Main

Linear one-dimensional π-conjugated polymers (1DCPs)1 have attracted great interest as semiconductor materials2 in (opto)electronic devices such as organic solar cells, organic field-effect transistors and organic photodetectors3. In 1DCPs, charge conduction effectively occurs along the polymer chain, whereas the interchain charge transfer sets a bottleneck for charge transport via inefficient hopping4. By expanding the dimensionality of conjugated polymers, multiple charge transport strands can be established to bypass potential defects5, narrow the bandgap6 and suppress vibrational degrees of freedom7,8 to facilitate effective band-like transport8,9,10,11 in the resulting two-dimensional conjugated polymers (2DCPs), leading to enhanced electronic performance12 and potentially unique electronic structures (for example, Dirac cones)13,14.

In this context, two-dimensional π-conjugated covalent organic frameworks (2D c-COFs)15,16,17,18 represent a unique class of layer-stacked, crystalline 2DCPs with in-plane π-conjugation, which allow control over the spatial arrangement of molecular building blocks7,19. Despite the growing interest in developing 2D c-COFs20,21,22,23, they typically suffer from poor π-electron delocalization24 due to the polarized imine linkage25,26,27, which results in large bandgaps and inefficient charge transport28. Recent advances in vinylene-linked 2D c-COFs (or 2D poly(arylene vinylene)s29,30,31,32,33,34) have demonstrated enhanced π-conjugation along with high chemical/thermal stability. Nevertheless, these polymer materials are jet limited by inefficient conjugation, thus exhibiting weak or moderate in-plane dispersion in the energy band diagram8,11,15,34,35,36,37. Accordingly, the reported intrinsic charge carrier mobilities (without doping treatment37,38) remain moderate with values typically below ~20 cm2 V−1 s−1 (refs. 15,37).

To increase the effective π-conjugation length, ladder-type conjugated polymers39,40 (for example, graphene nanoribbons41 and poly(benzimidazobenzophenanthroline) (BBL)39,40 with two or more independent but tied strands of bonds) represent a unique molecular geometry, which consists of linearly fused aromatic subunits with strengthened parallel p-orbital interactions42 (versus single–double bond alternation in polyimines and poly(arylene vinylene)s). Although ladder-type 2DCPs15,42,43 can provide independent control over the molecular arrangements to enhance charge conduction, a rational design in their polymer backbones with considerable electronic band dispersion and strong π-electron delocalization to achieve high charge carrier mobility has remained unexplored.

Here we report the first examples of two phthalocyanine-based BBL-ladder-type crystalline 2DCPs (termed as 2DCP-MPc, where M = Cu or Ni) with unique band transport and outstanding charge carrier mobilities. To optimize the conjugation degree in 2DCPs, we investigate various conjugated linkages by theoretical computations on representative model compounds, and find that the BBL-ladder-type structure exhibits delocalized π-electrons with a narrow highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap. Thus, we synthesize 2DCP-MPcs via a p-toluenesulfonic acid (PTSA)-modulated polycondensation between octaaminophthalocyaninato metal(ii) and naphthalenetetracarboxylic dianhydride under solvothermal conditions. 2DCP-MPcs display narrow optical bandgaps of ~1.3 eV. Density functional theory (DFT) calculations reveal strongly dispersive valence and conduction bands and thus a low electron–hole reduced effective charge carrier mass (m*) of 0.137m0 and 0.172m0 for the layer-stacked 2DCP-NiPc and 2DCP-CuPc, respectively. Terahertz (THz) spectroscopy demonstrates a Drude-type charge transport behaviour with room-temperature scattering times up to 76 fs. The delocalized charge transport, together with the small m*, gives rise to exceptionally high electron–hole sum mobility of up to ~970 cm2 V−1 s−1 in 2DCP-NiPc, which is comparable to that of crystalline silicon and significantly exceeds those for reported 1DCPs and 2DCPs. Moreover, temperature-dependent THz photoconductivity measurements show negative temperature coefficients of mobility (dμ/dT < 0) in 2DCP-MPcs, consistent with phonon-scattering-limited band transport.

Results

Design principle of conjugated linkages in 2DCPs

To endow 2DCPs with highly extended π-delocalization, we first perform DFT calculations on various possible conjugated linkages of the photo-/electro-active building block phthalocyanine15,35 (the model compounds MX (Fig. 1a) are employed to simplify the calculation), such as imine in M1, imidazole of 2-phenylimidazole in M2, pyrazine in M3, vinylene in M4, partially reduced pyrazine in M5 and imidazole of perinone in M6 (BBL ladder type39). Their molecular electronic structures and HOMO–LUMO energy levels are compared in Fig. 1b and Supplementary Figs. 1–6. Despite the slight shift in the HOMO–LUMO energy levels (gap, ~2.02 eV; Fig. 1b), the π-electrons in M1−M3 are localized within the phthalocyanine moiety (Supplementary Figs. 1–3), which suggests ineffective π-conjugation. The vinylene groups in M4 and reduced pyrazine units in M5 bond the neighbouring phthalocyanines with delocalized HOMO electrons (Supplementary Figs. 4 and 5), resulting in simultaneously raised HOMO–LUMO energy levels (M1 as the reference) and diminished energy gaps (down to 1.93 and 1.74 eV, respectively). It is noteworthy that when BBL-type imidazole serves as the linkage, the LUMO level of M6 considerably decreases by 0.53 eV compared with M1, and the HOMO−LUMO gap is narrowed to 1.54 eV. We account for these observations by the favourable intramolecular charge transfer in the linear skeleton (Fig. 1c; note that the isomers of M6 are energetically less stable and show a negligible change in the electronic structures and HOMO–LUMO energy levels; Supplementary Figs. 6 and 7). We further calculate the electronic structures of the related 1DCPs, and find that the energy levels/gaps follow the same trend as that of the model compounds (Supplementary Figs. 8 and 9). Therefore, we envision that the development of BBL-ladder-type 2DCPs would confer a narrow bandgap and dispersive electronic bands to the 2D frameworks.

Fig. 1: Design principle of phthalocyanine-based 2DCPs.
figure 1

a, Schematic showing the phthalocyanine-based 2DCPs connected by different conjugated linkages (in the pale ellipses) and the selected model compounds MX (X = 1−6). C, grey; N, lavender; H, white. b, HOMO−LUMO energy levels and gaps of M1−M6. c, Molecular electronic structures of the frontier orbitals of M6.

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Synthesis and characterizations of 2DCPs

Due to the harsh conditions (for example, ~200 °C temperature) required for the imidazole ring formation from o-diamine and anhydride (Fig. 2a, dark yellow scheme), the synthesis of crystalline BBL-ladder-type 2DCPs has not been realized so far. To achieve the imidazole ring formation under benign conditions, we investigated the reaction mechanism via multiple model reactions (Supplementary Figs. 9–18 and Supplementary Schemes 1−3) and DFT calculations (Supplementary Figs. 19 and 20). The results reveal that an organic acid (that is, PTSA) enhances the reactivity due to its unique protonation–deprotonation ability, compared with basic or catalyst-free conditions (Supplementary Figs. 10 and 19 and Supplementary Scheme 1).

Fig. 2: Phthalocyanine-based BBL-ladder-type 2DCP-MPcs.
figure 2

a, Schematic of the formation of the imidazole ring and synthesis of model compounds 3 and 6. b, Schematic of the synthesis of 2DCP-MPc. c, Experimental (violet and blue lines), Pawley refined (black dotted lines) and calculated (dark blue lines for slipped AA stacking; Supplementary Information) PXRD patterns as well as their difference plots (dark red lines) of 2DCP-MPcs. The calculated PXRD patterns of AA- and AB-stacked 2DCP-CuPc are shown in the dark yellow and light blue lines, respectively. d, Models of the monolayer (C, grey; N, dark blue; O, red; Cu, dark yellow; H, white) and slipped-AA-stacked 2DCP-CuPc.

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We then synthesized the crystalline phthalocyanine-based BBL-ladder-type 2DCP-MPc by 2D polycondensation between octaaminophthalocyaninato metal(ii) (4-M, M = Cu or Ni) and naphthalenetetracarboxylic dianhydride (1) using PTSA as the catalyst and 1,3-dimethyl-2-imidazolidinone (DMI)/o-dichlorobenzene (v/v = 2/1) as the solvent at 200 °C for 5 days (Fig. 2b; the model compounds are shown in Fig. 2a and Supplementary Figs. 21 and 22). For 2DCP-CuPc, a powder X-ray diffraction (PXRD) analysis reveals its crystalline nature with distinct 2θ peaks at 4.62°, 8.18°, 12.17° and 26.82° (Fig. 2c, blue line), which can be assigned to the (100), (200), (400) and (002) crystallographic planes, respectively, for a slipped-AA-stacking geometry (Fig. 2c,d; Supplementary Figs. 23–28 provide details and discussion of the isomeric structures). Pawley refinement provides a PXRD pattern matching well with the experimental results, as evidenced by the low Rwp and Rp (reliability factors) values of 3.39% and 2.26%, respectively (Supplementary Fig. 29). As expected, 2DCP-NiPc displays similar PXRD pattern and stacking geometry to 2DCP-CuPc (Fig. 2c, violet line, and Supplementary Figs. 30 and 31).

Field-emission scanning electron microscopy and transmission electron microscopy images reveal ordered spherical aggregated polycrystals up to ~500 nm in diameter and lattice fringes with parameters of a = b = ~2.1 nm in 2DCP-MPcs (Supplementary Figs. 32–35). The Fourier-transform infrared spectra of 2DCP-MPcs show C=N and C=O stretching vibrations at 1,660 and 1,701 cm−1, respectively, indicating the formation of imidazole rings (Supplementary Fig. 36)44, which is further confirmed by solid-state nuclear magnetic resonance, Raman and X-ray photoelectron spectroscopies (Supplementary Figs. 37–41; Supplementary Figs. 42–45 provide other characterizations). The intense peaks at 1,582−1,603 cm−1 in the Raman spectra (Supplementary Fig. 41) can be assigned to the ring stretching (C=C) pattern, analogous to those G-band peaks in graphene nanoribbons41, indicative of efficient conjugation in 2DCP-MPcs.

Electronic band structures and effective mass calculation

We calculated the energy band diagrams of the 2DCP-MPc monolayers and the slipped-AA-stacked structures via DFT/Perdew–Burke–Ernzerhof method. The results suggest that both 2DCP-NiPc (Fig. 3a) and 2DCP-CuPc (Fig. 3b) monolayers are direct-bandgap semiconductors with highly dispersive valence band maximum (VBM); two bands are nearly degenerate at the Γ point, forming the conduction band minimum (CBM). Taking the 2DCP-CuPc monolayer as an example, the dispersed VBM leads to a small averaged hole effective mass (\({m}_{\rm{h}({\rm{avg}})}^{* }=2{[\frac{1}{{m}_{{\rm{h}}(\Gamma {\rm{X}})}^{* }}+\frac{1}{{m}_{{\rm{h}}(\Gamma {\rm{M}})}^{* }}]}^{-1}\)) of 0.369m0 (Supplementary Table 1). The degenerate, relatively flat and dispersive CBM values correspond to two types of electron mass (for example, 1.67m0 and 0.34m0, respectively, along the Γ–M direction). Taking into account masses along different directions, we obtained an averaged electron effective mass (\({m}_{\rm{e}({\rm{avg}})}^{* }\)) of 0.427m0 (Supplementary Fig. 46). Although the isomeric 2DCP-MPc can, in principle, exist (for example, at the edges of the crystal domains), they do not change the band structure of the 2DCP (for example, bandgap, dispersion and effective mass; Supplementary Fig. 47).

Fig. 3: Energy band diagrams of 2DCP-MPcs.
figure 3

a,b, Electronic band structures and PDOS (Cp, Np, Op and Cu/Nid) of 2DCP-NiPc (a) and 2DCP-CuPc (b) monolayers. c,d, Electronic band structures and PDOS of the slipped-AA-stacked 2DCP-NiPc (c) and 2DCP-CuPc (d). The Fermi energy is shifted to 0 eV.

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We then explored the electronic structures of the slipped-AA-stacked 2DCP-MPcs in the full K path in space to address the degeneration of conduction bands (Fig. 3c,d). The direct bandgaps of the slipped-AA-stacked 2DCP-MPcs are reduced with respect to the monolayers due to the interlayer π-interaction. From the projected density of states (PDOS), we observe considerable hybridization of the Cp, Np and Op orbitals at CBM, whereas only the contribution of the Cp orbital to VBM is evident; it is also clear that the metal centres (that is, Ni or Cu) barely hybridize with the polymer backbone composed of C, N and O elements. To understand the role of the metal centre in the electronic structure15, we project metal d-orbital-resolved band structures for the slipped-AA-stacked 2DCP-MPcs. Despite the similar PDOS, the Nid orbital contributes more than the Cud orbital to the band edges (Supplementary Fig. 48; Supplementary Fig. 49 shows the calculation for the model compounds), thus resulting in a smaller effective mass for 2DCP-NiPc than that for 2DCP-CuPc (0.137m0 versus 0.172m0, as shown below).

It is notable that the slipped-AA-stacked 2DCP-MPcs present significant dispersion in VBM and CBM (Fig. 3c,d). Such strongly dispersive bands have not been observed so far in other 2DCPs11,15. Moreover, the effective masses are found to be anisotropic (Supplementary Table 2). For instance, the slipped-AA-stacked 2DCP-NiPc shows the smallest hole and electron effective masses of 0.125m0 and 0.139m0, respectively, along the Γ−Y path (and 0.129m0 and 0.145m0 for 2DCP-CuPc), whereas the Γ−Z direction provides larger hole and electron effective masses of 0.803m0 and 1.664m0 (and 2.338m0 and 2.275m0 for 2DCP-CuPc), respectively. We then individually calculated the averaged hole or electron effective mass (\({m}_{\mathrm{h}({\rm{avg}})}^{* }{\rm{or}}\,{m}_{\mathrm{e}({\rm{avg}})}^{* }=n{[\frac{1}{{m}_{1}^{* }}+\frac{1}{{m}_{2}^{* }}+\frac{1}{{m}_{3}^{* }}+\ldots \frac{1}{{m}_{n}^{* }}]}^{-1}\)), aiming at evaluating the overall transport properties of the charge carriers along the slipped-AA-stacked 2DCP-MPc backbone, which yields 0.240m0 and 0.319m0 for 2DCP-NiPc (0.310m0 and 0.386m0 for 2DCP-CuPc), respectively. Based on the obtained \({m}_{\mathrm{h}({\rm{avg}})}^{* }\) and \({m}_{\mathrm{e}({\rm{avg}})}^{* }\) values, we further infer the electron–hole reduced effective mass (\({m}^{* }\); \(\frac{1}{{m}^{* }}=\frac{1}{{m}_{\mathrm{e}({\rm{avg}})}^{* }}+\frac{1}{{m}_{\mathrm{h}({\rm{avg}})}^{* }}\)) to be 0.137m0 and 0.172m0 for 2DCP-NiPc and 2DCP-CuPc, respectively.

Optical absorption and time-resolved THz spectroscopy

To experimentally explore their transport properties, we grew 2DCP-NiPc and 2DCP-CuPc films (with facile charge migration9,11,12 compared with the powder samples) on fused silica substrates in the polycondensation reaction mixtures (~1 μm thickness; Supplementary Figs. 50–57 provide the characterizations). The ultraviolet–visible–near-infrared absorption spectra of the 2DCP-MPc films show a broad Q-band absorption in the range of 550−1,000 nm (Fig. 4a, top). This result suggests a considerable π-electron delocalization, which contributes to optical bandgaps as low as 1.33 and 1.28 eV for 2DCP-NiPc and 2DCP-CuPc, respectively (the Tauc plots are shown in Fig. 4a; Supplementary Fig. 58 provides a discussion). These bandgap values are the smallest among the reported 2D c-COFs (Fig. 5b)15,45, confirming that the BBL-ladder-type structure confers a narrow bandgap onto the polymer backbone.

Fig. 4: Optical absorption spectra and time-resolved THz spectroscopy of 2DCP-MPcs.
figure 4

a, Ultraviolet–visible–near-infrared absorption of 2DCP-MPc films on fused silica and the starting monomers dissolved in dimethyl sulfoxide (top) and the Tauc plots of the 2DCP-MPcs (bottom). b, Time-resolved THz photoconductivity of 2DCP-CuPc and 2DCP-NiPc films. The samples were photoexcited by above-bandgap excitation using 1.55 eV ultrashort laser pulses. Here ∆σ is the photoinduced conductivity.

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We then performed time-resolved photoconductivity measurements on 2DCP-MPc films using THz spectroscopy (Methods describes its working principle). Briefly, following the photoinjection of free charge carriers into 2DCP-MPcs by above-bandgap optical femtosecond laser excitation (1.55 eV photon energy; Supplementary Fig. 59 provides the discussion), the high-frequency THz conductivity is determined using a freely propagating THz pulse. Figure 4b depicts the pump-induced conductivity, that is, photoconductivity (∆σ), of 2DCP-NiPc and 2DCP-CuPc films as a function of time after optical excitation. Both samples show very similar features in the ∆σ dynamics: although their sub-picosecond rise is associated with free carrier generation following optical excitation, the subsequent decay in ~20 ps follows a biexponential function (Supplementary Table 3; Supplementary Fig. 60 shows the fluence-dependent THz photoconductivity dynamics) and can be interpreted as free carrier localization (for example, due to trapping or exciton formation46) within the 2DCP-MPcs.

Frequency-resolved THz photoconductivity measurements

To elucidate the charge transport mechanism, we further measured the complex frequency-resolved photoconductivity (∆σ(ω)) on the 2DCP-MPc films (Fig. 5a). We find that the conduction of photogenerated charge carriers can be well described by the Drude model (Methods)—a characteristic response seen in conventional high-mobility inorganic semiconductors47, for example, GaAs and Si. From the best fit to the data, we can infer the averaged charge carrier scattering times (τ) and consequently estimate the charge carrier mobilities (μ) as follows: \(\mu =\frac{e\tau }{{m}^{\ast }}\), where e is the elementary charge. Owing to the long τ (76 ± 3 and 45 ± 3 fs) and small m* (0.137m0 and 0.172m0) of the slipped-AA-stacked 2DCP-NiPc and 2DCP-CuPc, respectively, the estimate yields exceptionally high mobilities of 971 ± 44 cm2 V−1 s−1 for 2DCP-NiPc and 460 ± 31 cm2 V−1 s−1 for 2DCP-CuPc at room temperature, superior to those of the reported linear conjugated polymers including graphene nanoribbons41, COFs (for example, 165 cm2 V−1 s−1 for TPB-TFB COF11) and metal–organic frameworks (MOFs; for example, 211 cm2 V−1 s−1 for Fe3(THT)2(NH4)39) characterized by THz spectroscopy (Fig. 5b and Supplementary Fig. 61; Supplementary Table 4 describes μ, τ and m*). The outstanding mobility and relatively long carrier lifetime (compared with COFs15,36,37 characterized by the same technique) lead to diffusion lengths of ~237 and ~157 nm for 2DCP-NiPc and 2DCP-CuPc, respectively. As part of control studies, we also measured 2DCP-NiPc and 2DCP-CuPc in powder forms, similarly displaying very high charge carrier mobility of 219 ± 14 and 183 ± 19 cm2 V−1 s−1, respectively (Supplementary Fig. 62), largely exceeding the state-of-the-art powder-based COFs and MOFs.

Fig. 5: Frequency-resolved THz photoconductivity of 2DCP-MPcs.
figure 5

a, Frequency-resolved complex THz photoconductivity measured at ~0.5 ps after the maximum photoconductivity of 2DCP-CuPc (top) and 2DCP-NiPc (bottom). The solid lines correspond to the Drude fits describing the real and imaginary parts of the complex THz photoconductivity. b, Comparison of charge carrier mobilities and optical bandgaps of 2DCP-MPcs with reported COFs (light wine spots) and MOFs (light blue spots) measured by THz spectroscopy at ambient temperature (Supplementary Fig. 61 and Supplementary Table 4 provide a comprehensive comparison and references). The reported powder samples exhibit mobilities below 70 cm2 V−1 s−1 (underneath the dashed reference line). c, T-dependent frequency-resolved complex THz photoconductivity measured at ~0.5 ps after the maximum photoconductivity of 2DCP-NiPc. The dashed line highlights the shift in the intersection of the real and imaginary components of the complex THz photoconductivity; the intersection corresponds to the momentum scattering frequency following the Drude model, which is inversely proportional to the mobility. d, T-dependent THz mobilities (left y axis) and scattering times (right y axis) of 2DCP-CuPc and 2DCP-NiPc. The error bars originate from the uncertainty of the obtained charge scattering time from the Drude fit. The dashed lines serve as guides to the eye.

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Discussion

The Drude-like photoconductivity dispersion and outstanding charge carrier mobility in 2DCP-MPcs demonstrate the band-like transport character of the samples. To gain further insight, we conduct temperature (T)-dependent photoconductivity on 2DCP-MPc films grown on fused silica. As shown in Supplementary Figs. 63 and 64, the photoconductivity amplitude goes up slightly by lowering T. To disentangle the contributions eventually arising from changes in μ and those linked to charge carrier density N (Δσ = e × µ × N), we performed T-dependent frequency-resolved complex conductivity ∆σ(ω) measurements (Fig. 5c). We find that all the photoconductivity spectra can be described well by the Drude model. The T-dependent τ is summarized in Fig. 5d. The inferred τ increases substantially for both samples (for example, from 76 ± 3 to 108 ± 7 fs for 2DCP-NiPc by lowering T from 298 to 78 K). These results indicate that electron–phonon scattering is dominant in determining the charge carrier mobility in 2DCP-MPcs, entirely consistent with the band-like transport picture. At 78 K, phonon scattering is minimized, and the obtained τ implies mobilities as high as 1,386 ± 96 and 706 ± 37 cm2 V−1 s−1 in 2DCP-NiPc and 2DCP-CuPc, respectively. We observed a higher carrier mobility and its stronger dependence of τ on T in 2DCP-NiPc compared with 2DCP-CuPc. This observation can, in part, be attributed to the lower charge carrier effective mass in 2DCP-NiPc, and further rationalized by a scenario in which 2DCP-NiPc suffers much less from defect scattering (due to, for example, better film quality and thus reduced defect density; Supplementary Figs. 52 and 53 show the film quality characterizations). Electron–phonon scattering-limited transport proves our design principle of high-mobility 2DCPs, that is, the BBL-ladder-type structure confers significant in-plane conjugation to the 2DCP-MPcs, leading to predominant intralayer charge transfer; further, the ordered crystalline polymer networks ensure relatively low defect and impurity densities. Moreover, the inferred plasma frequency squared (\({w}_{\rm{p}}^{2}\)) and thus N (N ≈ \(\frac{{w}_{\rm{p}}^{2}}{{m}^{* }}\)) are decreased by ~18% and ~34% for 2DCP-NiPc and 2DCP-CuPc, respectively, by lowering T from 298 to 78 K (Supplementary Fig. 65). This may be attributed, for example, to the more favorable internal conversion of free carriers to excitons at low temperatures, which reduces the free carrier population8.

In this work, we have demonstrated highly delocalized π-electrons and dispersive electronic bands in two phthalocyanine-based BBL-ladder-type crystalline, semiconducting 2DCPs. They present narrow optical bandgaps of 1.3 eV and a band transport feature with high charge mobility on the order of hundreds of cm2 V−1 s−1 at room temperature, showing the potential of 2DCPs in high-performance organic (opto)electronics. Further efforts to develop highly crystalline or single-crystalline 2DCP-MPcs and delaminate them into thin layers will not only enable a fundamental understanding of the structure–property relationships (by exploring the role of intrinsic and extrinsic contributions and minimizing the extrinsic influence) but also render the integration of high-mobility semiconducting 2DCPs into organic (opto)electronic and nanoelectronic devices.

Methods

Synthesis of 2DCP-MPcs

A glass ampule was charged with 4-M (ref. 15) (8.0 mg, 8.1 μmol), 1 (4.3 mg, 16.0 μmol), PTSA (6.2 mg, 32.6 μmol) and DMI/o-dichlorobenzene (0.4/0.2 ml). The ampule was sonicated at room temperature for 10 min, degassed by three freeze–pump–thaw cycles, sealed under a vacuum and heated at 200 °C for 5 days. After cooling to room temperature, the precipitate was filtered and sequentially washed with dimethylformamide, dimethyl sulfoxide, H2O, ethanol and acetone. After Soxhlet extraction with tetrahydrofuran (4 h), ethanol (8 h) and diethyl ether (2 h), the sample was collected and dried under a vacuum at 150 °C overnight to give 2DCP-MPcs as dark green powders in ~90% yield.

To prepare 2DCP-MPc as a thin-film sample, a fused silica substrate cleaned by piranha solution (at 120 °C for 5 h) was placed vertically in the above reaction mixture in DMI/o-dichlorobenzene (0.50/0.25 ml). The obtained film on the substrate was washed by immersing in dimethylformamide and then in acetone. Each solvent was changed three times. After natural drying, 2DCP-CuPc and 2DCP-NiPc were obtained as dark green and greyish green films on the fused silica substrates, respectively.

Electronic band structures and effective mass estimates

DFT calculations were carried out using the Vienna ab initio simulation package version 5.4.1 (Supplementary Information provides details and references). We used the DFT + U approach to describe the localized d orbitals of Cu and Ni ions. The effective Coulomb (U) and exchange (J) terms were set to 4 and 1 eV, respectively. A Monkhorst–Pack Γ-centred grid with dimensions of 2 × 2 × 1 was used for the k-point sampling of the Brillouin zone for the monolayer during geometry optimization and dimensions of 4 × 4 × 1 during band structure calculations. In the computational protocol for the three-dimensional stacking of the studied 2DCPs, the k-point grid dimensions were changed to 2 × 2 × 5 for geometry optimization and to 4 × 4 × 10 for the band structure calculations, and Grimme’s D2 correction for the interlayer dispersion interactions was applied. All the models were subjected to full geometry optimization (cell parameters and ionic positions). The corresponding electronic band structures were evaluated along the Γ–X–M–Γ and Γ–X|Y–Γ–Z|R2–Γ–T2|U2–Γ–V2 path in the Brillouin zone for the monolayer and multilayered structures, respectively. The effective masses for the electrons and holes were calculated by a parabolic fit of the VBM and CBM using the sumo Python toolkit48 or manually in the case of nearly degenerate electronic states.

Time- and frequency-resolved THz photoconductivity measurements

THz photoconductivity49 measurements were performed by an optical pump THz probe spectrometer. The setup was powered by a titanium:sapphire laser amplifier system, which generated ultrafast laser pulses with a central wavelength of 800 nm. The pulses have a duration of ~50 fs and a repetition rate of 1 kHz, which are further used for optical excitation, THz generation and detection. Single-cycle THz pulses of ~1 ps duration were generated via optical rectification by pumping a 1-mm-thick (110) ZnTe crystal with 800 nm laser pulses. The time-dependent electric field of the generated THz pulse was mapped out by free-space electro-optic sampling. The measurements were performed in the transmission mode in a dry N2 environment, and the samples were photoexcited by the 800 nm laser pulses with pump fluences in the range of ~0.4−6.2 mJ cm–2. The temperature-dependent photoconductivity measurements of 2DCP-MPc film samples were conducted in the presence of a cryostat under vacuum conditions (pressure < 2 × 10−4 mbar). By measuring the transmitted THz traces with and without photoexcitation in the time domain (Epump(t) and E0(t)) and further converting them into the frequency domain by Fourier transform (Epump(ω) and E0(ω)), we can obtain their complex photoconductivity (∆σ(ω)) as per the following thin-film approximation:

$$\Delta{\sigma} \left(\omega \right)=-\frac{{n}_{1}+{n}_{2}}{{Z}_{0}l}\times \frac{({E}_{{\rm{pump}}}\left(\omega \right)-{E}_{0}\left(\omega \right))}{{E}_{0}(\omega )},$$

where Z0 = 377 Ω is the impedance of free space; n1 and n2 are the refractive indices of the media before and after the sample, respectively; and l is the excitation thickness.

Here ∆σ(ω) of 2DCP-MPc films was described by the Drude model, which accounts for the transport of delocalized free carriers in the material:

$$\sigma \left({{\omega }}\right)=\frac{{{{\omega }}}_{\rm{p}}^{2}{\varepsilon }_{0}\tau }{1-{\rm{i}}{{\omega }}\tau },$$

where ωp, ε0 and τ are the plasma frequency, vacuum permittivity and Drude scattering time, respectively.

The diffusion length L can be deduced from the charge mobility μ and carrier lifetime t as follows:

$$L=\sqrt{D{{\times }}t},\,{\rm{where}}\,{D}=\frac{\mu {k}_{\rm{B}}T}{e}$$

and kB and T denote the Boltzmann constant and temperature, respectively.