[Spin d’un monopole magnétique et réponse de Hall quantique dans des modèles sur réseau topologiques via des invariants locaux et la lumière]
Here, we elaborate on and develop the geometrical approach introduced in Le Hur, Phys. Rep. 1104 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum phase transitions. We introduce an effective magnetic moment for a monopole when applying an additional source field along $z$-direction which also mediates the quantum phase transition. We present its relation with the transverse pumped quantum Hall current. The magnetic susceptibility can be introduced as a measure of the topological invariant i.e. it remains quantized within the topological phase until the transition. We show the relation with two-dimensional topological lattice models such as a honeycomb Haldane model in real space. We develop the theory and present a numerical analysis between local invariants in momentum space introduced from Dirac points, a real space correspondence and the responses to circularly polarized light. We develop the formalism for coupled-planes materials including the possibility of quantum spin Hall effect and address a relation between the Ramanujan infinite alternating series and an interface in real space with a topological number one-half.
Nous élaborons et développons une approche géométrique introduite dans Le Hur, Phys. Rep. 1104 (2025) unifiant le monopole magnétique dû à l’application d’un champ (magnétique) radial, la physique quantique et les modèles sur réseau topologiques en présence de transitions de phase quantiques. Nous introduisons le moment magnétique pour le monopole en réponse à l’application d’un champ magnétique additionnel le long de la direction $z$, qui induit aussi la transition de phase quantique topologique. Nous présentons une correspondance avec le courant de Hall quantique. La susceptibilité magnétique associée peut ainsi être introduite comme une mesure de l’invariant topologique qui reste en effet quantifié dans la phase topologique jusqu’à la transition. Nous montrons la relation avec le modèle de Haldane sur le réseau en nid d’abeille hexagonal. Nous développons la théorie et présentons une analyse numérique des invariants topologiques locaux introduits aux points de Dirac dans l’espace réciproque, une correspondence dans l’espace réel, et étudions la réponse à la lumière polarisée circulaire. Nous développons le formalisme pour des matériaux en forme de planches incluant la possibilité d’un effet Hall quantique de spin et adressons une relation entre la série infinie alternée de Ramanujan et une interface topologique dans l’espace réel avec un nombre topologique un demi.
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Mots-clés : Système topologique, Géométrie, Lumière et Mathematique, Réponses quantifiées, Physique quantique topologique, Phase de Berry, Effet Hall quantique anormal et Effet Hall de spin
Karyn Le Hur 1 ; Andrea Baldanza 2
CC-BY 4.0
Karyn Le Hur; Andrea Baldanza. Spin response of a magnetic monopole and quantum Hall response in topological lattice models through local invariants and light. Comptes Rendus. Physique, Volume 27 (2026), pp. 323-351. doi: 10.5802/crphys.287
@article{CRPHYS_2026__27_G1_323_0,
author = {Karyn Le Hur and Andrea Baldanza},
title = {Spin response of a magnetic monopole and quantum {Hall} response in topological lattice models through local invariants and light},
journal = {Comptes Rendus. Physique},
pages = {323--351},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {27},
doi = {10.5802/crphys.287},
language = {en},
}
TY - JOUR AU - Karyn Le Hur AU - Andrea Baldanza TI - Spin response of a magnetic monopole and quantum Hall response in topological lattice models through local invariants and light JO - Comptes Rendus. Physique PY - 2026 SP - 323 EP - 351 VL - 27 PB - Académie des sciences, Paris DO - 10.5802/crphys.287 LA - en ID - CRPHYS_2026__27_G1_323_0 ER -
%0 Journal Article %A Karyn Le Hur %A Andrea Baldanza %T Spin response of a magnetic monopole and quantum Hall response in topological lattice models through local invariants and light %J Comptes Rendus. Physique %D 2026 %P 323-351 %V 27 %I Académie des sciences, Paris %R 10.5802/crphys.287 %G en %F CRPHYS_2026__27_G1_323_0
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