Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

Abstract

A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the continuum (BIC) for topological configurations of the scalar field. Fermion-soliton duality mappings are uncovered for the bound state spectrum, which interpolates the weak and strong coupling sectors of the model and give rise to novel Thirring-like and multi-frequency sine-Gordon models, respectively. The non-perturbative effects of the back-reaction of the fermion bound states on the kink are studied and it is shown that the zero mode would catalyze the emergence of a new kink with lower topological charge and greater slope at the center, in the strong coupling limit of the model. For special topological charges and certain relative phases of the fermion components the kinks can host Majorana zero modes. The Noether, topological and a novel nonlocal charge densities satisfy a formula of the Atiyah-Patodi-Singer-type. Our results may find applications in several branches of non-linear physics, such as confinement in QCD${}_2$, braneworld models, high $T_c$ superconductivity and topological quantum computation. We back up our results with numerical simulations for continuous families of topological sectors.

arXiv comment68 pages, 25 figures, LaTex. New sections present a formula of the Atiyah-Patodi-Singer-type, for non-zero and zero modes. Figs with numerical kinks and bound states added

References in corpus (44)

• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Spin and Majorana polarization in topological superconducting wires
• Fermion zero-modes on brane-worlds
• "Embedded solitons": solitary waves in resonance with the linear spectrum
• Criticality in self-dual sine-Gordon models
• Fermions on Thick Branes in the Background of Sine-Gordon Kinks
• Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric Solitons
• Critical properties of the double-frequency sine-Gordon model with applications
• The Relativistic Levinson Theorem in Two Dimensions
• Nonperturbative study of the two-frequency sine-Gordon model
• Vortices and chirality in multi-band superconductors
• Affine Toda Systems Coupled to Matter Fields
• Duality and bosonization of (2+1)d Majorana fermions
• Stable embedded solitons
• Remarks on bell-shaped lumps: stability and fermionic modes
• Heavy Fermion Stabilization of Solitons in 1+1 Dimensions
• The concept of quasi-integrability: a concrete example
• Fermions on Colliding Branes
• Fermions on one or fewer Kinks
• Fermions on the kink revisited
• Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models
• Example of a self-consistent solution for a fermion on domain wall
• The Faddeev-Jackiw Approach and the Conformal Affine sl(2) Toda Model Coupled to Matter Field
• Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion
• A nonperturbative study of phase transitions in the multi-frequency sine-Gordon model
• Coupled fermion-kink system in Jackiw-Rebbi model
• Noether and topological currents equivalence and soliton/particle correspondence in affine $sl(2{)}^{(1)}$ Toda theory coupled to matter
• Fully Localized Two-dimensional Embedded Solitons
• Quantum Kinks: Solitons at Strong Coupling
• Stable branches of a solution for a fermion on domain wall
• Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions
• Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
• Majorana zero modes and their bosonization
• Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality
• Casimir Energy for a Coupled Fermion-Soliton System
• Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions
• Affine Toda model coupled to matter and the string tension in QCD${}_2$
• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences
• Exact Solutions of a Fermion-Soliton System in Two Dimensions
• The fermion spectrum in braneworld collisions
• Quantum Field Theory Description of Tunneling in the Integer Quantum Hall Effect
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Relativistic dissipatons in integrable nonlinear Majorana type spinor model