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See detailOptical conductivity of triple point fermions
Habibi, Alireza UL; Farajollahpour, Tohid; Jafari, S A

in Journal of Physics: Condensed Matter (2021), 33

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian, which is parameterized by an angular parameter λ. We find strong λ dependence in both ... [more ▼]

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian, which is parameterized by an angular parameter λ. We find strong λ dependence in both Drude and interband optical absorption of these systems. The deviation of the T2 coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular λ = π/6 point, we find that the 'helicity' reversal optical transition matrix element is identically zero. Nevertheless, deviating from this point, the helicity reversal emerges as an absorption channel. [less ▲]

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See detailOptical properties of topological flat and dispersive bands
Habibi, Alireza UL; Musthofa, Ahmad Z.; Adibi, Elaheh et al

E-print/Working paper (2021)

We study the optical properties of topological flat and dispersive bands. Due to their topological nature, there exists an anomalous Hall response which gives rise to a transverse current without applied ... [more ▼]

We study the optical properties of topological flat and dispersive bands. Due to their topological nature, there exists an anomalous Hall response which gives rise to a transverse current without applied magnetic field. The dynamical Hall conductivity of systems with flat bands exhibits a sign change when the excitation energy is on resonance with the band gap, similar to the magnetotransport Hall conductivity profile. The sign change of the Hall conductivity is located at the frequency corresponding to the singularity of the joint density of states, i.e., the van Hove singularity (VHS). For perfectly flat bands, this VHS energy matches the band gap. On the other hand, in the case of dispersive bands, the VHS energy is located above the band gap. As a result, the two features of the Hall conductivity, i.e., the resonant feature at the band gap and the sign change at the VHS energy, become separated. This anomalous Hall response rotates the polarization of an electric field and can be detected in the reflected and transmitted waves, as Kerr and Faraday rotations, respectively, thus allowing a simple optical characterization of topological flat bands. [less ▲]

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See detailTopological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya interaction
Habibi, Alireza UL; Ghadimi, Rasoul; Jafari, S. A.

in Journal of Physics: Condensed Matter (2019), 32(1), 015604

The topological index of a system determines its edge physics. However, in situations such as strong disorder where due to level repulsion the spectral gap closes, the topological indices are not well ... [more ▼]

The topological index of a system determines its edge physics. However, in situations such as strong disorder where due to level repulsion the spectral gap closes, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined by the transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices of the ‘relative’ Hamiltonians. As a case study, we study a generalized XY model (2XY model) further augmented by a generalized Dziyaloshinskii–Moriya-like (DM) interaction parameterized by that after fermionization breaks the time-reversal invariance. The parent Hamiltonian at which belongs to the BDI class is indexed by an integer winding number while the daughter Hamiltonian which belongs to class D is specified by a Z 2 index . We show that the localization length, in addition to determining Z 2, can count the number of Majorana zero modes leftover at the boundary of the daughter Hamiltonian—which are not protected by the winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian. [less ▲]

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