## Properties of the spin-momentum locked state

By: Mauro M. Doria

From: Instituto de Física - Universidade Federal do Rio de Janeiro

At: Online - Zoom (https://videoconf-colibri.zoom.us/j/89309150748)

[2021-10-26]

Recently there has been growing evidence that spin is locked perpendicularly to the momentum (spin momentum locking) in several condensed matter systems such as, topological insulators [1, 2], evanescent electromagnetic waves [3, 4] and high-temperature cuprate superconductors [5]. The development of angle-resolved photoemission spectroscopy able to also determine the spin (SARPES) has been instrumental to detect spin-momentum locking in such systems [5]. In this seminar I show that the existence of a local magnetic field is a direct consequence of the spin-momentum locking condition. Although residual, this local magnetic field is important because it brings the topological stability that transforms particles into quasi-particles. The present approach shows that the Rashba term is already contained in the SchrÃ¶dinger kinetic energy and a Dirac linear spectrum can be obtained without invoking a Dirac equation for the particles. These are consequences of the so-called three-term decomposition theorem, also known as the Lichnerowicz-WeitzenbÃ¶ck decomposition [6], which states that the SchrÃ¶dinger kinetic energy is the sum of the square of the spin-momentum interaction, plus the curvature interaction, and the Rashba term or spin-orbit interaction [7, 8].

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[3] Mechelen T V and Jacob Z, Optica 2016 3 118.

[4] Triolo C, Cacciola A, Patan`e S, Saija R, Savasta S, and Nori F, ACS Photonics 2017 4 2242.

[5] Gotlieb K, Lin C-Y, Serbyn M, Zhang W, Smallwood C L, Jozwiak C, Eisaki H, Hussain Z, Vishwanath A, and Lanzara A, Science 2018 362 1271.

[6] Vargas-Paredes A A, Doria M M, and Neto J A H, J. of Math. Phys. 2013 54 013101.

[7] Doria M M and Perali A, 2017 Europhys. Lett. 119 21001.

[8] Doria M M, 2019 Euro. Phys. J. B 92 64.

**Project**UIDB/00618/2020