The field of topological states of matter is right now a well stablished area of research in several areas of Physics[1]. These systems were initially identified as insulators, as the quantized nature of their topological invariant was intimately tied to their insulating character[2]. From some years, the geometrical notions associated to topology in momentum space also jumped to metallic systems. There, the quantized value of some topological markers is traded for the possibility of finding fingerprints of this geometry in dissipative quantities, as magnetoconductivity or non linear optical responses[3]. In this seminar I will give an account of these facts, and how it is possible to give to this phenomenon a name that high energy physicists love a lot: quantum anomalies[4], explaining in terms of these topological ideas that condensed matter physicists are now familiar with[5].
1.X-L- Qi and S-C. Zhang ”Topological insulators and superconductors”. Rev. Mod. Phys. 83, 1057 (2011).
2.R. Resta “Electron Localization in the Quantum Hall Regime” Phys. Rev. Lett. 95, 196805 (2005)
3.N. P. Armitage, E. J. Mele, A. Vishwanath “Weyl and Dirac semimetals in three dimensional solids” Rev. Mod. Phys. 90, 015001 (2018)
4.K. Landsteiner. “Notes on Anomaly related Transport” Acta Phys. Pol. B 2617 (2016)
5. A. Cortijo. “Linear magnetochiral effect in Weyl semimetals”. Phys. Rev. B 94, 241105R (2016). J. D. Hannukainen, Y. Ferreiros, A. Cortijo, J. H. Bardarson. ”Axial anomaly generation by domain wall motion in Weyl semimetals”. Phys. Rev. B 102, 241401R (2020)
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