Nitrides: a promising class of nonlinear optical material candidates

Abstract

Nonlinear optical (NLO) materials play a crucial role in all-solid-state lasers, as their frequency conversion effects enable the expansion of the limited and fixed frequency outputs of lasers to encompass both ultraviolet and infrared regions. Nitrides have emerged as highly promising NLO candidate materials, primarily due to their potentially large second-order NLO coefficients and extensive band gaps. In recent years, nitride NLO crystals have garnered significant interest from researchers, leading to the discovery of several NLO nitrides. This review provides a comprehensive overview of both reported and potential NLO nitrides, with a particular focus on their crystal structures, in order to gain a deeper understanding of the correlations between their structure and properties. Potential NLO nitrides are analyzed using density functional theory (DFT) as a basis. Additionally, this review addresses the existing challenges and offers insights into the prospective advancements in the field of NLO nitrides, fostering further discussion and exploration.

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1. Introduction

Nonlinear optical (NLO) crystals have garnered significant attention due to their crucial role in advancing laser science and technology.^1–7 The conversion of laser frequency can be achieved through various up- and down-conversion processes in NLO crystals, such as second-order harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), optical parametric oscillation (OPO), and optical parametric amplification (OPA).⁸ Over the past few decades, several promising deep-ultraviolet (DUV), ultraviolet-visible (UV-Vis), and infrared (IR) crystals have been discovered and extensively researched, such as KBe₂BO₃F₂ (KBBF),⁹ LiB₃O₅ (LBO),¹⁰ β-BaB₂O₄ (β-BBO),¹¹ KH₂PO₄ (KDP),¹² KTiOPO₄ (KTP),¹³ AgGaS₂(AGS),¹⁴ AgGaSe₂(AGSe)¹⁵ and ZnGeP₂(ZGP).¹⁶ In general, an outstanding NLO crystal should exhibit a comprehensive set of performance characteristics, including: (i) a strong second-order harmonic generation (SHG) response, (ii) a high laser damage threshold (LDT) inherently related to wide band gaps (E_g) of materials, (iii) a wide optical transparency range, (iv) appropriate birefringence (Δn) for achieving the phase-matching behavior, and (v) favourable physical and chemical properties.

Over the past decades, the exploration of inorganic NLO crystals in the DUV and UV-Vis regions has mainly focused on borates, carbonates, nitrates, phosphates and sulfates.^17–22 Borates have been extensively synthesized and reported as UV and DUV NLO crystals due to their remarkable structural diversity, which combines various structural motifs such as BO₃³⁻, BO₄⁵⁻, B₂O₅⁴⁻, B₃O₆³⁻ and B₃O₇⁵⁻ anionic groups, resulting in exceptional properties. Carbonates and nitrates have exhibited significant SHG responses and birefringence, attributed to their π-conjugated planar triangles. Phosphates and sulfates, on the other hand, possess broad band gaps and optical transparency, but their hyperpolarizabilities and optical anisotropy are weaker. As regarding the study of IR NLO materials, inorganic chalcogenides,²³ halides,²⁴ and pnictides^25,26 have been widely acknowledged as promising systems for IR NLO materials. Among these, chalcogenides have received the most attention due to their comprehensive NLO properties. Generally, halides exhibit excellent IR transparency and large band gaps resulting in high laser damage threshold (LDT). However, their SHG coefficients are typically much smaller compared to chalcogenides and pnictides. In contrast, pnictides tend to have larger effective nonlinear coefficients (d_eff) but smaller band gaps (E_g < 2.5 eV) when compared to chalcogenides and halides.

Nitrides are considered multifunctional materials with widespread applications in various fields, such as semiconductors, catalysis, energy storage, and spintronics.^27–29 In fact, nitrides hold great potential as a system for developing NLO crystals, owing to their several advantages: (i) a wide band gap and high thermal conductivity, which contribute to a high LDT in crystals; (ii) excellent thermal stability; (iii) broad transparency windows ranging from the UV to mid-IR region. Consequently, nitrides have garnered significant interest among researchers, and several nitrides have been investigated as NLO materials through experimental approaches and computational tools, such as Zn₂NX (X = Cl, Br), MoZn₃N₄, TiZnN₂ and AGeN₂ (A = Sr, Ba).^30–33 However, NLO nitrides with outstanding properties remain scarce, and the structure–property relationships in NLO nitrides have not been thoroughly explored. Therefore, a comprehensive study of the characteristics and structure–property correlations in NLO nitrides is urgently needed. In this work, we summarize and categorize recently reported and potential NLO nitrides into three groups based on their structural features: (i) 19 diamond-like (DL) type NLO nitrides; (ii) 19 polyhedra-stacking type NLO nitrides; and (iii) 7 other NLO nitrides with distinctive structures, the structural features of the three categories of NLO nitrides are illustrated in Fig. 1. A detailed analysis of these compounds' crystal structures, NLO properties, and structure–property correlations was provided. Furthermore, the current challenges and future directions for the development of NLO nitrides were discussed.

Fig. 1 Schematic representation of the three categories of NLO nitrides according to structural features.

2. Diamond-like type NLO nitrides

Diamond-like (DL) structures represent a rich source of non-centrosymmetric (NCS) structures found in nature. These DL compounds have garnered significant interest as potential mid-IR NLO candidates due to several key advantages: (i) their intrinsic NCS crystal structures and diverse building motifs, which are formed by MQ₄ (M = Si, Ge, Sn, Ga, In, Zn, Cd, Hg, Cu, Ag and Li; Q = S, Se, N and P) tetrahedra, (ii) their broad IR transparency range, which is attributed to the covalent M–Q bonds; and (iii) the fundamental building blocks of [MQ₄] tetrahedra in DL structures, which are consistently interconnected through an aligned arrangement.³⁴ This alignment is anticipated to lead to an additive superposition of the microscopic second-order susceptibility, thereby facilitating a strong SHG response. As a result, numerous DL metal chalcogenides and pnictides with exceptional NLO performance have been reported, such as Li₄MgGe₂S₇, HgCuPS₄, Li₂ZnGeS₄, MnSiP₂, M^II₃P_nI₃ (M^II = Zn and Cd, P_n = P and As) and Mg₂In₃Si₂P₇.^35–40 DL nitrides, when employed as NLO materials, may offer the following benefits: (i) large NLO coefficients ascribed to the parallel alignment of [MN₄] tetrahedra; (ii) wide band gaps and high thermal conductivity, which contribute to a significant LDT; and (iii) stable physical and chemical properties.

2.1. GaN and AlN

Group-III nitrides are promising materials for various technological applications, such as short-wavelength light-emitting diodes, semiconductor lasers, and optical detectors.⁴¹ The linear and nonlinear optical properties of GaN and AlN have been both theoretically and experimentally studied in the past decades.^42,43 GaN and AlN crystalized in the hexagonal crystal system with space group of P6₃mc, and the structure of AlN was shown in Fig. 2a. The [AlN₄] tetrahedra were interconnected by sharing corners and aligned along the c-axis. The experimental optical band gaps of GaN and AlN were 3.50 and 6.20 eV,^44,45 respectively, and their band gaps between valence bands and conduction bands are mainly dominated by the covalent Al–N and Ga–N bands (Fig. S9a and b, ESI†). As listed in Table 1, the calculated NLO coefficients were d₃₁ = 2.42, d₃₃ = −3.64 pm V⁻¹ for GaN, and d₃₁ = 0.23, d₃₃ = 0.86 pm V⁻¹ for AlN, and the calculated birefringence is 0.017 for GaN and 0.023 for AlN at 1064 nm.

Fig. 2 Crystal structure of AlN (a), LiGe₂N₃ (b), BeSiN₂ (c) and Mg₂PN₃ (f).

Table 1 The NLO data of diamond-like type Nitrides

Compounds	Space group	Band gap (eV)			NLO coefficients^a (pm V^−1)	Δn^a
		GGA^a	HSE06^a	Exp.^b		At 1064 nm	At 2050 nm
a This work. b Other work from ref. 27, 41, 42, 44, 45, 48, 49, 53.
GaN	P63mc	1.93	2.87	3.5	d 31 = 2.42, d33 = −3.64	0.017	0.015
AlN	P63mc	3.86	5.12	6.2	d 31 = 0.23, d33 = 0.86	0.023	0.022
LiSi2N3	Cmc21	5.16	6.45	6.4	d 31 = 1.01, d32 = 0.24, d33 = −0.32	0.043	0.042
LiGe2N3	Cmc21	1.45	2.57	3.9	d 31 = 4.14, d32 = 5.30, d33 = −2.60	0.071	0.069
BeSiN2	Pna21	5.22	6.53	—	d 31 = 0.74, d32 = 0.91, d33 = 0.45	0.031	0.030
MgSiN2	Pna21	4.18	5.49	4.8	d 31 = 0.52, d32 = 1.86, d33 = 0.32	0.017	0.017
MgGeN2	Pna21	2.21	3.35	3.2	d 31 = 6.05, d32 = 5.59, d33 = −12	0.032	0.033
ZnSiN2	Pna21	3.41	4.58	3.7	d 31 = −3.01, d32 = −6.05, d33 = 7.61	0.051	0.049
ZnGeN2	Pna21	2.01	3.01	3.2	d 31 = −4.82, d32 = −5.2, d33 = 8.13	0.039	0.038
Zn3MoN4	Pmn21	1.91	2.77	2.4	d 31 = 13.4, d32 = 14.57	0.098	0.088
Mg2PN3	Cmc21	3.20	4.43	5.0	d 31 = 1.99, d32 = 2.73, d33 = −2.33	0.072	0.071
Zn2PN3	Cmc21	2.83	4.00	3.7	d 31 = 4.43, d32 = 6.70, d33 = −9.03	0.003	0.003
Mg2SbN3	Cmc21	1.45	2.51	—	d 31 = 0.26, d32 = 1.50, d33 = 3.47	0.031	0.027
LiPN2	I4̄2d	3.93	5.21	—	d 14 = d36 = 0.20	0.022	0.016
CuPN2	I4̄2d	2.12	3.19	—	d 14 = d36 = −8.26	0.019	0.018
Zn2NCl	Pna21	2.25	3.31	3.21	d 31 = 5.14, d32 = 7.30, d33 = 12.89	0.065	0.062^b
Zn2NBr	Pna21	2.38	3.09	2.28	d 31 = 4.51, d32 = 6.35, d33 = 11.15	0.071	0.069^b
LiSiON	Pca21	5.48	7.03	—	d 31 = 1.33, d32 = −2.40, d33 = −0.14	0.044	0.043
Li2P2ON	Cmc21	5.21	6.82	—	d 31 = 0.18, d32 = 0.33, d33 = 0.75	0.045	0.044

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2.2. LiSi₂N₃ and LiGe₂N₃

Both LiSi₂N₃⁴⁶ and LiGe₂N₃⁴⁷ crystalized in the space group of Cmc2₁. Taking LiGe₂N₃ as an example, the [LiN₄] tetrahedra and [GeN₄] tetrahedra connected through sharing N atoms, the [LiN₄] and [GeN₄] tetrahedra in LiGe₂N₃ are perfectly aligned parallel to the c-axis (Fig. 2b). However, [SiN₄] tetrahedra in LiSi₂N₃ are at an acute angle to the c-axis (Fig. S1a, ESI†). As shown in Table 1, the experimental band gaps of LiSi₂N₃ and LiGe₂N₃ are 6.40 and 3.90 eV,⁴⁸ and their band gaps between valence bands and conduction bands are mainly dominated by the covalent Si–N and Ge–N bands (Fig. S9c and d, ESI†). The calculated NLO coefficients were d₃₁ = 1.01, d₃₂ = 0.24, d₃₃ = −0.32 pm V⁻¹ for LiSi₂N₃, and d₃₁ = 4.14, d₃₂ = 5.3, d₃₃ = −2.60 pm V⁻¹ for LiGe₂N₃. Additionally, their calculated birefringence is about 0.043 (LiSi₂N₃) and 0.071 (LiGe₂N₃) at 1064 nm.

2.3. A–M^IV–N₂ (A = Be, Mg, Zn; M^IV = Si, Ge) system

BeSiN₂,⁴⁹ MgSiN₂, MgGeN₂,⁵⁰ ZnSiN₂ and ZnGeN₂⁵¹ are isostructural and their space group is Pna2₁, thus BeSiN₂ was chosen for the analysis of their structural features. Both [BeN₄] and [SiN₄] tetrahedra in BeSiN₂ are arranged along the same direction and connected by sharing corners (Fig. 2c). The calculated band gap of BeSiN₂ is 6.53 eV (HSE06), and the experimental band gaps are 4.80, 3.20, 3.70 and 3.20 eV for MgSiN₂, MgGeN₂, ZnSiN₂ and ZnGeN₂, respectively. Their band gaps between valence bands and conduction bands are mainly dominated by the covalent A–N and M^IV–N bands (Fig. S9e, f and S10a–c, ESI†). In addition, the calculated NLO coefficients and birefringence of A–M^IV–N₂ (A = Be, Mg, Zn; M^IV = Si, Ge) system were listed in Table 1. The results show that MgGeN₂ (E_g = 3.2 eV, d₃₃ = −12 pm V⁻¹) exhibits balanced NLO properties.

2.4. Zn₃MoN₄

The compound Zn₃MoN₄⁵² crystallizes the space group of Pmn2₁ and its structure is displayed in Fig. 3a. The crystal structure of Zn₃MoN₄ is formed by stacking [ZnN₄] and [MoN₄] tetrahedra along the c-axis, and these tetrahedra are connected by sharing tetrahedral vertices. As shown in Table 1, the calculated band gap by HSE06 is 2.77 eV for Zn₃MoN₄, and the band gap between valence bands and conduction bands is mainly dominated by the covalent Mo–N bands (Fig. S10d, ESI†). Moreover, the calculated NLO coefficients are d₃₁ = 13.4, d₃₂ = 14.57 and d₃₃ = −26.04 pm V⁻¹, and the d₃₃ coefficient is about 1.7 times that of AGS (15.3 pm V⁻¹). According to the results, its calculated birefringence is about 0.098 at 1064 nm, illustrating that Zn₃MoN₄ could achieve phase-matching behavior in the IR NLO application.

Fig. 3 Crystal structure of Zn₃MoN₄ (a), LiPN₂ (b), Zn₂NCl (c), Li₂PO₂N (d) and LiSiON (e).

2.5. A–M–N (A = Li, Cu, Mg, Zn; M = P, Sb) system

Mg₂PN₃, Zn₂PN₃ and MgSbN₃. Mg₂PN₃,⁵³ Zn₂PN₃⁵⁴ and MgSbN₃⁵⁵ crystalized in the same space group Cmc2₁. Taking Mg₂PN₃ as an example, its crystal structure featured densely packed layers consisting of [MgN₄] and [PN₄] tetrahedra, which were all oriented towards the c-axis (Fig. 2d). The experimental band gaps were 5.0 and 3.7 eV for Mg₂PN₃ and Zn₂PN₃,⁵⁶ and the calculated band gap of MgSbN₃ was 2.51 eV (HSE06). The band gaps of Mg₂PN₃ and MgSbN₃ between valence bands and conduction bands are mainly dominated by the covalent Mg–N, P–N and Sb–N bands, while the band gap of Zn₂PN₃ is mainly contributed by Zn–N bonds (Fig. S10e, f and S11a, ESI†). Furthermore, the calculated NLO coefficients are d₃₁ = 1.99, d₃₂ = 2.73, d₃₃ = −2.33 pm V⁻¹ for Mg₂PN₃, d₃₁ = 4.43, d₃₂ = 6.70, d₃₃ = −9.03 pm V⁻¹ for Zn₂PN₃, and d₃₁ = 0.26, d₃₂ = 1.50, d₃₃ = 3.47 pm V⁻¹ for MgSbN₃, respectively. In addition, the calculated birefringence of Mg₂PN₃, Zn₂PN₃ and MgSbN₃ is 0.072, 0.003 and 0.031 at 1064 nm, respectively (Table 1).

LiPN₂ and CuPN₂. LiPN₂⁵⁷ and CuPN₂⁵⁸ are isostructural with the space group of I4̄2d. LiPN₂ was chosen as an example to describe the structure (Fig. 3b), which was composed of [LiN₄] and [PN₄] tetrahedra, and they were arranged in nearly the same direction. As shown in Table 1, the HSE06 band gaps of LiPN₂ and CuPN₂ were 5.21 and 3.19 eV, respectively, which were larger than LiGaS₂ (3.62 eV), and their band gaps between valence bands and conduction bands are mainly dominated by the Li–N, Cu–N and P–N bands (Fig. S11b and c, ESI†). The NLO coefficients of LiPN₂ and CuPN₂ were calculated to be d₁₄ = d₃₆ = 0.20 pm V⁻¹ (LiPN₂) and d₁₄ = d₃₆ = −8.26 pm V⁻¹ (CuPN₂), and their calculated birefringence is 0.022 and 0.019 at 1064 nm, respectively.

2.6. Diamond-like nitrides with mixed anions

Zn₂NX (X = Cl, Br). Zn₂NX (X = Cl, Br) were synthesized and reported as mid-IR NLO materials in 2021 by our group.³⁰ These two compounds are isostructural and crystallize in space group Pna2₁. In the structure of Zn₂NCl, the distorted [ZnN₂Cl₂] tetrahedra are connected to each other via sharing N and Cl atoms and stacked along the same direction (Fig. 3c). The two compounds exhibit excellent mid-IR NLO performances. The experimental band gaps are 3.21 and 3.28 eV for Zn₂NCl and Zn₂NBr, both of which are larger than 3.00 eV. The two compounds exhibit large SHG responses which are 0.9 and 0.8 times that of AGS at 2050 nm, respectively. They also have high LDTs of 20.7 and 25.9 times that of AGS respectively. All the mentioned above mid-IR NLO properties are listed in Table 1. These results showed that Zn₂NX (X = Cl, Br) are potential candidates as good IR NLO materials.

LiSiON. LiSiON⁵⁹ crystallizes in space group Pca2₁ and its crystal structure is displayed in Fig. 3e. The [SiN₃O] and [LiNO₃] tetrahedra with mixed anions were interconnected via sharing the N and O atoms, which were aligned in nearly the same direction. The calculated results of LiSiON are given in Table 1, the HSE06 band gap is 7.03 eV, which is mainly dominated by the covalent Si–O and Si–N bands (Fig. S11d, ESI†). LiSiON has three independent non-vanishing NLO tensor components (d₃₁, d₃₂, d₃₃), and the calculated value are d₃₁ = 1.33, d₃₂ = −2.40 and d₃₃ = −0.14 pm V⁻¹. LiSiON exhibits a large birefringence with the calculated value of 0.044 at 1064 nm.

Li₂PO₂N. The compound Li₂PO₂N⁶⁰ crystallizes in space group Cmc2₁. In the structure of Li₂PO₂N, [PN₂O₂] tetrahedra are stacked parallel to the c-axis, and [LiNO₃] tetrahedra are at an acute angle to the c-axis, both of which are connected by sharing N and O atoms (Fig. 3d). The HSE06 band gap of Li₂PO₂N is 6.82 eV, which is mainly dominated by the covalent P–O and P–N bands (Fig. S11e, ESI†). The calculated NLO coefficients are d₃₁ = 0.18, d₃₂ = 0.33 and d₃₃ = 0.75 pm V⁻¹. Notably, the computational birefringence of Li₂PO₂N is 0.045 at 1064 nm (Table 1).

3. Polyhedra-stacking type NLO nitrides

The design of polyhedra-stacking type compounds serves as a prevalent and effective approach for discovering exceptional NLO crystals. These compounds are characterized by a three-dimensional (3D) framework formed through the combination of [MQ₄] (M = Ag, Cd, Ga, P, S,Ge, etc. Q = P, O, S and Se) with highly electropositive alkali earth elements (Li, Na, K, Rb, Cs) and alkali metals (Mg, Ca, Sr, Ba), or rare earth elements (La, Sc, Y, Lu) possessing a full shell. Polyhedra-stacking type NLO nitrides offer two primary advantages. Firstly, the structural frameworks of these compounds exhibit a wide variety, presenting opportunities for the development of innovative structures. Secondly, the structure of these compounds possesses the potential for rational adjustment, allowing for the achievement of a balance between a robust SHG response and a broad bandgap. This can be accomplished by modifying the cations to enable parallel alignment of the [MQ₄] tetrahedra.

3.1. Alkali metal-based polyhedra-stacking type NLO nitrides

NaSi₂N₃ and NaGe₂N₃. NaSi₂N₃⁶¹ and NaGe₂N₃⁶² are isostructural and their space group is Cmc2₁. In their structure, the adjacent [Si/GeN₄] tetrahedra connected by sharing N atoms to form a layer in b–c plane, the structural framework made up by connecting layers and Na⁺ filled in the holes (Fig. 4). The calculated band gaps by HSE06 are 5.31 eV for NaSi₂N₃ and 4.17 eV for NaGe₂N₃, which are mainly dominated by the covalent Si/Ge–N bonds and ionic Na–N interactions (Fig. S12a and b, ESI†). The calculated NLO coefficients are d₃₁ = 0.33, d₃₂ = 0.73, d₃₃ = −0.65 pm V⁻¹ for NaSi₂N₃ and d₃₁ = 4.74, d₃₂ = 1.59, d₃₃ = −4.36 pm V⁻¹, respectively. In addition, their calculated birefringence is 0.064 and 0.048 at 1064 nm, respectively. All the above results are listed in Table 2.

Fig. 4 Crystal structure of NaSi₂N₃ (a) and (b) and Ba₂Si₅N₈ (c) and (d).

Table 2 The NLO data of polyhedra-stacking type nitrides

Compounds	Space group	Band gap (eV)			NLO coefficients^a (pm V^−1)	Δn^a
		GGA^a	HSE06^a	Exp.^b		At 1064 nm	At 2050 nm
a This work. b Other work from ref. 74, 76.
NaSi2N3	Cmc21	4.02	5.31	—	d 31 = 0.33, d32 = 0.73, d33 = −0.65	0.064	0.063
NaGe2N3	Cmc21	2.88	4.17	—	d 31 = 4.74, d32 = 1.59, d33 = −4.36	0.048	0.047
NaPN2	I4̄2d	4.77	6.16	—	d 14 = d36 = −1.9	0.042	0.042
CaGeN2	I4̄2d	3.16	4.31	—	d 14 = d36 = −5.7	0.060	0.061
CaP2N4	P63	4.37	5.77	—	d 31 = −0.02, d33 = 0.58	0.008	0.007
SrP2N4	P63	3.35	4.59	—	d 31 = 0.29, d33 = 0.94	0.014	0.013
Sr2Si5N8	Pmn21	3.25	4.45	—	d 31 = 1.01, d32 = 0.24, d33 = −0.32	0.023	0.023
Ba2Si5N8	Pmn21	2.92	4.03	—	d 31 = 1.01, d32 = 0.24, d33 = −0.32	0.024	0.023
SrSi7N10	Pc	4.05	5.27	—	d 11 = −0.22, d12 = 0.57, d13 = 3.44	0.018	0.018
					d 31 = −0.49, d32 = 4.21, d33 = 0.44
BaSi7N10	Pc	3.93	5.17	—	d 11 = −0.23, d12 = 0.57, d13 = −4.64	0.011	0.011
					d 31 = −0.52, d32 = −3.77, d33 = 0.41
SrSi6N8	Imm2	3.21	4.46	—	d 31 = −1.18, d32 = −0.30, d33 = 3.82	0.043	0.042
α-Ca2Si5N8	Cc	3.47	4.72	—	d 11 = −0.23, d12 = 0.21, d13 = −0.08	0.009	0.009
					d 31 = −0.10, d32 = −0.47, d33 = 0.05
β-Ca2Si5N8	P21	2.65	3.74	—	d 14 = 0.35, d21 = −1.90, d22 = −0.71, d23 = −3.04	0.016	0.015
Ca3Al2N4	P212121	2.26	3.29	—	d 14 = −0.28	0.031	0.029
SrAlSi4N7	Pna21	2.83	4.04	—	d 31 = −1.02, d32 = 1.43, d33 = −1.34	0.028	0.027
SrYSi4N7	P63mc	2.98	4.21	3.3–3.5	d 31 = −1.25, d33 = 6.45	0.012	0.011
CrB4O5N	P63mc	1.96^b	—	—	0.8 × SiO2^b	—	—
LaSi3N5	P212121	3.38	4.53	—	d 14 = 2.50	0.037	0.036
Pb2Si5N8	Pmn21	2.18	3.17	—	d 31 = 6.46, d32 = −3.71, d33 = −11.84	0.064	0.042

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NaPN₂. NaPN₂^63,64 crystallizes in the tetragonal space group I4̄2d. In this structure, [PN₄] tetrahedra attached by sharing corners and expanded in the space to form the structural framework, while Na⁺ filled in the intervals to balance the residual charge (Fig. 5a). As listed in Table 2, the calculated band gap of NaPN₂ is 6.16 eV (HSE06), which is mainly dominated by the covalent P–N bonds and ionic Na–N interactions (Fig. S11f, ESI†). The calculated NLO coefficient is d₁₄ = d₃₆ = −1.97 pm V⁻¹, and the birefringence of NaPN₂ was calculated to be 0.042 at 1064 nm.

Fig. 5 Crystal structure of NaPN₂ (a), LaSi₃N₅ (b), CaP₂N₄ (c) and (e), SrP₂N₄ (f) and CaGeN₂ (d).

3.2. Alkaline earth metals-based polyhedra-stacking type NLO nitrides

CaGeN₂. CaGeN₂⁶⁵ crystallizes in tetragonal space group I4̄2d. In the structural framework of CaGeN₂, [GeN₄] tetrahedra interconnected by vertex-sharing and arranged along the same direction (Fig. 5d). CaGeN₂ has a wider HSE06 band gap of 4.31 eV compared to ZnGeN₂ (3.01 eV), which is mainly dominated by the covalent Ge–N bonds (Fig. S12c, ESI†). The calculated NLO coefficient d₁₄ and birefringence are −5.74 pm V⁻¹ and 0.060 at 1064 nm, respectively (Table 2).

CaP₂N₄ and SrP₂N₄. CaP₂N₄⁶⁶ and SrP₂N₄⁶⁷ are isostructural and they crystallized in the polar space group P6₃. Taking CaP₂N₄ as an example, the [PN₄] tetrahedra stacked according to the symmetry of 6₃ screw axis and connected via vertex-sharing, while Ca²⁺ are added into the holes to balance the framework (Fig. 5c, e and f). Their computational band gaps are 5.77 and 4.59 eV (HSE06), respectively, which are mainly dominated by the covalent P–N bonds (Fig. S12d and e, ESI†). The calculated NLO coefficients are d₃₁ = −0.02, d₃₃ = 0.58 pm V⁻¹ for CaP₂N₄ and d₃₁ = 0.29, d₃₃ = 0.94 pm V⁻¹ for SrP₂N₄ (Table 2), respectively. In addition, the calculated birefringence of CaP₂N₄ and SrP₂N₄ is 0.008 and 0.014 at 1064 nm.

Sr₂Si₅N₈ and Ba₂Si₅N₈. Sr₂Si₅N₈ and Ba₂Si₅N₈⁶⁸ are isostructural and crystallized in the orthorhombic space group Pmn2₁. In their structure, [SiN₄] tetrahedra interconnected via corners sharing to form interlayers in a–c plane, which consist of the structural framework through [SiN₄] tetrahedra, and Sr²⁺/Ba²⁺ are accessed to empty positions to balance the framework (Fig. 4c and d). The optical properties of Sr₂Si₅N₈ and Ba₂Si₅N₈ were calculated and listed in Table 2, the calculated band gaps are 4.45 eV for Sr₂Si₅N₈ and 4.03 eV for Ba₂Si₅N₈ (HSE06), which are mainly dominated by the covalent Si–N bonds (Fig. S12f and S13a, ESI†). The calculated NLO coefficients are d₃₁ = 1.7, d₃₂ = 1.73, d₃₃ = 0.76 pm V⁻¹ for Sr₂Si₅N₈ and d₃₁ = −1.22, d₃₂ = −0.91, d₃₃ = −0.4 pm V⁻¹ for Ba₂Si₅N₈. In addition, the calculated birefringence are 0.023 (Sr₂Si₅N₈) and 0.024 (Ba₂Si₅N₈) at 1064 nm, respectively.

SrSi₇N₁₀ and BaSi₇N₁₀. SrSi₇N₁₀⁶⁹ and BaSi₇N₁₀⁷⁰ are isostructural and their space group is Pc. In their structure, the structural framework is formed by layers (in a–c plane) and chains (parallel to c-axis) with Sr²⁺/Ba²⁺ filled in the holes, where the layers are made up of corner-shared [SiN₄] tetrahedra as well as the chains constructed of corner- and prism-shared [SiN₄] tetrahedra (Fig. 6a and b). The calculated band gaps of SrSi₇N₁₀ and BaSi₇N₁₀ are 5.27 and 5.17 eV, respectively, which are mainly dominated by the covalent Si–N bonds (Fig. S13b and c, ESI†). Moreover, the calculated NLO coefficients are d₁₁ = −0.22, d₁₂ = 0.57, d₁₃ = 3.44, d₃₁ = −0.49, d₃₂ = 4.21, d₃₃ = 0.44 pm V⁻¹ for SrSi₇N₁₀ and d₁₁ = −0.23, d₁₂ = 0.57, d₁₃ = −4.64, d₃₁ = −0.52 pm V⁻¹, d₃₂ = −3.77, d₃₃ = 0.41 pm V⁻¹ for BaSi₇N₁₀. The calculated birefringence of SrSi₇N₁₀ and BaSi₇N₁₀ is 0.018 and 0.011 at 1064 nm, respectively.

Fig. 6 Crystal structure of BaSi₇N₁₀ (a) and (b) and SrSi₆N₈ (c) and (d).

SrSi₆N₈. The synthesis and crystal structure of SrSi₆N₈⁷¹ were first reported in 2005 by Schnick et al. SrSi₆N₈ crystallize in the orthorhombic space group Imm2. As described in Fig. 6, the structural framework is constructed by [SiN₄] tetrahedra and [N₃Si–SiN₃] entities, which are bridged through N atoms with Sr²⁺ distributed in the holes. Interestingly, [N₃Si–SiN₃] entities contain additional Si–Si single bonds, which might enhance the SHG performance of SrSi₆N₈. The HSE06 band gap of SrSi₆N₈ is 4.46 eV, and the band gap between valence bands and conduction bands is mainly dominated by the covalent Si–N bonds (Fig. S13d, ESI†). The calculated NLO coefficient are d₃₁ = −1.18, d₃₂ = −0.3, d₃₃ = 3.82 pm V⁻¹. Notably, the computational birefringence of SrSi₆N₈ is 0.043 at 1064 nm (Table 2).

α-Ca₂Si₅N₈ and β-Ca₂Si₅N₈. α-Ca₂Si₅N₈^72,73 and β-Ca₂Si₅N₈⁷⁴ are isomers, where the former crystallizes in the monoclinic space group Cc and the latter crystallizes in the monoclinic space group P2₁. As can be seen in Fig. 7, both α-Ca₂Si₅N₈ and β-Ca₂Si₅N₈ have a structural framework similar to Ba₂Si₅N₈, including layers made up of [SiN₄] tetrahedra and the ways they connected. The HSE06 band gaps are 4.72 and 3.74 eV for α-Ca₂Si₅N₈ and β-Ca₂Si₅N₈, respectively, which are mainly dominated by the covalent Si–N bonds (Fig. S13e and f, ESI†). The calculated NLO coefficients are d₁₁ = −0.23, d₁₂ = 0.21, d₁₃ = −0.08, d₃₁ = 0.1, d₃₂ = −0.47, d₃₃ = 0.05 pm V⁻¹ for α-Ca₂Si₅N₈ and d₂₁ = −1.99, d₂₂ = −0.71, d₂₃ = −3.04, d₁₄ = 0.35 pm V⁻¹ for β-Ca₂Si₅N₈. Furthermore, the calculated birefringence of α-Ca₂Si₅N₈ and β-Ca₂Si₅N₈ is 0.009 and 0.016 at 1064 nm.

Fig. 7 Crystal structure of α-Ca₂Si₅N₈ (a) and (b) and β-Ca₂Si₅N₈ (c) and (d).

Ca₃Al₂N₄. The compound Ca₃Al₂N₄⁷⁵ crystallizes in orthorhombic space group P2₁2₁2₁. In the structure, [AlN₄] tetrahedra are connected by sharing corners and prisms to form chains, which extend into the space to constitute the framework with Ca²⁺ dispersed in the intervals to stabilize the structure (Fig. 8a and b). The calculated band gap of Ca₃Al₂N₄ is 3.29 eV (HSE06), which is mainly dominated by the covalent Al–N bonds and ionic Ca–N interactions (Fig. S14a, ESI†). The calculated NLO coefficient is d₁₄ = −0.28 pm V⁻¹. In addition, the birefringence of Ca₃Al₂N₄ is calculated to be 0.031 at 1064 nm. All these results were listed in Table 2.

Fig. 8 Crystal structure of Ca₃Al₂N₄ (a) and (b) and SrAlSi₄N₇ (c) and (d).

SrAlSi₄N₇. The compound SrAlSi₄N₇ was first synthesized and studied in 2009 by Schnick et al.⁷⁶ SrAlSi₄N₇ crystallize in the polar space group Pna2₁, its structure featured layers consisting of [SiN₄] tetrahedra, which were linked inside the layers by sharing N atoms. And the layers are attached using [AlN₄] tetrahedra and N atoms as bridges to form the structural framework of SrAlSi₄N₇, where Sr²⁺ are added into the pores to balance the framework (Fig. 8c and d). The band gap calculated by HSE06 of SrAlSi₄N₇ is 4.04 eV, which is mainly dominated by the covalent Si–N bonds (Fig. S13b, ESI†). The calculated NLO coefficients are d₃₁ = −1.02, d₃₂ = 1.43, d₃₃ = −1.37 pm V⁻¹, respectively. In addition, the birefringence of SrAlSi₄N₇ is calculated to be 0.028 at 1064 nm. All the above results were listed in Table 2.

SrYSi₄N₇. The synthesis and crystal structure of the compound SrYSi₄N₇ were reported in 2004.⁷⁷ SrYSi₄N₇ crystallizes in the hexagonal space group P6₃mc and features C₂-type supertetrahedra.⁷⁸ The structural framework of SrYSi₄N₇ is assembled from layers constructed by [Si₄N₁₁] C₂-type supertetrahedra, which are connected by sharing the corners of the bottom [SiP₄] tetrahedra, and Sr²⁺ cations as well as [YN₆] octahedra are filled in the pores (Fig. 9a and b). The experimental band gap of SrYSi₄N₇ is 3.3–3.5 eV, while the calculated band gap is 4.21 eV (HSE06), which is mainly dominated by the covalent Y–N and Si–N bonds (Fig. S14c, ESI†). Moreover, the calculated NLO coefficients of SrYSi₄N₇ are d₃₁ = −1.25 and d₃₃ = 6.45 pm V⁻¹. The birefringence of SrYSi₄N₇ is calculated to be 0.012 at 1064 nm.

Fig. 9 Crystal structure of SrYSi₄N₇ (a) and (b) and CrB₄O₅N (c) and (d).

3.3. Other polyhedra-stacking type NLO nitrides

CrB₄O₅N. The synthesis and physical properties (including SHG performance) of CrB₄O₅N were investigated in 2021 by Huppertz et al.⁷⁹ CrB₄O₅N crystallizes in hexagonal space group P6₃mc. Interestingly, the structure of the chromium oxonitridoborate CrB₄O₅N is similar to that of the nitridosilicates SrYSi₄N₇. The structural framework of CrB₄O₅N could be regarded that the [Si₄N₁₁] C₂-type supertetrahedra were replaced by [B₄O₉N₂] C₂-type supertetrahedra(Fig. 9c and d). The calculated band gap of CrB₄O₅N is 1.96 eV (GGA), and the frontier orbitals (top of valence band and bottom of conduction band) of this compound are mainly occupied by the Cr-3d, indicating that the optical band gap is mainly decided on the Cr-3d orbital. Furthermore, the SHG response of CrB₄O₅N was about 0.8 times that of quartz.

LaSi₃N₅. LaSi₃N₅ was first synthesized and studied in 1995.⁸⁰ LaSi₃N₅ crystallizes in orthorhombic space group P2₁2₁2₁ and its crystal structure is depicted in Fig. 5b. In this structure, the [SiN₄] tetrahedra are interconnected by sharing N atoms and extend in space with La³⁺ added into the intervals to build the framework of LaSi₃N₅. The calculated results demonstrate that LaSi₃N₅ owns a wide band gap 4.53 eV (HSE06), which is mainly dominated by the covalent La–N bonds (Fig. S14d, ESI†). The NLO coefficient based on the DFT calculation for LaSi₃N₅ is d₁₄ = 2.50 pm V⁻¹, and LaSi₃N₅ exhibits large birefringence with the calculated value of 0.037 at 1064 nm.

Pb₂Si₅N₈. The compound Pb₂Si₅N₈⁸¹ crystallizes in orthorhombic space group Pmn2₁. Pb₂Si₅N₈ is isomorphic to Sr₂Si₅N₈ and Ba₂Si₅N₈, and features layers consisting of [SiN₄] tetrahedra. Notably, cations filled in the structural framework of Pb₂Si₅N₈ are different from that of Sr₂Si₅N₈ and Ba₂Si₅N₈ (Fig. S1b, ESI†), because Pb²⁺ contains activated lone pair electrons, which could improve the SHG response for Pb₂Si₅N₈ compared with Sr₂Si₅N₈ and Ba₂Si₅N₈.^82–84 The calculated band gap of Pb₂Si₅N₈ is 3.17 eV (HSE06), which is mainly dominated by the covalent Si–N bonds (Fig. S14e, ESI†). Its calculated NLO coefficients are d₃₁ = 6.46, d₃₂ = −3.71, d₃₃ = −11.84 pm V⁻¹, and the largest NLO tensor of Pb₂Si₅N₈ is larger than that of Sr₂Si₅N₈ (−1.22 pm V⁻¹) and Ba₂Si₅N₈ (1.73 pm V⁻¹). Furthermore, the birefringence of Pb₂Si₅N₈ is calculated to be 0.064 at 1064 nm.

4. Other NLO nitrides with featured structures

The structures of some nitrides exhibit low-dimensional special features, such as zero-dimensional (0D) molecules, one-dimensional (1D) chains and two-dimensional (2D) layers, and excellent properties may be realized in these nitrides with unique structures. Low-dimensional units, including [BN₂] entities in Ba₃B₂N₄, [Si₂N₆] dual-tetrahedra in Ba₂Si₂N₆, [MoN₄]_n/[WN₄]_n chains in Na₃MoN₃/Na₃WN₃, [SnN₃]_n layers in NaSnN and [ZrN₆]_n layers in ZnZrN₂ are discussed in detail in this section. Results indicated that these NLO nitrides with low-dimensional structures exhibited large NLO coefficients and birefringence.

NaSnN

The synthesis and physical properties (including SHG performance) of compound NaSnN were first reported in 2005 by Clarke et al,⁸⁵ and the NLO properties were study by Lin et al. based on the first-principles calculations recently.⁸⁶ NaSnN crystallizes in hexagonal space group P6₃mc, and its structural framework built by infinite two-dimensional (2D) layers with Na⁺ dispersed between layers, which are made up of [SnN₃] triangular pyramids connecting each other through N atoms (Fig. 10a and b). In addition, the activated lone pair electrons in Sn²⁺ could enhance the second-order NLO response. The band gap by HSE06 of NaSnN is 1.70 eV, and the band gap between valence bands (VB) and conduction bands (CB) is dominated by the ionic Na–N coupling and covalent Sn–N hybridization. Moreover, the calculated NLO coefficients and birefringence are d₁₃ = d₂₃ = −2.7; d₃₃ = 27 pm V⁻¹ and 0.629 at 2.0 μm, respectively. All these results were listed in Table 3. The SHG-weighted density of NaSnN suggested that the [SnN₃]_∞ backbone with the lone electron pairs effect leading to the large NLO coefficients.

Fig. 10 Crystal structure of NaSnN (a), (b) and (d) Na₃MoN₄ (c) and (d).

Table 3 The NLO data of other nitrides with featured structures

Compounds	Space group	Band gap (eV)			NLO coefficients^a (pm V^−1)	Δn^a
		GGA^a	HSE06^a	Exp.^b		At 1064 nm	At 2050 nm
a This work. b Other work from ref. 29, 83, 91–93.
NaSnN	P63mc	1.07	1.70	—	d 31 = d32 = −2.7, d33 = −27 ^b	0.578^a	0.629^b
Na3MoN3	Cc	1.25	2.10	—	d 11 = 11.98, d12 = −5.98, d13 = −6.07	0.119	0.086
				—	d 31 = −5.74, d32 = −3.42, d33 = −1.52
Na3WN3	Cc	1.51	2.41	—	d 11 = 6.21, d12 = −4.51, d13 = −3.04	0.079	0.042
				—	d 31 = −0.65, d32 = −3.93, d33 = −1.49
Ba3B2N4	P212121	2.45	3.41	—	d 14 = d25 = d36 = −1.18	0.189	0.182
Ba5Si2N6	P212121	1.45	2.32	—	d 14 = d25 = d36 = 1.88	0.104	0.096
ZrZnN2	P3m1	1.98^b	3.11^b	—	d 15 = 10.06, d33 = 2.15^b	0.276^b	—
MoSi2N4	—	1.78^b	2.24^b	—	300 × SiO2	—	—

---

Na₃MoN₃ and Na₃WN₃

Na₃MoN₃⁸⁷ and Na₃WN₃⁸⁸ are isostructural and crystallize in the monoclinic space group Cc. Their crystal structure featured one-dimensional (1D) infinite chains parallel to each other, constructed by vertex-sharing [MoN₄] tetrahedra, and Na⁺ are distributed between chains to balance the charge (Fig. 10c and d). Their computational band gaps are 2.1 and 2.41 eV (HSE06), respectively. The band gaps of Na₃MoN₃ and Na₃WN₃ between valence bands and conduction bands are dominated by the ionic Na–N bands and covalent Mo/W–N bands (Fig. S14f and S15a, ESI†). The calculated NLO coefficients are d₁₁ = 11.98, d₁₂ = −5.98, d₁₃ = −6.04, d₃₁ = −5.74, d₃₂ = −3.42, d₃₃ = −1.52 pm V⁻¹ for Na₃MoN₃ and d₁₁ = 11.98, d₁₂ = −5.98, d₁₃ = −6.04, d₃₁ = −5.74, d₃₂ = −3.42, d₃₃ = −1.52 pm V⁻¹ for Na₃WN₃ (Table 3), respectively. In addition, the calculated birefringence of Na₃MoN₃ and Na₃WN₃ is 0.119 and 0.079 at 1064 nm.

Ba₃B₂N₄

The compound Ba₃B₂N₄⁸⁹ crystallizes in the orthorhombic space group P2₁2₁2₁. The structural framework of Ba₃B₂N₄ was made up of dumbbell-shaped [BN₂] entities with Ba²⁺ cations filled in the framework. Moreover, the dumbbell-shaped [BN₂] entities were almost parallel to the b-axis (Fig. 11a). According to calculated results, the HSE06 band gap of Ba₃B₂N₄ is 3.41 eV, and the band gap between valence bands and conduction bands is mainly dominated by the ionic Ba–N bands (Fig. S15b, ESI†). The calculated NLO coefficient is d₁₄ = −1.18 pm V⁻¹. Furthermore, the birefringence of Ba₃B₂N₄ is calculated to be 0.189 at 1064 nm.

Fig. 11 Crystal structure of Ba₃B₂N₄ (a), Ba₅Si₂N₆ (b) and ZrZnN₂ (c) and (d).

Ba₅Si₂N₆

The synthesis and crystal structure of compound Ba₅Si₂N₆⁹⁰ was reported in 1996 by DiSalvo et al. Ba₅Si₂N₆ crystallizes in the orthorhombic space group P2₁2₁2₁. In this structure, the isolated prism-sharing [Si₂N₆] dual-tetrahedra are the backbone of the structural framework of Ba₅Si₂N₆, and Ba²⁺ are dispersed in intervals between these tetrahedra to balance the charge (Fig. 11b). The calculated results implied that Ba₅Si₂N₆ owns a wide band gap of 2.32 eV (HSE06), and the band gap between valence bands and conduction bands is mainly dominated by the ionic Ba–N bands (Fig. S15c, ESI†). The calculated NLO coefficient is d₁₄ = 1.88 pm V⁻¹. Moreover, the calculated birefringence of Ba₅Si₂N₆ is 0.104 at 1064 nm.

ZrZnN₂

ZrZnN₂ with high thermal conductivity has been studied as an IR NLO material by Yang et al. recently.³² ZrZnN₂ crystalizes in the trigonal space group P3m1, in this structure, [ZrN₆] octahedra are connected by edge-sharing to build octahedral layers, which are stacked in the c direction and connected by [ZnN₄] tetrahedral (Fig. 11c and d). The band gap of ZrZnN₂ based on HSE06 is 3.11 eV, which is larger than that of AgGaS₂ (2.73 eV). Furthermore, ZrZnN₂ show balanced optical performance with the NLO coefficient of about 0.9 × AGS and the birefringence is of 0.276 at 1064 nm. Both [ZrN₆] octahedra and [ZnN₄] tetrahedra contributed to the NLO properties, including wide band gap and large NLO coefficients.

MoSi₂N₄

The growth of centimeter-scale monolayer films of MoSi₂N₄ was achieved in 2020 by Hong et al,⁹¹ and the NLO properties were further studied by Lin et al. based on the first-principles calculations recently.^91,92 The atomic structure of MoSi₂N₄ was shown in Fig. 12, its structure features infinite two-dimensional (2D) N–Si–N–Mo–N–Si–N layers, which can be viewed as a MoN₂ layer sandwiched between two Si–N bilayers. The experimental optical band gap of monolayer MoSi₂N₄ film is 1.94 eV, and the band gap between valence bands (VB) and conduction bands (CB) is dominated by Mo–N bonds and Mo⁴⁺ nonbonding states. Furthermore, the SHG response of MoSi₂N₄ was about 300 times that of quartz, and the SHG response of MoSi₂N₄ mainly comes from the inner Mo–N bands of MoN₂ layers.

Fig. 12 The atomic structure of MoSi₂N₄.

Conclusions and outlooks

In this review, we systematically summarize the potential and recent advancements in nitride-based NLO crystals, which include 45 nitrides. These crystals are classified into three categories based on their structural features: diamond-like type NLO nitrides, polyhedra-stacking type NLO nitrides, and other NLO nitrides with unique structures. We consistently discuss their crystal structures, physical properties, and structure–property relationships. Our findings indicate that nitrides possess wide band gaps and transparency windows, ranging from the ultraviolet to the infrared region. Notably, several NLO nitrides exhibit outstanding NLO properties including BeSiN₂, LiSi₂N₃, LiSiON, LiPO₂N, Zn₃MoN₄, Zn₂NX (X = Cl, Br), NaPN₂, Pb₂Si5N₈, NaSnN, Na₃MoN₄ and ZrZnN₂. Furthermore, approximately 40% of these NLO nitrides contain elemental silicon, suggesting that Si-based nitrides warrant further exploration as NLO materials. However, the investigation of NLO nitrides is far from complete and faces numerous challenges, such as difficult synthesis conditions and unclear property influencing mechanisms. Consequently, the following aspects should be considered for the further application and development of NLO nitrides:

1. The development of new synthetic methods and advanced equipment technology is necessary to obtain more NLO nitrides with exceptional properties. Currently, most non-centrosymmetric nitrides are obtained using traditional solid-state synthesis technology under high temperature and pressure conditions. Advanced equipment technology is crucial for meeting these demanding conditions. Additionally, the ammonothermal method and salt-flux method may be effective ways to synthesize more NLO nitrides. Moreover, since high-performance NLO nitrides are predominantly available in powder or micron-sized crystal forms, further research on large-size crystal growth is needed.

2. A deeper understanding of the chemical bonding mechanisms between nitrides and pnictides is essential. Nitrogen and phosphorus belong to the same main group VA, while homo-cationic and homo-anionic bonds often form in pnictide crystal structures, they do not in nitrides. These homoatomic bonds significantly impact linear optical and NLO properties. Therefore, studying the bonding habits of nitrides and pnictides is crucial for designing excellent NLO materials.

3. Prioritizing the exploration of mixed-anion inorganic nitrides as NLO materials is recommended. Combining different anions into one structure can effectively enhance NLO properties. Consequently, halogens (Cl, Br, I) and phosphorus (P) can be introduced into nitrides to form [MN_yX_4−y] (M = mental elements, X = Cl, Br, I, P) mixed anionic tetrahedra. These distorted tetrahedra possess large anisotropic polarizability and strong hyperpolarizability, which can improve the SHG response and birefringence.

4. Developing metal nitrides with triangular anionic groups MN₃ (M = Sb, Te, Sn) is suggested. MN₃ groups possess stereochemically active lone-pair electrons, and compounds containing these electrons exhibit significant SHG response and birefringence, as seen in NaSnN. Therefore, more in-depth investigations should be conducted to design NLO nitrides with triangular anionic groups.

Author contributions

Xin Zhao performed the theoretical calculation, data analysis, and paper writing; Chensheng Lin and Haotian Tian offered help in theoretical calculation; Chao Wang offered help in analyzing data; Ning Ye and Min Luo guided and revised the manuscript. All authors contributed to the general discussion.

Conflicts of interest

There are no conflicts to declare. The authors declare no competing financial interests.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22222510, 21975255 and 21921001), Natural Science Foundation of Fujian Province (2023J02026), the Foundation of Fujian Science & Technology Innovation Laboratory (2021ZR202), Youth Innovation Promotion Association CAS (2019303).

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Footnote

† Electronic supplementary information (ESI) available: The method of theoretical calculation, band structure (HSE06), PDOS, calculated frequency-dependent coefficients and calculated refractive index dispersion curves of compounds. See DOI: https://doi.org/10.1039/d3qm00657c

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