To investigate cationic disorder arising from the entropy stabilization effect, appropriate cations were incorporated into the SnSe lattice, and quasi-random structures of NaSn₂SbSe₄ were constructed via the SQS method, as illustrated in Figure 1. The optimized lattice parameters of NaSn₂SbSe₄ are a = 5.954 Å and b = c = 5.931 Å, with α = β = γ = 90°, consistent with a typical tetragonal phase structure. Compared with cubic-phase SnSe, the lattice parameters along the a and b/c axes of NaSn₂SbSe₄ exhibit changes of 1.636% and 2.016%, respectively [Supplementary Table 1]. These variations are primarily attributed to the significantly greater contraction of Sb-Se, Na-Se, and Sn-Se bond lengths along the b/c-axes relative to those along the a-axis [Supplementary Table 2]. Analysis of bond lengths reveals that the random distribution of Na and Sb atoms, together with their distinct local bonding environments, results in significant structural deviations from pristine SnSe, with structural distortion degrees of 1.619% and 2.016% along the a and b/c-axes, respectively. This degree of distortion effectively mitigates excessive lattice strain while preserving the structural stability of the tetragonal phase, and is anticipated to maintain favorable electronic transport properties. As shown in Supplementary Table 3, the calculated optical dielectric constants of NaSn₂SbSe₄ along the a and b/c directions are approximately 4.17 and 3.70 times those of SnSe, respectively, confirming its significantly enhanced electronic polarizability. Higher electronic polarizability is closely associated with band structure features favorable for electron transport, predicting that NaSn₂SbSe₄ exhibits excellent electrical transport properties.

Furthermore, the structural distortion in NaSn₂SbSe₄ is strongly correlated with significant changes in its bonding characteristics^[28]. To systematically investigate this effect, we employed projected Crystal Orbital Hamilton Population (-pCOHP) and Electron Localization Function (ELF) analyses. As shown in Figure 1B, the -pCOHP spectra of SnSe and NaSn₂SbSe₄ provide detailed insights into orbital interactions and bond strength, with negative and positive regions corresponding to antibonding and bonding states, respectively. In SnSe, the Sn-Se bonding is primarily attributed to the hybridization between Sn(5p) and Se(4p) orbitals, whereas the antibonding states arise mainly from the coupling of Sn(5s) and Se(4p) orbitals. In NaSn₂SbSe₄, the introduction of Na and Sb enhances the bonding interactions between Sn (5p) and Se (4p), which is expected to influence the electrical transport properties via band structure modification. Additionally, it introduces significant orbital interactions predominantly originating from Sb, where Sb(5s) forms a distinct antibonding state with Se(4p) and further enhances the existing Sn(5s)-Se(4p) antibonding interaction. It has been established in prior work that the formation of s-p antibonding states below the Fermi level plays a decisive role in shaping the phonon dynamics^[29]. Consequently, the pronounced intensification of Sn(5s)-Se(4p) antibonding states from -1 eV to 0 eV in NaSn₂SbSe₄ relative to SnSe is expected to induce significantly stronger lattice anharmonicity, thereby contributing to a reduction in lattice thermal conductivity. We further investigated the influence of Sb and Na incorporation on electronic localization [Figure 1C and D]. The results reveal that the ELF distribution in SnSe exhibits weakly covalent bonding characteristics, whereas NaSn₂SbSe₄ displays covalency and ionicity: the Sb atom significantly strengthens the covalent character of both Sn-Se and Sb-Se bonds, while the introduction of Na induces a partial transition of certain Sn-Se bonds from covalent to Na-Se ionic bonds^[30]. We further employ the ICOBI to quantify bonding heterogeneity in NaSn₂SbSe₄. This index reflects differences in bond strength and allows direct comparison among bonds within a structure, making it a reliable indicator of bond non-uniformity^[31]. As shown in Figure 1E, the calculated ICOBI values for the Sb-Se and Sn-Se bonds in NaSn₂SbSe₄ are 0.40 and 0.38, respectively - both notably higher than that of the Sn-Se bond in SnSe (0.13) - whereas the ICOBI value for the Na-Se bond is 0.08, which is lower than that of the Sn-Se bond in SnSe. This provides additional evidence that NaSn₂SbSe₄ exhibits mixed covalent-ionic bonding character, with the heterogeneous nature of strong and weak bonds acting to enhance lattice anharmonicity, strengthen phonon scattering, and consequently reduce lattice thermal conductivity^[32]. Notably, structural distortion induces charge polarization, resulting in an inhomogeneous charge density distribution, with pronounced electron delocalization observed between Sn-5p and Se-4p orbitals. This modification is expected to further influence the band dispersion, thereby helping to preserve high electrical conductivity. These findings collectively demonstrate that the introduction of aliovalent cations and the resultant structural distortion profoundly influence the chemical bonding nature of the material. In this configuration, the synergistic interaction between Sb and Na fosters the formation of a complex chemical bonding network, giving rise to a unique electronic environment characterized by heterogeneous bonding interactions with varying orbital overlap strengths and bond polarizations. Such heterogeneous bonding characteristics are expected to suppress lattice thermal conductivity and concurrently maintain favorable electronic transport, thereby offering new avenues for the synergistic optimization of thermoelectric performance^[33,34].

To investigate the influence of chemical bonding variations on thermal transport properties, we calculate the phonon dispersion curves and phonon density of states (PhDOS) for both SnSe and NaSn₂SbSe₄. To enable a systematic comparison, the high-symmetry q-point path along Γ-X-M-Γ-R-M was employed. Within the harmonic approximation, the phonon dispersion of NaSn₂SbSe₄ was calculated at 0 K using Phonopy, and imaginary frequencies are observed in the resulting spectrum [Supplementary Figure 1]. Previous studies have shown that such behavior commonly occurs in strongly anharmonic materials^[35], indicating that the reference structure of NaSn₂SbSe₄ does not correspond to a stable local minimum of the effective potential energy surface within the harmonic approximation. Instead, this behavior is consistent with a complex, multi-well potential energy surface, which is a characteristic feature of strongly anharmonic systems. In contrast, as shown in Figure 2A and B, the finite-temperature phonon spectra obtained using the TDEP method at 300 K show that these harmonic instabilities are removed through anharmonic renormalization, demonstrating that both SnSe and NaSn₂SbSe₄ are dynamically stable at 300 K^[36-37]. Meanwhile, NaSn₂SbSe₄ shows a calculated formation energy of approximately -4 eV, indicating the thermodynamic stability of the corresponding structures. To accurately assess the phonon transport properties, the correction of the nonanalytic term and the Γ point splitting between transverse and longitudinal optical (TO-LO) phonon branches were incorporated into the analysis^[38,39]. Notably, NaSn₂SbSe₄ shows a splitting of the optical branches at the Γ point. Compared to SnSe, NaSn₂SbSe₄ also demonstrates more pronounced softening of the optical phonon branches, which primarily originate from the vibrational contributions of the Sb, Sn, and Se atoms. For example, at the high-symmetry Γ point and in the frequency range of 0-50 cm^-1, the phonon dispersion of NaSn₂SbSe₄ reveals low-frequency optical phonon branches, which are associated with lattice anharmonicity^[23,40]. This observation is consistent with our initial prediction that the Sb/Na-induced disorder perturbs the local bonding environment and disrupts the periodicity required for coherent phonon propagation, thus strengthening the lattice anharmonicity. Concurrently, the phonon dispersion of NaSn₂SbSe₄ displays significant coupling between the acoustic and low-frequency optical modes - a feature that enhances phonon scattering and will reduce lattice thermal conductivity^[39,41].

Lattice thermal conductivity κ_L quantifies the phonon contribution to thermal transport. For materials with pronounced anharmonicity, such as NaSn₂SbSe₄, it is essential to consider quartic anharmonicity effects to predict κ_L values accurately^[42,43]. Therefore, we investigated κ_L using three-phonon (3ph) and combined three- and four-phonon (3,4ph) scattering models, with results presented in Figure 2C. For both SnSe and NaSn₂SbSe₄, the κ_L exhibits a steady decline, approximately inversely proportional to temperature in the range of 300-800 K. This phenomenon arises primarily from enhanced lattice vibrations at elevated temperatures, which facilitate phonon interactions and strengthen phonon scattering processes^[39,42]. Notably, NaSn₂SbSe₄ exhibits an approximately 50% reduction in κ_L relative to SnSe, aligned with the observations extracted from the phonon dispersion assessment. Additionally, for NaSn₂SbSe₄, κ_3,4ph is significantly reduced relative to κ_3ph due to the inclusion of the 4ph scattering mechanism, highlighting the significant impact of 4ph scattering processes on phonon thermal transport. Specifically, the theoretically obtained κ_3ph and κ_3,4ph values are 3.0 and 1.6 W m^-1 K^-1 at 600 K for NaSn₂SbSe₄, respectively. At 800 K, the κ_3,4ph of NaSn₂SbSe₄ is 1.1 W m^-1 K^-1, showing a reduction from the 2.9 W m^-1 K^-1 of SnSe. This reduction can be theoretically attributed to additional phonon scattering channels introduced by 4ph processes, which increase the overall scattering rates and further suppress the κ_L^[44,45]. As shown in Supplementary Figure 2, we further compare the reductions in lattice thermal conductivity of NaSn₂SbSe₄ arising from 3ph scattering alone and from the additional inclusion of 4ph scattering. The results show that the reduction in κ_L induced by 4ph processes, defined relative to the 3ph-only case, is larger than that caused by 3ph scattering alone. This comparison clearly demonstrates that, in NaSn₂SbSe₄, 4ph scattering processes play a dominant role in suppressing lattice thermal transport. As illustrated in Figure 2D, we further calculated scattering rates. The analysis reveals that most of both 3ph and 4ph scattering rates are higher in NaSn₂SbSe₄ than in SnSe across the entire frequency range, indicating more pronounced lattice vibrations anharmonicity in NaSn₂SbSe₄. These elevated scattering rates are the main origin of the ultralow κ_L of NaSn₂SbSe₄. Notably, in NaSn₂SbSe₄, the 4ph scattering rates are comparable to or even exceed those of 3ph processes over the entire frequency spectrum. This result is consistent with the preceding comparative analysis of the contributions of 3ph and 4ph scattering to the reduction of κ_L, indicating that 4ph scattering exhibits overall significant strength in NaSn₂SbSe₄. Additionally, the purple solid line in Figure 2D represents the scattering rate for phonons with identical frequencies, indicating that the phonon lifetime corresponds closely to the oscillation period of the phonon quasiparticle^[46,47]. Figure 2D demonstrates that the majority of 3ph and 4ph scattering events are located within the reference curve, supporting the applicability of the phonon BTE. The frequency-dependent cumulative lattice thermal conductivity shown in Supplementary Figure 3 indicates that the main contributions to κ_L for both SnSe and NaSn₂SbSe₄ come from phonon branches in the 10-120 cm^-1 range. At frequencies between 25 and 50 cm^-1, the cumulative 3ph lattice thermal conductivity of NaSn₂SbSe₄ is slightly lower than that of SnSe, showing a similar growth trend because the 3ph scattering in NaSn₂SbSe₄ is not significantly stronger than in SnSe in this range. When 4ph scattering processes are included, the contributions to κ_L from low-frequency branches, especially below 50 cm^-1, are notably suppressed due to additional scattering channels. Furthermore, as indicated by the calculated phonon group velocity (v_ph) (see Supplementary Figure 4 in the Supporting Information), the overall magnitude of the phonon group velocity of NaSn₂SbSe₄ remains relatively low, which is conducive to the suppression of κ_L.

Phonon scattering rates are primarily determined by two factors: the anharmonic scattering strength, typically characterized by the Grüneisen parameters γ^[48], and the number of available scattering channels, quantified by the phonon scattering phase space W. The phonon scattering phase space is defined as the set of all accessible final states in momentum space, thereby quantifying the number of scattering channels permitted by simultaneous energy and momentum conservation^[41,49]. To clarify the underlying origin of the low κ_L, both the Grüneisen parameter γ and the scattering phase space W were analyzed. As shown in Figure 3A, the magnitude of γ in NaSn₂SbSe₄ within the 0-25 cm^-1 frequency range is significantly larger than that in SnSe, thereby indicating its stronger anharmonicity. This finding further supports that a high Grüneisen parameter γ plays an important role in enhancing phonon scattering in NaSn₂SbSe₄. Figure 3B presents the calculated 3ph scattering phase space (W_3ph). Under the conservation of energy and momentum, low-frequency phonons mainly participate in combination processes that up-convert population into high-frequency phonons, while high-frequency phonons primarily evolve via intrinsic 3ph scattering. Therefore, within the 3ph phase space, phonon scattering is predominantly governed by splitting processes (λ → λ′ + λ″) in the 50-200 cm^-1 range, and by combination processes (λ + λ′ → λ″) at frequencies below 50 cm^-1. As shown in Figure 3C, NaSn₂SbSe₄ possesses a large 4ph scattering phase space (W_4ph). This enlarged phase space indicates more scattering channels, which consequently lead to high scattering rates^[50]. Additionally, redistribution processes (λ + λ′ → λ″+ λ‴) dominate the entire 4ph scattering phase space (W_4ph) because the energy selection rule is more readily satisfied. Previous investigations have demonstrated that the 4ph redistribution processes significantly hinder phonon propagation in highly anharmonic systems, emphasizing the importance of 4ph scattering processes^[51]. Moreover, the splitting (λ → λ′ + λ″+ λ‴) and recombination (λ + λ′+ λ″ → λ‴) within the 4ph scattering phase space align with the mechanisms of 3ph scattering interactions. Overall, compared with SnSe, NaSn₂SbSe₄ exhibits both larger Grüneisen parameters γ and a large 3ph and 4ph scattering phase space. These features consistently indicate that the enhanced three- and four-phonon scattering rates in NaSn₂SbSe₄ arise from stronger lattice anharmonicity and the availability of more scattering channels. Figure 3D shows the decomposition of the 4ph scattering rates into normal and Umklapp processes^[47,51]. Normal scattering processes primarily mediate the transfer of phonon momentum. In contrast, Umklapp processes generate heat conduction and impede phonon movement. Throughout the entire 4ph scattering processes, Umklapp processes are dominant, implying that the diminished κ_L primarily results from heat conduction. Building on the above analysis, the pronounced anharmonicity of NaSn₂SbSe₄ is attributed to the combined effects of Sb/Na-induced local structural disorder and the occupation of antibonding states arising from Sn(5s)/Sb(5s)-Se(4p) covalent interactions below the Fermi level. This conclusion is further supported by the high 3ph and 4ph scattering rates as well as the large Grüneisen parameter γ, collectively providing evidence that chemically engineered bonding plays a critical role in suppressing lattice thermal conductivity κ_L.

To systematically characterize the influence of structural disorder on electrical transport properties, we built a supercell and conducted a preliminary investigation of the electronic structure of NaSn₂SbSe₄, as shown in Supplementary Figures 5 and 6. Upon the incorporation of SOC in the calculations, NaSn₂SbSe₄ exhibits a relatively narrow band gap (~0.25 eV)^[52]. Furthermore, as shown in Supplementary Figure 6C, the charge density at the valence band maximum (VBM) demonstrates significant delocalization and hole transport pathways between the Sn and Se atoms. This is further supported by Supplementary Figure 7, where the projected density of states confirms the hybridization of Sn-5p and Se-4p orbitals, also highlighting their contribution to the valence band edge. The above observation not only indicates enhanced hole transport capability in NaSn₂SbSe₄ but also corroborates the prior chemical bonding analysis, which revealed that strengthened hybridization between Sn-5p and Se-4p orbitals leads to greater delocalization and increased covalency. This effect of strengthened hybridization gives rise to an electronic environment that modulates the band structure, thereby creating favorable conditions for carrier transport and electrical conductivity in NaSn₂SbSe₄^[33,53].

To comprehensively evaluate and compare the electronic transport properties of SnSe and NaSn₂SbSe₄, we employed Boltzmann transport theory to calculate and analyze how the Seebeck coefficient (S), electrical conductivity (σ), and PF vary with carrier concentration and temperature. As shown in Figure 4A, the Seebeck coefficients of SnSe and NaSn₂SbSe₄ display an inverse dependence on carrier concentration, initially increasing at low doping levels and then decreasing at higher concentrations. According to the Mott relation^[54], the Seebeck coefficient varies with carrier concentration n as S ∝ n^-2/3. At low p-type doping levels, the observed deviation from the expected trend can be attributed to the bipolar conduction effect induced by a small bandgap. This effect occurs because, although holes dominate charge transport at low carrier concentrations, intrinsically excited minority electrons also make a non-negligible contribution^[55]. The opposite-sign contributions of these two types partially compensate each other, thereby markedly suppressing the Seebeck response in the low-doping regime. By contrast, at high carrier concentrations, the Seebeck coefficient is mainly determined by the majority hole carriers and thus follows the expected trend.

The carrier relaxation time (τ) was calculated for SnSe and NaSn₂SbSe₄ according to the deformation potential theory^[56,57], with the results presented in Supporting Information Supplementary Table 4. NaSn₂SbSe₄ consistently demonstrates a longer relaxation time than SnSe at the same temperature. This behavior is primarily attributed to the reduction in the hole effective mass^[52,58]. Electrical conductivity was calculated based on the obtained relaxation time, and the results are shown in Figure 4B. At a given temperature, the electrical conductivities of SnSe and NaSn₂SbSe₄ increase with increasing charge carrier concentration. At the same temperature and carrier concentration, NaSn₂SbSe₄ shows higher electrical conductivity than SnSe, mainly because its longer relaxation time reduces electron scattering^[59]. For example, at a carrier concentration of 10²¹ cm^-3 and 600 K, the electrical conductivity increases from 1.976 × 10³ S cm^-1 in SnSe to 6.063 × 10³ S cm^-1 in NaSn₂SbSe₄. Moreover, the electronic thermal conductivity (κ_e) quantifies the contribution of charge carriers to thermal transport within the material. Supplementary Figure 8 presents the calculated κ_e values for SnSe and NaSn₂SbSe₄, showing that κ_e is higher in NaSn₂SbSe₄ than in SnSe under identical temperature and hole concentration conditions, which reflects proportional dependence on electrical conductivity.

The power factor PF, expressed as PF = S²σ, measures the effectiveness of electronic transport in thermoelectric materials. To further explore the contradictory dependence between the Seebeck coefficient and electrical conductivity, the power factors of SnSe and NaSn₂SbSe₄ were analyzed with respect to carrier concentration, as shown in Figure 4C. Despite the reduction in the Seebeck coefficient, the significant enhancement in electrical conductivity ensures that NaSn₂SbSe₄ maintains a higher optimal power factor compared to SnSe. Specifically, at 300 K, the peak power factor of NaSn₂SbSe₄ reaches 203.42 μW cm^-1 K^-2 at a hole concentration of 8.69 × 10²⁰ cm^-3, which is twice as high as that of SnSe.

Based on the analysis of structural features and chemical bonding characteristics, together with thermal and electrical transport properties, it is evident that, compared to SnSe, the incorporation of aliovalent cations in NaSn₂SbSe₄ induces pronounced local structural distortions and establishes a heterogeneous bonding environment. The Sb(5s)/Sn(5s)-Se(4p) antibonding states located below the Fermi level correlate with the softening of low-frequency optical phonon branches in NaSn₂SbSe₄. This softening, coupled with the strong lattice anharmonicity, significantly enhances four-phonon scattering rates and effectively suppresses the lattice thermal conductivity. Furthermore, the incorporation of aliovalent cations enhances the hybridization between Sn-5p and Se-4p orbitals, leading to greater electronic delocalization and increased covalency - factors that promote high carrier mobility and enable superior electrical conductivity. The synergistic optimization of low thermal conductivity and high electrical conductivity leads to a significant enhancement in thermoelectric performance. To assess its practical potential, we calculated the thermoelectric figure of merit, given by ZT = S²σT/ (κ_e + κ_L), with the results shown in Figure 5. The optimal ZT values of NaSn₂SbSe₄ surpass those of SnSe. Specifically, at 800 K, the maximum ZT value reaches 0.88 with an optimized carrier concentration of 2.39 × 10²⁰ cm^-3. These results demonstrate that the regulation of chemical bonding is a promising approach for enhancing the thermoelectric performance of SnSe-derived alloys such as NaSn₂SbSe₄, thereby validating its significant potential as a novel thermoelectric compound for practical applications. At the intermediate temperature of 600 K, the ZT value of NaSn₂SbSe₄ at the optimal carrier concentration is 0.75, surpassing the ZT value of 0.63 for SnSe. Furthermore, the ZT values calculated using κ_3ph are also presented as lower bounds (see Supplementary Figure 9), confirming the favorable thermoelectric properties of NaSn₂SbSe₄. Moreover, the temperature-dependent optimized ZT values of SnSe and NaSn₂SbSe₄ are plotted in Figure 5B, where NaSn₂SbSe₄ consistently demonstrates superior ZT values across the entire temperature range. Notably, the constructed crystal structure introduces only a limited degree of disorder that affects thermal transport, resulting in an overestimation of the lattice thermal conductivity and underestimation of the ZT values. The excellent thermoelectric performance of NaSn₂SbSe₄ highlights its potential as a high-performance thermoelectric material.