Nonlinear effects in topological materials

doi:10.1007/s12200-020-1088-x

Front. Optoelectron.

2021, Vol. 14

Issue (1) : 99-109 https://doi.org/10.1007/s12200-020-1088-x

REVIEW ARTICLE

Nonlinear effects in topological materials

Jack W. ZUBER, Chao ZHANG(

)

School of Physics, University of Wollongong, New South Wales 2522, Australia

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Abstract

Materials, where charge carriers have a linear energy dispersion, usually exhibit a strong nonlinear optical response in the absence of disorder scattering. This nonlinear response is particularly interesting in the terahertz frequency region. We present a theoretical and numerical investigation of charge transport and nonlinear effects, such as the high harmonic generation in topological materials including Weyl semimetals (WSMs) and a-T₃ systems. The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix. We show that the nonlinear response is strongly dependent on temperature and topological parameters, such as the Weyl point (WP) separation b and Berry phase $φ B$ . A ﬁnite spectral gap opening can further modify the nonlinear effects. Under certain parameters, universal behaviors of both the linear and nonlinear response can be observed. Coupled with experimentally accessible critical ﬁeld values of $104 − 105 V/m$ , our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.

Keywords terahertz nonlinear effects topological materials Weyl semimetals (WSMs) a-T₃ systems')" href="#">a-T₃ systems

Corresponding Author(s): Chao ZHANG

Just Accepted Date: 20 October 2020 Online First Date: 09 December 2020 Issue Date: 19 April 2021

Cite this article:

Jack W. ZUBER,Chao ZHANG. Nonlinear effects in topological materials[J]. Front. Optoelectron., 2021, 14(1): 99-109.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-020-1088-x
https://academic.hep.com.cn/foe/EN/Y2021/V14/I1/99

Fig.1 Dispersion relation of Eq. (2) with: (a) v_F?|b|?>? D: WSM phase, (b) v_F?|b|?=? D: MDSM phase, and (c) v_F?|b|?<? D: GSM phase. The arrows in Fig. 1(a) show two types of intraband current contributions for an electric ﬁeld parallel to b

Fig.2 Dispersion relation for the a-T₃ lattice. The lines on the right show two interband transitions, E_-?→? E₀?→? E₊ and E₀?→? E₊ as well as one intraband transition E₊?→? E₊

Fig.3 Band gap dependence of the first- and third-order conductivities of WSM with

μ

?=?80?meV, T?=?300?K, and

ω

?=?1?THz for the field directed parallel to b

Fig.4 Temperature dependence of the ﬁrst- and third-order conductivities of WSM with µ?=?80?meV, D?=?53?meV, and w?=?1?THz for the ﬁeld directed parallel to b?=?

b x x^

?=?0.8?×?10⁸

ℏ x^

Fig.5 Band gap dependence of the anisotropy of (a) ﬁrst-order conductivities, (b) third-order conductivities, and (c) critical ﬁelds in WSM with µ?=?80?meV, T?=?300?K, and w?=?1?THz for a ﬁeld directed parallel to b?=?

b x x^

?=?0.8?×?10⁸?

ℏ x^

Fig.6 Temperature dependence of the anisotropy of (a) ﬁrst-order conductivities, (b) third-order conductivities, and (c) critical ﬁelds in WSM with µ?=?80?meV, D?=?53?meV, and w?=?1?THz

Fig.7 First-order conductivity of the

α - T 3

lattice with (a) a?=?0, (b) a?=?0.5, and (c) a?=?1. In each graph, a?=?0.0142?nm, t?=?3?eV, and µ?=?1?meV are the original values. The µ?→?∞ values are 100?meV (Fig. 7(a)) and 20?meV (Figs. 7(b) and 7(c)); the T>?0 value is 4?K in each graph, and the D>?0 values are 0.5?meV ((Fig. 7(a)), 1?meV (Fig. 7(b)), and 2?meV (Fig. 7(c))

Fig.8 Third-order conductivity in the

α - T 3

lattice for different Berry phases with a?=?0.0142?nm,

τ 1

?=?

τ 2

?=?3?eV, and µ?=?1?meV

Fig.9 Frequency dependence of the critical ﬁeld in the

α - T 3

lattice for different Berry phases with a?=?0.0142?nm,

τ 1

?=?

τ 2

?=?3?eV, and µ?=?1?meV

Fig.10 Berry phase dependence of the critical ﬁeld in the

α - T 3

lattice for different frequencies with a?=?0.0142?nm,

τ 1

?=?

τ 2

?=?3?eV, and µ?=?1?meV

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