Magnetization Dynamics and Peierls Instability in Topological Josephson Structures

Abstract

We study a long topological Josephson junction with a ferromagnetic strip between two superconductors. The low-energy theory exhibits a non-local in time and space interaction between chiral Majorana fermions, mediated by the magnonic excitations in the ferromagnet. While short ranged interactions turn out to be irrelevant by power counting, we show that sufficiently strong and long-ranged interactions may induce a ${\mathbb{Z}}_2$-symmetry breaking. This spontaneous breaking leads to a tilting of the magnetization perpendicular to the Majorana propagation direction and the opening of a fermionic gap (Majorana mass). It is analogous to the Peierls instability in the commensurate Fröhlich model and reflects the nontrivial interplay between Majorana modes and magnetization dynamics. Within a Gaussian fluctuation analysis, we estimate critical values for the temporal and spatial non-locality of the interaction, beyond which the symmetry breaking is stable at zero temperature -- despite the effective one-dimensionality of the model. We conclude that non-locality, i.e., the stiffness of the magnetization in space and time, stabilizes the symmetry breaking. In the stabilized regime, we expect the current-phase relation to exhibit an experimentally accessible discontinuous jump. At nonzero temperatures, as usual in the 1D Ising model, the long-range order is destroyed by solitonic excitations, which in our case carry each a Majorana zero mode. In order to estimate the correlation length, we investigate the solitons within a self-consistent mean-field approach.

arXiv comment10 pages, 6 figures

References in corpus (21)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• New directions in the pursuit of Majorana fermions in solid state systems
• Bosonization and Strongly Correlated Systems
• Probing Neutral Majorana Fermion Edge Modes with Charge Transport
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Magnetic moment manipulation by a Josephson current
• Phase Diagram of the Interacting Majorana Chain Model
• Observing Majorana bound states of Josephson vortices in topological superconductors
• Magnetoelectrics in Disordered Topological Insulator Josephson Junctions
• Josephson Junction through a Disordered Topological Insulator with Helical Magnetization
• Anomalous Supercurrent from Majorana States in Topological Insulator Josephson Junctions
• Microscopic theory of the pseudogap and Peierls transition in quasi-one-dimensional materials
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• A topological Josephson junction platform for creating, manipulating, and braiding Majorana bound states
• Electrical control of magnetization in S/F/S junctions on a 3D topological insulator
• Short-distance breakdown of the Higgs mechanism and the robustness of the BCS theory for charged superconductors
• Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
• Vortex spin-valve on a topological insulator
• Current--phase relation in a topological Josephson junction: Andreev bands vs. scattering states

Cited by in corpus (3)

• Berezinskii-Kosterlitz-Thouless transitions in a topological superconductor-ferromagnet-superconductor junction
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Emergence of multiple zero modes bound to vortices in extended topological Josephson junctions