For a detailed discussion of the phase diagram of this model we refer the reader to refs 16, 56. Current measurements show a strong angular dependence25, but the direct relation to the chiral anomaly is subtle26. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Note this assumes the intensity I should remain constant throughout the sample, so light absorption should be small.
Burkov, A. Phys. The transfer of carriers at the surface of crystallites is assumed to be hindered by the presence of some unspecified layer with different properties, thus cancellation of consecutive Dember voltages is being prevented. This is much larger than the reported CPGE current of 10–100 pA for a topological insulator thin film32, and thus its measurement is experimentally feasible. The dashed lines outline four different chemical potentials μ for which the injection current is calculated using equation (3) and shown in panel b). Phys.
Nature Communications Phys.
The attenuation constant is expressed in terms of the dielectric function as, which is related to conductivity by . X 5, 031023 (2015). It can also describe materials where the band edge takes the form of a 3D Rashba-like Hamiltonian43 . There are several situations in which APE can arise. and JavaScript. Lett. Soluyanov, A. B 85, 241101 (2012). 57, The j1 term describes the shift current in the case of linearly polarized light. 1 English. We also note that the quantized value of the CPGE response is independent of any tilting of the nodes as long as they remain of type I, but the frequency window to observe it will depend on the tilt parameter52. A. In all plots μ coincides with a Weyl node; other choices behave qualitatively as described in Fig. The CPGE injection current is defined as the second order response. For this case, The existence of an extra band now modifies the sum rules to, Using that with the quantization will be preserved if for every direction a.
Okada, K. N. et al. Mater. Active experimental research on optical orientation in semiconductors performed in the Ioffe Institute attracted Pikus's attention and resulted in the Bir-Aronov-Pikus mechanism of spin relaxation and prediction of optical alignment of excitons. The argument and the evidence were further strengthened by Claude Pouillet in 1827 and 1838. The dashed vertical line in b corresponds to the frequency above which additional transitions, denoted by a solid vertical line in a, that preclude quantization are allowed. 2a) shows the band structure for representative parameters as a function of the momentum along separating the Weyl nodes (kz). Phys. For isotropic Weyl fermions (that is, linear dispersion with isotropic Fermi velocity and no tilting), measuring only one component of CPGE already suffices since βxx=βyy=βzz=iβ0/3. Nat. After the graduation, he became a student in the physical-engineering department of Leningrad (currently St. Petersburg) Polytechnic University in the fall of 1940. Here we find that in a class of Weyl semimetals (for example, SrSi2) and three-dimensional Rashba materials (for example, doped Te) without inversion and mirror symmetries, the injection contribution to the CPGE trace is effectively quantized in terms of the fundamental constants e, h, c and with no material-dependent parameters. A weyl fermion semimetal with surface fermi arcs in the transition metal monopnictide TaAs class. 47, 250 (1988). Rev. In conclusion, we have shown that the trace of the circular photogalvanic tensor is quantized for Weyl semimetals and 3D Rashba materials that break inversion and all mirror symmetries. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. Absorption is thus negligible for typical thin film dimensions. A. Rogachev, Circular photogalvanic effect in optically active crystals, Solid State Communications. Kourtis, S. Bulk spectroscopic measurement of the topological charge of weyl nodes with resonant x rays.
The occupation of the Floquet bands is determined by coupling to a heat bath which we assume to have the Fermi energy between the valence and conduction bands. 115, 216806 (2015). Contents. McIver, J. W., Hsieh, D., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Control over topological insulator photocurrents with light polarization. The main finding of this paper is that in a Weyl semimetal where nodes of opposite chirality lie at different energies, the circular photogalvanic effect (CPGE) becomes a truly quantized response that depends only on fundamental constants and the monopole charge of a Weyl node. This is the case of all non-trivial cases in Fig. & Pesin, D. A. Chiral magnetic effect and natural optical activity in metals with or without weyl points. For an interband effect like the CPGE, when 2|ɛL|<ħω<2|ɛR|, one Weyl node contributes exactly with the monopole charge, while the other has zero contribution due to Pauli blocking. The oblique deposition can lead to several structure asymmetries in the films.
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