Substituent-controlled quantum interference tuning of spin and thermoelectric transport in triphenylmethyl diradical junctions

Abstract

Achieving effective control of spin and thermoelectric transport at the molecular scale remains a key challenge for advancing next-generation molecular devices. In this study, we employ density functional theory (DFT) combined with the non-equilibrium Green's function (NEGF) method to systematically investigate the spin-resolved charge and thermoelectric transport properties of diradical molecular junctions, in which two triphenylmethyl (TPM) cores are symmetrically bridged by fluorene units functionalized with four different substituents. The results demonstrate that substituent-modulated charge transfer at the molecule–electrode interface can effectively regulate the spin transport properties of the molecular junction, leading to pronounced spin filtering and tunnel magnetoresistance effects. Furthermore, the characteristics of quantum interference and the resonance orbitals near the Fermi level (E_F) are highly sensitive to the nature of the substituents, resulting in significant variations in conductance and the Seebeck coefficient that synergistically enhance the thermoelectric performance. These findings provide guidelines for designing multifunctional molecular devices with enhanced spintronic and thermoelectric functionalities.

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1. Introduction

Molecular spintronics, an emerging field combining molecular electronics and spintronics, has attracted increasing attention for its application potential in next-generation nanoscale technologies, including high-density data storage, quantum computing, magnetic sensors, and spin caloritronic devices.^1–6 Recent advances in molecular design,^7–13 as well as in chemical functionalization and electrode–molecule interface engineering,^14–18 have provided promising strategies for spin injection, manipulation, and detection in molecular junctions (MJs). However, achieving stable and efficient spin transport remains a significant challenge, mainly due to the high sensitivity of molecular orbitals to structural conformation and interfacial coupling.^19–21 Consequently, it is essential to develop molecular design strategies for the precise and robust regulation of charge and spin transport.

With unpaired electrons and high electron affinity, radical molecules exhibit diverse spin states and pronounced charge-transfer behavior in MJs.^22–26 Compared to conventional closed-shell molecules, the frontier orbitals of radical molecules lie closer to the E_F, making them more prone to spin polarization and magnetic response.^27–29 For example, molecules functionalized with side-substituted radicals have been demonstrated to enable efficient spin filtering and significant magnetoresistance when incorporated into molecular junctions.^30,31 In addition, in π-conjugated radical systems, chemical modification of the radical sites can not only induce transitions between spin states but also trigger spin-dependent quantum interference, resulting in significant conductance variations in the two spin channels at room temperature.^32,33 Moreover, previous studies have demonstrated that destructive quantum interference (DQI) can markedly enhance the Seebeck coefficients (S) in thermoelectric devices, owing to the direct correlation between the S and the energy derivative of the electronic transmission spectrum.^26,34–36 Combined with the inherently lower thermal conductivity of MJs compared to conventional semiconductors,^37–40 the overall thermoelectric performance of the devices can be synergistically improved, as quantified by the dimensionless figure of merit ZT = S²σT/κ.

Triphenylmethyl (TPM) groups, carbon-centered open-shell molecules stabilized by the steric hindrance of their three phenyl rings and π-electron delocalization, find extensive applications in molecular spintronics, catalysis, optics, and sensing fields.^41–45 Moreover, through rational chemical design, two TPM units can be linked via functionalized molecular bridges to form diradical systems, thereby enabling controllable spin interactions and tunable electronic properties for molecular devices.⁴⁶ Recent work reported by Euringer et al. showed that the electronic coupling and magnetic exchange in bridged bis-triarylamine (TAA) systems can be systematically tuned by modifying the electron density of the bridging unit.⁴⁷ Inspired by this, in the present work, we theoretically investigate the spin-dependent charge and thermoelectric transport properties of substituted TPM-based diradical molecular junctions. The results indicate that substituents can effectively regulate the spin transport properties of molecular junctions by modulating charge transfer at the molecule–electrode interface, resulting in pronounced spin filtering and tunneling magnetoresistance effects. Furthermore, the nature of the substituents strongly affects quantum interference and the resonance orbitals near the E_F, leading to significant variations in conductance and the Seebeck coefficient that synergistically enhance thermoelectric performance. Notably, the maximum spin-dependent figure of merit reaches up to 15.5.

2. Methodology

Fig. 1(a) illustrates the schematic configuration of MJs, in which two triphenylmethyl units are symmetrically linked by a fluorenyl bridge with various substituents (thiofulvalene, dimethyl, keto, and dicyanovinylene) and covalently attached to semi-infinite Au (111) electrodes via thio (–S) anchors. For simplicity, the MJs are denoted as R1, R2, R3, and R4 according to their substituents. The spin-dependent charge transport properties are investigated using the NEGF-DFT framework as implemented in the Atomistix Toolkit package.⁴⁸ The exchange–correlation functional is described within spin-polarized generalized gradient approximation (SGGA) of the Perdew–Burke–Ernzerhof (PBE) method. A single-ζ polarization (SZP) basis set is used for Au atoms, while a double-ζ polarization (DZP) basis set is employed for all other atomic species. To balance computational accuracy and efficiency, a mesh cutoff of 300 Ry is used with Brillouin zone sampling using 3 × 3 × 100 k-points. The self-consistent energy tolerance is set to 10⁻⁵ eV, whereas the residual forces on all the atoms are less than 0.05 eV Å⁻¹. The initial spin orientations were defined by assigning a net spin of +1 µB to each triphenylmethyl radical center for the FM state, and antiparallel spins for the AFM state. The spin-dependent current generated through the MJs is obtained using the Landauer–Büttiker current formula,^49,50where n_f(ε) denotes the Fermi–Dirac distribution function and μ_L/R represents the chemical potential of the left/right electrode. The spin-dependent transmission coefficients can be given by T_σ(ε) = Tr[G^rΓ_LG^aΓ_R]^σ.

Fig. 1 (a) Schematic of a molecular junction consisting of two triphenylmethyl groups bridged by a fluorene unit, with different substituents functionalized to the fluorene. (b)–(e) Spin-resolved molecular orbital energies and the corresponding spin-density distributions for the four substituted molecules (R1–R4). Red and blue lines denote spin-up and spin-down states, respectively. The isosurfaces (± 0.002 e Å⁻³) illustrate the spatial localization of spin density.

Besides, the spin thermoelectric transport properties are calculated using the MATLAB codes. The Seebeck coefficient can be expressed as,

where the intermediate function L_n,σ(μ,T) is defined as,

3. Results and discussion

To explore the electronic properties of the four molecules (R1–R4), we first analyzed the spin-resolved molecular energy levels and the corresponding spin density distributions of the four molecules in the ferromagnetic (FM) configuration, as shown in Fig. 1(b)–(e). For R1 and R2 with electron-donating substituents, a pronounced spin polarization is observed near the E_F, where the spin-up and spin-down orbitals exhibit nearly mirror-symmetric distribution. In contrast, orbitals far from the E_F remain largely spin-degenerate, indicating that electron-donating substituents do not significantly alter the spin-related properties of the molecule. By comparison, R3 and R4 with electron-withdrawing substituents show an obvious rearrangement of molecular orbitals near E_F. Specifically, the unoccupied orbitals shift downward toward the E_F, while the occupied orbitals move upward, indicating strong acceptor-induced modifications of the electronic structure. The corresponding spin density distributions further corroborate this observation. The spin states of all four molecules are predominantly localized on the two triphenylmethyl units, whereas the contribution from the central fluorene bridge is negligible. Notably, the presence of electron-donating substituents further suppresses the spin density on the fluorene bridge.

The spin-resolved transmission spectra of the four MJs under FM configuration are presented in Fig. 2(a)–(d). Clearly, all junctions except R4 exhibit pronounced spin polarization near the E_F. Specifically, the transmission characteristics of the junctions are relatively similar below E_F. However, above E_F, R1–R3 display spin-up resonant transmission peaks near E_F, whereas the spin-down channels show resonant features around 0.25 eV. At higher energies, sharp transmission dips appear in the spin-up channels of R1 (1.38 eV) and spin-down channels of R3 (0.75 eV), indicative of destructive quantum interference (DQI).^51–53 In contrast, R2 shows a much more gradual attenuation of transmission with energy. Notably, although the isolated R4 molecule exhibits intrinsic spin polarization arising from unpaired π electrons, this effect is quenched in the device configuration. This behavior arises because the electron-withdrawing groups substantially lower the molecular orbital energy levels, bringing the lowest unoccupied molecular orbitals (LUMOs) closer to the electrodes' E_F and facilitating electron transfer to high-work function Au.^54–56 Mulliken population analysis (see the SI, Table S1) reveals a charge transfer of 0.30 e, which quenches the unpaired electron and converts the system into a closed-shell configuration, resulting in no spin-polarized transport for R4. Furthermore, the spin-resolved transmission spectra under the antiferromagnetic (AFM) configuration (see the SI, Fig. S1) reveal that all four molecular junctions preserve similar quantum interference and Fano resonance features within the energy range of −2 to 2 eV. The corresponding mechanisms and characteristics are elaborated in detail in the SI, Section S2.

Fig. 2 (a)–(d) The energy dependence of the spin-resolved electron transmission spectra for four different devices in the parallel spin configuration. The transmission spectra for spin-up and spin-down are represented by red and blue curves, respectively, while the energy levels corresponding to the molecular orbital eigenvalues are indicated by red and blue triangles.

To elucidate the quantum interference (QI) mechanisms in R1–R3 molecular junctions, we conducted molecular orbital (MO) analysis following Yoshizawa et al.'s approach, which identifies QI features by examining the phase, amplitude, and spatial distribution of MOs at electrode-contacting atoms.⁵⁷ The final conductance depends on (where C_l,i and represent the MO coefficients of orbital i at the left and right contact sites, respectively). As shown in Fig. 3, for the spin-up channel of R1, the MO coefficients of the two sulfur atoms are both negative in LUMO+1 and both positive in LUMO+2. These opposite-phase contributions from LUMO+1 and LUMO+2 effectively cancel each other, resulting in DQI in R1. Similarly, in the spin-down channel, the contributions from LUMO+2 and LUMO+3 also interfere destructively, resulting in DQI. While for R2 MJs, the MO coefficients on the sulfur atoms are opposite in sign for the LUMO and identical for LUMO+1 in both spin channels. This phase relationship yields a negative product for the LUMO and a positive product for LUMO+1, resulting in CQI. In the case of R3, for both spin channels, the relevant orbitals (LUMO+1 and LUMO+2 or LUMO+2 and LUMO+3) show positive coefficients on the sulfur atoms, resulting in DQI similar to that in R1. To further support the QI analysis, we computed the spin-resolved transmission pathways and eigenchannels for R1–R4 (see the SI, Fig. S2 and S3). The transmission pathways reveal strong electron scattering from the radical groups and backward transmission signals at the molecule–electrode interfaces, indicative of interference effects. Moreover, the spin-up eigenchannels in R1–R3 display delocalized distributions across the junctions, consistent with enhanced transmission. These observations further elucidate the influence of substituent groups on spin-dependent transport characteristics.

Fig. 3 Spatial distributions of the frontier MPSH orbitals of R1–R3 in the molecular junctions. The red and blue colors represent the positive and negative phases of the molecular orbitals, respectively. An isovalue of 0.02 a.u. is used and the coefficients at the anchoring sulfur atoms are labeled as +1 and −1.

Furthermore, to verify that quantum interference persists under practical operating voltages, we calculated the spin-resolved transmission spectra of R1 within a bias range of −0.2 to 0.2 V (see the SI, Fig. S4). The results demonstrate that the interference features remain clearly visible throughout this bias window, confirming the robustness of the interference behavior and highlighting its potential applicability in practical device operations.

To further explore the transport properties of the R1–R4 systems, the calculated spin-resolved current–voltage (I–V) characteristics are presented in Fig. 4. It can be seen that the MJs of R1–R3 exhibit pronounced spin-polarized transport, in sharp contrast to the nearly spin-symmetric behavior of R4. For the MJs of R1 and R2, the spin-down current is almost completely suppressed across the entire bias range, whereas the spin-up current increases approximately linearly within −0.1 to 0.1 V and subsequently exhibits distinct negative differential resistance (NDR) beyond this range. Consequently, a nearly 100% spin filtering efficiency (SFE), defined as SFE = (I_up − I_down)/(I_up + I_down), is achieved in the low-bias region for both R1 and R2. For R3, the spin-down current is partially activated because the LUMO-derived resonance lies closer to the E_F, yet it remains substantially lower than the spin-up current. Notably, the spin-up channel also displays clear NDR behavior at biases above ±0.15 V. In contrast, R4 does not exhibit distinct I–V characteristics. Within the same bias range, the spin-up and spin-down currents are nearly identical, resulting in a spin polarization efficiency close to zero, suggesting negligible spin selectivity for R4.

Fig. 4 (a)–(d) Spin-resolved current–voltage (I–V) characteristics of the R1–R4 molecular junctions, respectively, under the FM magnetic configuration. Red squares and blue circles denote spin-up and spin-down currents, respectively, and the insets display the corresponding spin-filtering efficiency.

In addition, we have also calculated the current–voltage (I–V) characteristics of R1–R4 under the AFM configuration, as shown in Fig. 5. Notably, although the spin-resolved transmission spectra remain nearly spin-degenerate at zero bias under the AFM configuration (see the SI, Fig. S1), the application of a finite bias induces a certain amount of spin polarized in the current of the molecular junctions, with the exception of R4. To understand the origin of this bias-induced spin selectivity, we examined the projected density of states (PDOS) under different bias voltages, as shown in the SI, Fig. S5. It is evident that the spin symmetry of PDOS around the E_F is gradually broken as the bias increases. The spin-up states experience an upward shift, whereas the spin-down states move downward in energy, thereby inducing an imbalance in the transmission channels for opposite spins. This asymmetric redistribution of density of states near the transport window effectively leads to spin-polarized current even in the antiferromagnetic ordering. The bias-driven modification of the local electronic structure thus plays a crucial role in triggering spin filtering behavior in the AFM state. In contrast, the degree of such splitting in R4 is less pronounced, likely due to the relative alignment of frontier molecular orbitals being less sensitive to the applied electric field. These findings highlight that the interplay between molecular orbital alignment and bias-induced symmetry breaking can give rise to finite spin polarization even in AFM-configured molecular junctions, providing an alternative route for achieving spin-dependent transport without requiring a ferromagnetic ground state. Given the substantial differences in the I–V characteristics between the FM and AFM configurations, we further evaluated the tunnel magnetoresistance (TMR), defined as TMR = (I_PC − I_APC)/I_APC as shown in the inset of Fig. 5. The results show that the maximum TMR values for R1–R3 reach approximately 900%, 600%, and 300%, respectively. These findings highlight the critical role of substituents in modulating spin transport in long-range organic radical molecules.

Fig. 5 (a)–(d) Current–voltage characteristics of R1–R4, respectively, in the AFM spin configuration. The inset shows the TMR for R1–R3.

Building on the favorable electronic properties discussed above, we further applied a temperature gradient across the electrodes to explore the spin-dependent thermoelectric transport characteristics. The calculated spin-resolved Seebeck coefficients and electronic conductance are presented in Fig. 6. As shown in Fig. 6(a)–(c), the S for both spin channels exhibit pronounced oscillations as a function of energy, with the peak values reaching 800 µV K⁻¹. This behavior is consistent with the relation S ∝ −∂_E ln T(E).⁵⁸ In particular, the asymmetry between S_up and S_down around E_F results in an enhanced spin-dependent Seebeck coefficient (S_sp = S_up − S_down). Besides, distinct Seebeck peaks are observed near 1.3 eV and 0.8 eV for R1 and R3, respectively, which can be attributed to DQI effects, with the maximum values of S_down reaching 571 µV K⁻¹ and 597.8 µV K⁻¹. Additionally, the conductance characteristics of the three MJs are shown in Fig. 6(d)–(f). Within the energy range of −1 to 2 eV, the charge conductance (G_ch = G_up + G_down) curve almost coincides with the spin-dependent conductance (G_sp = |G_up − G_down|) curve. This similarity arises mainly because both the spin-up and spin-down conductances are dominated by the highest occupied molecular orbital (HOMO) and the LUMO, respectively (see the insets of Fig. 6(d)–(f)).

Fig. 6 (a)–(c) Spin-up (S_up), spin down (S_down), charge (S_ch) and spin-dependent (S_sp) Seebeck coefficients as a function of energy at room temperature for the R1, R2, and R3 molecular junctions, respectively. (d)–(f) Charge-dependent (G_ch) and spin-dependent (G_sp) for the corresponding MJs.

To further investigate the spin-dependent thermoelectric properties of the R1–R3 MJs, we calculated the power factor (S²σ), the electronic and phononic contributions to the thermal conductivity (κ_el and κ_ph), and the resulting final figure of merit (ZT), as shown in Fig. 7. As illustrated in Fig. 7(a), the spin-related power factor (PF_sp) of all three MJs markedly exceeds the charge-related power factor (PF_ch), with maximum PF_sp values reaching 5.7, 6.6, and 3.4 pw K⁻² for R1, R2, and R3, respectively. This substantial difference highlights the potential of spin-related effects to enhance thermoelectric performance. The electronic thermal conductivity (κ_el) of the molecular junctions was calculated directly from the spin-resolved transmission spectra T(E) using the Landauer–Büttiker formalism, defined as: κ_el = κ_up + κ_down. Fig. 7(b) and (c) show κ_el and κ_ph for the three MJs. The κ_el curves show sharp peaks near the E_F, with R3 exhibiting the highest peak value of approximately 129.8 pW K⁻¹, indicating strong electronic heat transport around the resonance energy. In contrast, the κ_ph values of the three MJs gradually increase with temperature and tend to saturate around 300 K, reaching values of 36.63, 34.32, and 31.75 pW K⁻¹ for R1, R2 and R3, respectively. Notably, these values are about 3–4 times lower than their corresponding κ_el, suggesting that thermal transport is predominantly governed by electrons. It means that the introduction of appropriate substituents can effectively tune both electronic and phononic contributions to thermal transport, optimizing the overall thermoelectric performance of molecular junctions. To further evaluate the overall thermoelectric performance of the three MJs, we calculated the ZT values at room temperature, as shown in Fig. 7(d). It is evident that the overall ZT of the three MJs is mainly determined by the ZT_sp, with the maximum values of 11.4, 15.5, and 8.8 for R1, R2, and R3, respectively. These values are significantly higher than the corresponding maximum ZT_ch values of 5.3, 6.8, and 4.9. It should be emphasized that the reported ZT_sp value is a theoretical prediction under idealized model conditions, and does not directly correspond to a practically achievable experimental value at this stage. This result is consistent with previous theoretical reports on spin-dependent thermoelectric performance in molecular junctions.^59,60 In addition, we have also calculated the temperature dependence of thermoelectric properties for the three MJs at E_F as shown in Fig. S7 (see the SI). It suggests that both PF_sp and ZT_sp will increase with temperature up to a maximum value, and then decrease with higher temperature, which is consistent with the trends observed in other studies.^61,62 These findings demonstrate that the combined effects of tunable molecular substituents and stable radical groups are a highly effective strategy to enhance the spin thermoelectric performance of the molecular junctions.

Fig. 7 Room-temperature thermoelectric properties of R1, R2, and R3 molecular junctions with respect to charge and spin contributions: (a) power factor (S²σ); (b) electronic thermal conductivity (κ_e); (c) phononic thermal conductivity (κ_ph); and (d) thermoelectric figure of merit (ZT), decomposed into charge-driven (ZT_ch) and spin-driven (ZT_sp) components.

4. Conclusion

In summary, we have systematically studied the spin-resolved charge and thermoelectric transport properties of diradical molecular junctions, employing DFT and NEGF methods. The results reveal that substituent-modulated charge transfer at the molecule–electrode interface plays a crucial role in controlling the spin transport properties, resulting in pronounced spin filtering and tunnel magnetoresistance effects. The quantum interference and resonance orbital characteristics near the E_F are highly sensitive to the nature of the substituents, which leads to significant variations in both conductance and the Seebeck coefficient. These variations synergistically enhance the thermoelectric performance of the junctions. The maximum ZT_sp value in the R2 junction reaches as high as 15.5. The findings offer valuable insights into the design of multifunctional molecular devices with improved spintronic and thermoelectric functionalities, providing a promising strategy for enhancing spin filtering efficiency and thermoelectric performance by modulating substituent effects at the molecular scale.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp03724g.

Acknowledgements

This work was supported by the Natural Science Foundation of Jiangxi Province (Grant No. 20242BAB26013), Jiangxi Provincial Cultivation Program for Academic and Technical Leaders of Major Subjects (20243BCE51080), and the Scientific Research Fund of Jiangxi Provincial Education Department (Grant No. GJJ210840).

References

1. L. Guo, X. Gu, X. Zhu and X. Sun, Adv. Mater., 2019, 31, 1805355.
2. E. Moreno-Pineda and W. Wernsdorfer, Nat. Rev. Phys., 2021, 3, 645–659.
3. G. Yang, L. Sang, C. Zhang, N. Ye, A. Hamilton, M. S. Fuhrer and X. Wang, Nat. Rev. Phys., 2023, 5, 466–482.
4. E. Coronado, Nat. Rev. Mater., 2020, 5, 87–104.
5. D. Wu, X.-Y. Liu, B.-Y. Gan, W.-S. Tang, Z.-Q. Fan and X.-H. Cao, Appl. Phys. Lett., 2024, 125, 093901.
6. M. V. Vaganov, N. Suaud, F. Lambert, B. Cahier, C. Herrero, R. Guillot, A.-L. Barra, N. Guihéry, T. Mallah and A. Ardavan, Nat. Chem., 2025, 1–7.
7. J. Yi, G. Zhang, H. Yu and H. Yan, Nat. Mater., 2024, 9, 46–62.
8. Y. Zheng, S. Zhang, J. B.-H. Tok and Z. Bao, J. Am. Chem. Soc., 2022, 144, 4699–4715.
9. T. Zhang, T. Li, J. Li, Z. Yu, H. Chen, M. Li, J. Yu, S. Zhen and Z. Zhao, Chem. Eng. J., 2025, 165691.
10. I. A. Elayan, M. Zhou and A. Brown, Phys. Chem. Chem. Phys., 2025, 27, 3873–3884.
11. M. Smeu, O. L. Monti and D. McGrath, Phys. Chem. Chem. Phys., 2021, 23, 24106–24110.
12. P. Zhang, S. Tang, D. Wan, X. Li, P. Ai, W. Guo, T. Yan, Y. Zhang, Q. Li and S. Bai, Chem. Mater., 2025, 37, 1891–1905.
13. D. Wu, X.-H. Cao, S.-Z. Chen, L.-M. Tang, Y.-X. Feng, K.-Q. Chen and W.-X. Zhou, J. Mater. Chem. A, 2019, 7, 19037–19044.
14. M. Ge, Z. Liu, T. Chen, L. Xu and L. Huang, Phys. Chem. Chem. Phys., 2025, 27, 6255–6262.
15. N. Xin, J. Guan, C. Zhou, X. Chen, C. Gu, Y. Li, M. A. Ratner, A. Nitzan, J. F. Stoddart and X. Guo, Nat. Rev. Phys., 2019, 1, 211–230.
16. C. R. Prindle, W. Shi, L. Li, J. Dahl Jensen, B. W. Laursen, M. L. Steigerwald, C. Nuckolls and L. Venkataraman, J. Am. Chem. Soc., 2024, 146, 3646–3650.
17. E. York, I. Stone, W. Shi, X. Roy and L. Venkataraman, Nano Lett., 2025, 25, 13697–13702.
18. X. Wei, X. Cao, J. Hao, X. Chang, P. Duan, L. Cheng, K. Chen, J. Wang, C. Jia and X. Guo, Chem. Eng. J., 2024, 500, 157053.
19. C. Nicolaides, E. Nicolaidou, P. Papagiorgis, G. Itskos, S. C. Hayes and T. Trypiniotis, Phys. Rev. Mater., 2022, 6, 095601.
20. S. Xia, X. Xu, Y. Tian, J. Zhong and Z. Yang, Appl. Surf. Sci., 2025, 688, 162367.
21. L. Huang, Y.-J. Zeng, D. Wu, N.-N. Luo, Y.-X. Feng, Z.-Q. Fan, L.-M. Tang and K.-Q. Chen, J. Mater. Chem. C, 2021, 9, 5876–5884.
22. L. Li, C. R. Prindle, W. Shi, C. Nuckolls and L. Venkataraman, J. Am. Chem. Soc., 2023, 145, 18182–18204.
23. R. Andika, G. G. Redhyka, R. Yamada and H. Tada, Phys. Chem. Chem. Phys., 2025, 27, 13812–13816.
24. C. Franco, P. M. Burrezo, V. Lloveras, R. Caballero, I. Alcón, S. T. Bromley, M. Mas-Torrent, F. Langa, J. T. Lopez Navarrete and C. Rovira, J. Am. Chem. Soc., 2017, 139, 686–692.
25. L. Wang, W. Peng, N. Chen, Y. Xie, S. Qiu and Y. Li, Analyst, 2025, 150, 4997–5005.
26. Y.-C. Chen and Y.-C. Chang, ACS Nano, 2025, 19, 34906–34917.
27. Y. Zhao, K. Jiang, C. Li, Y. Liu, C. Xu, W. Zheng, D. Guan, Y. Li, H. Zheng and C. Liu, J. Am. Chem. Soc., 2020, 142, 18532–18540.
28. H. Liu, M. B. Plenio and J. Cai, Phys. Rev. Lett., 2017, 118, 200402.
29. L. Li, J. Z. Low, J. Wilhelm, G. Liao, S. Gunasekaran, C. R. Prindle, R. L. Starr, D. Golze, C. Nuckolls and M. L. Steigerwald, Nat. Chem., 2022, 14, 1061–1067.
30. R. Hayakawa, M. A. Karimi, J. Wolf, T. Huhn, M. S. Zöllner, C. Herrmann and E. Scheer, Nano Lett., 2016, 16, 4960–4967.
31. M. Suda, Y. Thathong, V. Promarak, H. Kojima, M. Nakamura, T. Shiraogawa, M. Ehara and H. M. Yamamoto, Nat. Commun., 2019, 10, 2455.
32. Y. Chelli, S. Sandhu, A. H. Daaoub, S. Sangtarash and H. Sadeghi, Nano Lett., 2023, 23, 3748–3753.
33. L. Huang, J. Wang, T. Chen, L. Xu, F. Ning, D. Wu and K.-Q. Chen, Appl. Phys. Lett., 2024, 124, 102403.
34. M. H. Garner, H. Li, Y. Chen, T. A. Su, Z. Shangguan, D. W. Paley, T. Liu, F. Ng, H. Li and S. Xiao, Nature, 2018, 558, 415–419.
35. R. Miao, H. Xu, M. Skripnik, L. Cui, K. Wang, K. G. Pedersen, M. Leijnse, F. Pauly, K. Warnmark and E. Meyhofer, Nano Lett., 2018, 18, 5666–5672.
36. J. P. Bergfield, Nano Lett., 2024, 24, 15110–15117.
37. X.-K. Chen, J. Zhu, M. Qi, P.-Z. Jia and Z.-X. Xie, Phys. Rev. Appl., 2025, 23, 034085.
38. W. X. Zhou, Y. Cheng, K. Q. Chen, G. Xie, T. Wang and G. Zhang, Adv. Funct. Mater., 2020, 30, 1903829.
39. L. Cui, S. Hur, Z. A. Akbar, J. C. Klöckner, W. Jeong, F. Pauly, S.-Y. Jang, P. Reddy and E. Meyhofer, Nature, 2019, 572, 628–633.
40. P.-Z. Jia, L.-Q. Deng, X.-K. Chen, Z.-X. Xie and K.-Q. Chen, Appl. Phys. Lett., 2025, 127, 044052.
41. F. Bejarano, I. J. Olavarria-Contreras, A. Droghetti, I. Rungger, A. Rudnev, D. Gutiérrez, M. Mas-Torrent, J. Veciana, H. S. Van Der Zant and C. Rovira, J. Am. Chem. Soc., 2018, 140, 1691–1696.
42. A. M. Heuer, S. C. Coste, G. Singh, B. Q. Mercado and J. M. Mayer, J. Org. Chem., 2023, 88, 9893–9901.
43. M. E. Arnold, A. Lebzelter, P. Thielert, R. Blinder, J. Schmid, J. Zolg, E. Spatola, F. Jelezko, M. von Delius and S. Richert, Chem. Sci., 2025, 16, 14616–14624.
44. P. Murto, B. Li, Y. Fu, L. E. Walker, L. Brown, A. D. Bond, W. Zeng, R. Chowdhury, H.-H. Cho and C. P. Yu, J. Am. Chem. Soc., 2024, 146, 13133–13141.
45. N. Asanbaeva, D. S. Novopashina, O. Y. Rogozhnikova, V. M. Tormyshev, A. Kehl, A. Sukhanov, A. V. Shernyukov, A. Genaev, A. A. Lomzov and M. Bennati, Phys. Chem. Chem. Phys., 2023, 25, 23454–23466.
46. V. Lloveras, J. Vidal-Gancedo, T. M. Figueira-Duarte, J.-F. Nierengarten, J. J. Novoa, F. Mota, N. Ventosa, C. Rovira and J. Veciana, J. Am. Chem. Soc., 2011, 133, 5818–5833.
47. L. Euringer, M. Holzapfel, I. Krummenacher, M. Franz, S. Richert, H. Braunschweig and C. Lambert, J. Am. Chem. Soc., 2024, 146, 27679–27689.
48. S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellendorff, J. Schneider, T. Gunst, B. Verstichel, D. Stradi, P. A. Khomyakov and U. G. Vej-Hansen, J. Phys.: Condens. Matter., 2019, 32, 015901.
49. R. Landauer, Philos. Mag., 1970, 21, 863–867.
50. M. Büttiker, Phys. Rev. Lett., 1986, 57, 1761.
51. J. E. Greenwald, J. Cameron, N. J. Findlay, T. Fu, S. Gunasekaran, P. J. Skabara and L. Venkataraman, Nat. Nanotechnol., 2021, 16, 313–317.
52. J. Bai, A. Daaoub, S. Sangtarash, X. Li, Y. Tang, Q. Zou, H. Sadeghi, S. Liu, X. Huang and Z. Tan, Nat. Mater., 2019, 18, 364–369.
53. P. Li, S. Hou, B. Alharbi, Q. Wu, Y. Chen, L. Zhou, T. Gao, R. Li, L. Yang and X. Chang, J. Am. Chem. Soc., 2022, 144, 15689–15697.
54. A. Daaoub, L. Ornago, D. Vogel, P. Bastante, S. Sangtarash, M. Parmeggiani, J. Kamer, N. Agraït, M. Mayor and H. van der Zant, J. Phys. Chem. Lett., 2022, 13, 9156–9164.
55. H. Guo, C.-Y. Yang, X. Zhang, A. Motta, K. Feng, Y. Xia, Y. Shi, Z. Wu, K. Yang and J. Chen, Nature, 2021, 599, 67–73.
56. J. Park, L. Belding, L. Yuan, M. P. Mousavi, S. E. Root, H. J. Yoon and G. M. Whitesides, J. Am. Chem. Soc., 2021, 143, 2156–2163.
57. K. Yoshizawa, T. Tada and A. Staykov, J. Am. Chem. Soc., 2008, 130, 9406–9413.
58. Z. K. Ding, Y. J. Zeng, W. Liu, L. M. Tang and K. Q. Chen, Adv. Funct. Mater., 2024, 34, 2401684.
59. Y. Dubi, M. Di Ventra and M. Physics, Phys. Lett. A, 2009, 79, 081302.
60. S. Koley, R. Bhowmick, S. Sen, S. Chakrabarti and C. O. Solids, J. Phys. Chem. Solids., 2021, 153, 110009.
61. Q. H. Al-Galiby, H. Sadeghi, D. Z. Manrique and C. J. Lambert, Nanoscale, 2017, 9, 4819–4825.
62. B. Qin, D. Wang, X. Liu, Y. Qin, J.-F. Dong, J. Luo, J.-W. Li, W. Liu, G. Tan and X. Tang, Science, 2021, 373, 556–561.

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