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. 2016 Aug 5;7:12375. doi: 10.1038/ncomms12375

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Copyright © 2016, The Author(s)

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(a) The system studied: a spherical Bi₂Se₃ nanoparticle of radius R located at the origin is subject to an EM wave propagating along its c axis—. The collective response of the bulk states is described using the dielectric function , whereas the surface states are treated quantum mechanically. (b) The dielectric function of Bi₂Se₃ comprises two phonons at 2.0 (α) and 3.72 THz (β), as well as a contribution from bulk free charge carriers (f) at low frequencies²⁵. (c) In the nanoparticle, the surface Dirac cone consists of discrete levels symmetrically placed with respect to the Dirac point (E=0)¹⁷. They have constant energy spacing A/R where A=3.0 eV·Å. An electron in a surface state couples to other states under the influence of light producing a time-dependent surface charge density. (d) The absorption cross-section of a bare nanoparticle (δ_R=0, blue dashed line) is dictated by the dielectric function of the material. It is modified when electrons occupy delocalized topological surface states (δ_R≠0, red solid line). The resultant spectrum contains an additional mode (SToP) and a zero in absorption (marked with an arrow).

Inline graphic — (a) The system studied: a spherical Bi₂Se₃ nanoparticle of radius R located at the origin is subject to an EM wave propagating along its c axis—. The collective response of the bulk states is described using the dielectric function , whereas the surface states are treated quantum mechanically. (b) The dielectric function of Bi₂Se₃ comprises two phonons at 2.0 (α) and 3.72 THz (β), as well as a contribution from bulk free charge carriers (f) at low frequencies²⁵. (c) In the nanoparticle, the surface Dirac cone consists of discrete levels symmetrically placed with respect to the Dirac point (E=0)¹⁷. They have constant energy spacing A/R where A=3.0 eV·Å. An electron in a surface state couples to other states under the influence of light producing a time-dependent surface charge density. (d) The absorption cross-section of a bare nanoparticle (δ_R=0, blue dashed line) is dictated by the dielectric function of the material. It is modified when electrons occupy delocalized topological surface states (δ_R≠0, red solid line). The resultant spectrum contains an additional mode (SToP) and a zero in absorption (marked with an arrow).