal
• Electronic structure of topological superconductors in the presence of a vortex lattice
• Interacting Majorana Fermions
• Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Majorana-Hubbard model on the square lattice
• Physical Implementation of a Majorana Fermion Surface Code for Fault-Tolerant Quantum Computation
• Odd frequency pairing of interacting Majorana fermions
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Majorana-Hubbard model on the honeycomb lattice
• Emergent vortex Majorana zero mode in iron-based superconductors
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Interaction-enabled topological phases in topological insulator-superconductor heterostructures
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice
• Phase diagrams of Majorana-Hubbard ladders
• Size Constraints on Majorana Beamsplitter Interferometer: Majorana Coupling and Surface-Bulk Scattering
• Topological Larkin-Ovchinnikov phase and Majorana zero mode chain in bilayer superconducting topological insulator films
• Necessary and sufficient conditions for flat bands in $M$-dimensional $N$-band lattices with complex-valued nearest-neighbour hopping
• Majorana bound states in vortex lattices on iron-based superconductors
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Spontaneous vortex-antivortex lattice and Majorana fermions in rhombohedral graphene
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Searching for Majorana quasiparticles at vortex cores in iron-based superconductors
• Supersymmetry in an interacting Majorana model on the kagome lattice
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Practical new platform for interaction-enabled topological phases
• Observation and characterization of the zero energy conductance peak in the vortex core state of FeTe${}_{0.55}$Se${}_{0.45}$
• Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
• Specific heat of 2D interacting Majorana fermions from holography
• Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure
• Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairings
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Complete zero-energy flat bands of surface states in fully gapped chiral noncentrosymmetric superconductors
• Topological Josephson junction in transverse magnetic field
• Lowest energy states of an $O(N)$ fermionic chain
• Exactly solvable Majorana-Anderson impurity models
• Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus
• Manipulation of Majorana wave packets at surfaces of nodal noncentrosymmetric superconductors
• A proposal to extract and enhance four-Majorana interactions in hybrid nanowires