N. Dombrowski, F. Germinet, G. D. Raikov, Quantization of edge currents along magnetic barriers and magnetic guides, Ann. H. Poincaré 12, (2011), 1169 - 1197.

Cited by:

• 1. N. Raymond, Une excursion semi-classique dans l’univers des guides d’ondes, Gaz. Math., No. 131 (2012), 5-15.

  2. A. Taarabt, Localisation dynamique et égalité des conductances de Hall pour des opérateurs de Schrödinger magnétiques aléatoires, Thèse de Doctorat, Université de Cergy-Pontoise, 2013.

  3. N. Raymond, Breaking a magnetic zero locus: Asymptotic analysis, Math. Models Methods Appl. Sci. 24 (2014), 2785–2817.

  4. N. Raymond, Geometry and bound states of the magnetic Schrödinger operator, Mémoire d’Habilatation à Diriger les Recherches, Université de Rennes 1, 2014.

  5. M. Kotani, H. Schulz-Baldes, C. Villegas-Blas, Quantization of interface currents, J. Math. Phys. 55 (2014), 121901, 9 pp.

  6. P. D. Hislop, E. Soccorsi, Edge states induced by Iwatsuka Hamiltonians with positive magnetic fields, J. Math. Anal. Appl. 422 (2015), 594–624.

  7. P. Exner, H. Kovarık, Quantum Waveguides, Theoretical and Mathematical Physics, Springer, Berlin-New York, 2015.

  8. H. D. Cornean, R. Purice, Spectral edge regularity of magnetic Hamiltonians, J. London Math. Soc. 92 (2015), 89-104.

  9. P. D. Hislop, N. Popoff, N. Raymond, M. P. Sundqvist, Band functions in the presence of magnetic steps, Math. Models Methods Appl. Sci. 26 (2016), 161-184.

  10. P. Miranda, Eigenvalue asymptotics for a Schrödinger operator with nonconstant magnetic field along one direction, Ann. H. Poincaré, 17 (2016), 1713-1736.

  11. M. Tusek, On an extension of the Iwatsuka model, J. Phys. A: Math. Theor. 49 (2016), 365205, 13pp.

  12. N. Raymond, Bound States of the Magnetic Schrödinger Operator, EMS Tracts in Mathematics 27, EMS, Z ̈urich, 2017.

  13. P. Miranda, N. Popoff, Spectrum of the Iwatsuka Hamiltonian at thresholds, J. Math. Anal. Appl. 460 (2018), 516-545. 

  14. P. Exner, T. Kalvoda, and M. Tušek, A geometric Iwatsuka type effect in quantum layers, Journal of Mathematical Physics 59 (2018), 042105. 

  15. N. Popoff, Magnetic fields and boundary conditions in spectral and asymptotic analysis, Mémoire d’Habilatation à Diriger les Recherches, Université de Bordeaux, 2019. 

  16. J. Asch, O. Bourget, A. Joye, Chirality induced interface currents in the Chalker-Goddington model, J. Spectral Theory 9 (2019), 1405-1429.  

  17. Esteban Andrés Gutierrez Cordero, Quantization of Edge Currents along Magnetic Interfaces : A K-Theory Approach, Master thesis, Pontificia Universidad Católica de Chile, 2020.

  18. Giuseppe De Nittis, Esteban Gutiérrez, Quantization of edge currents along magnetic interfaces: A K-theory approach, Acta Applicandae Mathematicae 175 (2021), article number: 6.

  19. Tom Stoiber, Index theory and bulk-boundary correspondence of topological insulators and semimetals, Ph.D. Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2023. 

  20. Guillaume Bal, Topological charge conservation for continuous insulators, J. Math. Phys. 64 (2023), article number: 031508.

  21. Arianna Giunti, Juan J. L. Velázquez, Edge states for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve, Ann. Henri Poincaré 24 (2023), 73–105. 

  22. D.P. Ojito, C*-Algebraic methods for transport phenomena, Ph.D. thesis, Pontificia Universidad Católica de Chile, 2023.

  23. Mourad Choulli, Nour Kerraoui, Eric Soccorsi, Determining an Iwatsuka Hamiltonian through quantum velocity measurement, Preprint arXiv:2305.03320, 2023.

  24. Solomon Quinn, Asymmetric transport in continuous topological insulators, Ph.D. thesis, University of Chicago, 2023. 

  25. Abhijeet Alase, Emilio Cobanera, Gerardo Ortiz, Lorenza Viola, Wiener–Hopf factorization approach to a bulk-boundary correspondence and stability conditions for topological zero-energy modes, Annals of Physics 458 (2023), part 3, article 169457, 47 pp.

  26. Danilo Polo Ojito, Interface currents and corner states in magnetic quarter-plane systems, Advances in Theoretical and Mathematical Physics, 27 (2023), no. 6, 1813 – 1855.

  27. Nour Kerraoui, Analyse mathématique de modèles quantiques: identification du potentiel d’Iwatsuka et asymptotique spectrale de l’opérateur de Dirac, Thèse de

Doctorat, Aix-Marseille Université, 2023.

• 28. S. Chen, New critical point theorem and infinitely many small-magnitude solutions of a nonlinear Iwatsuka model, J. Math. Anal. Appl. 529 (2024), no.1, 127605. 

  29. Guillaume Bal, Semiclassical propagation along curved domain walls, SIAM Journal on Multiscale Modeling and Simulation, 22 (2024), no.1, 66-105.

  30. Solomon Quinn, Guillaume Bal, Asymmetric transport for magnetic Dirac equations, Pure and Applied Analysis 6 (2024), no. 2, 353–377.

  31. Y. Kordyukov, Exponential localization for eigensections of the Bochner–Schrödinger operator. Russ. J. Math. Phys. 31 (2024), 461–476. https://doi.org/10.1134/S1061920824030099 .

  32. Jiayu Qiu, Hai Zhang, Generalized bulk-interface correspondence for non-quantized spin transport, Preprint arXiv:2505.16331, 2025.

  33. Johannes Kellendonk, Tom Stoiber, The role of self-adjoint extensions in the bulk-edge, Preprint arXiv:2510.01368, 2025.

  34. Habib Ammari, Jiayu Qiu, Alexander Uhlmann, Topological interface modes in aperiodic subwavelength resonator chains, Preprint arXiv:2511.18363, 2025.

  35. Giuseppe De Nittis, Jaime Gomez, Danilo Polo Ojito, On the K-theory of magnetic algebras: Iwatsuka case, Mathematische Zeitschrift 312 (2026), article number 56. 

  36.  Guillaume Bal, Continuous Topological Insulators Classification and Bulk-Edge Correspondence. In: Alpay, D., Colombo, F., Sabadini, I. (eds) Operator Theory. Springer, Basel, first online, 2026. https://doi.org/10.1007/978-3-0348-0692-3_76-1