Dimensional Control of Excitonic Interactions in Exfoliated 2D Molecular Crystals

Introduction

Understanding excitons and their behavior in the low-dimensional limit has profoundly influenced modern materials science, as dimensional reduction can fundamentally reshape how electronic excitations are generated, propagate and decay, as shown in quantum dots and carbon nanotubes. Such quantum confinement effects are also manifested in two-dimensional (2D) materials in a distinctive manner[1, 2]. When a crystal is thinned to only a few layers, dielectric screening is reduced[3], lattice order is modified[4] and translational periodicity is broken along the out-of-plane direction[5]. Novel electronic structures[6] and designed potential landscapes[7] with moiré potentials[8] can be generated by artificially stacking multiple 2D crystals[9]. These changes can strongly influence exciton energies[10], oscillator strength[11], transport pathways[12] and relaxation channels[13], while enabling functionalities[2, 14, 15] inaccessible in bulk materials. Such opportunities have stimulated intense interest in inorganic 2D semiconductors and van der Waals (vdW) heterostructures, yet their molecular counterparts remain largely unexplored.

Molecular crystals can provide a compelling platform for confinement-enabled excited-state engineering[16, 17, 18]. Optical excitation of these solids leads to the formation of molecular excitons[19, 20] that are Frenkel-type in nature and are dictated by delicate intermolecular interactions[21] of a non-covalent type. Consequently, optical and excited-state properties are highly sensitive to molecular packing[17], orbital overlap[22], polarization screening[23] and thermal lattice fluctuations[24]. This sensitivity intricately influences various characteristics of molecular excitons such as Davydov splitting (DS)[25, 26], superradiance[27], vibronic progression[28], Frenkel-charge transfer (CT) mixing[21, 26] and singlet fission[29], which in turn have significant implications for new developments of light harvesting, emissive devices, exciton transport and emerging photonic technologies. Because interactions in these molecular crystals are intrinsically weak and dependent on geometry and dielectric screening, reducing dimensionality can provide an effective route to tune molecular excitons with layer-by-layer precision. Despite this promise, systematic studies of 2D molecular crystals (2DMCs) have been limited by the lack of established routes to structurally well-defined, thickness-controlled materials. Most previous investigations have relied on multiple quantum wells[16], evaporated thin films[24] or epitaxially grown layers[30], where polymorphism[25], structural disorder[31], substrate-specific growth[32] or limited layer-number precision[16] can obscure intrinsic dimensional effects. Mechanical exfoliation[1], which transformed the study of inorganic layered materials, offers an attractive alternative because it can generate clean crystals with well-defined thicknesses and minimal chemical perturbation. Despite a few episodic reports[33, 34, 35], however, whether molecular solids held together only by relatively weak van der Waals interactions can be exfoliated down to the monolayer or few-layer limit while preserving crystalline order has remained uncertain.

Among molecular crystals, tetracene (Tc) serves as an ideal case study because its singlet excitons exhibit pronounced optical anisotropy[36], Davydov-split states[37], strong vibronic

Results and Discussion

Thickness-defined 2D molecular crystals by mechanical exfoliation. 2D materials provide a powerful route to tune electronic and optical properties through layer number, interfacial coupling and dielectric environment. Extending this concept to molecular solids, however, has remained difficult because organic crystals are often regarded as mechanically fragile and structurally prone to disorder during thinning. We therefore first asked whether high-quality molecular crystals can be isolated into thickness-defined 2D forms while preserving their intrinsic packing motifs.

Mechanical exfoliation[1] should be most effective in crystals with strongly anisotropic intermolecular cohesion (as shown in Figure 1), where robust in-plane interactions (within the $x$-$y$ plane) coexist with comparatively weak out-of-plane binding along the $z$ axis. Tc crystals satisfy this requirement: their herringbone lattice with two basis molecules on the (001) facet, or $\mathbf{a}$-$\mathbf{b}$ plane in Figure 1, forms an extended $\pi$-stacked network, constituting a single-layer (1L) Tc. In contrast, adjacent Tc layers are connected primarily through weaker peripheral C–H contacts (Figure 1). Density functional theory calculations on a 1L-slab in Figure 1 support this structural picture: among the 4 low-index facets considered (fig:S1 and Methods), cleavage along the (001) plane exhibits the lowest cleavage energy[39], substantially lower than competing crystallographic directions (Figure 1). The (001) energy is ~50% smaller than the cleavage energy of graphite[40], placing mechanical isolation of 2D Tc within the range of established exfoliable materials[41]. We also note that the interlayer binding energy calculated without lattice relaxation was 5–15% smaller in a 2L-slab model (fig:S1), suggesting that the crystalline structure is significantly affected by the presence of vdW-bound neighboring layers.

Guided by this analysis, we developed a mechanical exfoliation procedure for molecular crystals (Methods and fig:S2). Atomic force microscopy (AFM) revealed laterally extended terraces with nanometer-scale flatness over micron-scale distances (Figure 1). The minimum step height matched the interplanar spacing of the bulk crystal (Figure 1, top), indicating that exfoliation proceeds in discrete molecular layers (Figure 1, bottom) rather than through fracture-induced amorphization. Few-layer regions down to 2L were routinely obtained across multiple substrates (Si wafers, quartz and sapphire), demonstrating that thickness reduction can be achieved without chemical processing or epitaxial templating. To test the broader scope of this strategy, we applied the same procedure to three additional molecular semiconductors: Pc, DIP, and PTZ. For each crystal with anisotropic bonding motifs, ultrathin crystalline flakes were successfully isolated (Figure 1 and fig:S3), indicating that exfoliation is not unique to Tc but is accessible across a wider class of quasi-layered molecular solids. Notably, 1L Pc in Figure 1 could be identified with topographic analysis (fig:S3). For rapid thickness identification, we established substrate-specific optical-contrast calibrations spanning tens of layers (Figure 1). The optical contrast, defined in Methods, scaled monotonically with thickness and enabled non-destructive layer counting prior to spectroscopy. These results show that mechanical exfoliation yields molecular crystals with layer number defined at near-molecular precision, without chemical processing or epitaxial templating.

Structural integrity and polymorph selectivity of 2D Tc. Any interpretation of thickness-dependent excitonic behavior requires establishing that exfoliation does not introduce disorder, mosaicity (domain misorientation) or unintended structural phase changes. We therefore examined the crystalline integrity of few-layer Tc using polarization-resolved photoluminescence (PL) imaging and electron diffraction. The former, implemented in a wide-field format (Methods), exploits the fact that the lowest Tc emission is polarized along a crystallographically defined in-plane axis, allowing molecular orientation to be mapped optically across extended flakes[25]. As depicted in Figure 2, the lowest electronic transition of an isolated Tc molecule splits into a doublet of lower and upper Davydov states (LDS and UDS) in bulk[22] and 2D[25] crystals with two basis molecules. Polarized PL spectra of exfoliated 11L Tc (Figure 2) mainly consist of two vibronic transitions from LDS, 0-0 and 0-1, exhibiting dipolar character aligned along the b axis[25] (inset in Figure 2). Wide-field polarimetric imaging of a multi-terraced sample (Figure 2) revealed uniform emission anisotropy across several thickness domains: Two orthogonal polarization-resolved PL images, horizontal ($I_{\mathrm{H}}$ in Figure 2) and vertical ($I_{\mathrm{V}}$ in Figure 2), lead to the orientation ($\theta_{\mathrm{b}}$) image of the sample (Figure 2). $\theta_{\mathrm{b}}$, representing the azimuthal angle of the b axis with respect to the laboratory y axis (inset of Figure 2), can be approximated as the following equation[25]: $\theta_{\mathrm{b}} = \pm\tan^{-1}\left[\left(I_{\mathrm{H}}/I_{\mathrm{V}}\right)^{1/2}\right]$, the accuracy and noise-dependence of which were systematically verified (Figure 2 and Figure 2). Despite stepwise variations in layer number (5–20L), the in-plane orientation remained constant across the entire flake (Figure 2), indicating that exfoliation preserves single-crystal registry during cleavage, not producing misoriented fragments. The narrow angular distribution (FWHM = 1.9°), comparable to the ~1.9° orientational precision achieved at high signal-to-noise ratios, places an upper bound on the orientational disorder within the measured region (Figure 2 and Figure 2).

Selected-area electron diffraction (SAED) independently confirmed long-range order. The five-layer exfoliated Tc crystal in Figure 2 displayed sharp reciprocal-lattice features indexed to the known high-temperature polymorph of bulk Tc[42]. As summarized in Table 1, the lattice constants of exfoliated Tc crystals were within 1% of the bulk reference values and remained essentially unchanged across the measured thickness range of 5–27L. Therefore, mechanical thinning to a few molecular layers does not induce substantial lattice reconstruction. This structural fidelity is a key distinction from many deposited organic thin films[43], where strain[44], substrate templating[25, 30] or kinetically trapped polymorphs[45] can obscure intrinsic dimensional trends.

Samples	$a$ (Å)	$b$ (Å)	$\gamma$ (°)	Notes
Assembly-grown Tc	7.60(10)	6.01(5)	89.0(9)	1–4L
	[-3.9%]	[-0.3%]	[+3.2%]	(15 samples)
Exfoliated Tc	7.90(15)	5.98(12)	87.8(14)	5–27L
	[0.0%]	[-0.8%]	[+1.7%]	(6 samples)
Bulk Tc	7.90	6.03	86.3	Ref. 42

By contrast, assembly-grown ultrathin Tc on graphene exhibited a measurable in-plane lattice contraction (4% along the a-axis) unlike exfoliated crystals (Table 1). Although modest in magnitude, such packing changes are expected to strongly influence intermolecular electronic couplings that govern excitonic states because Coulomb and exchange interactions depend sensitively on intermolecular separation and slip geometry[17]. This contrast highlights the structural fidelity of exfoliated crystals and helps distinguish the effects of molecular packing from those of thickness on the excitonic states. Based on these observations, exfoliated 2D Tc provides a structurally robust model system for examining how reduced dimensionality modifies characteristics of molecular excitons without substantial changes in crystal packing.

Excitonic manifold reconstructed by packing and dimensionality. We next examined how out-of-plane confinement modifies the elementary excitonic structure of 2D Tc. We adopt the established Frenkel-CT mixing framework by Spano and coworkers[17], in which the two Davydov-split excited states of bulk Tc crystals arise from the interplay between direct Coulombic and CT-mediated couplings (fig:2a). As described in Supplementary Note, we consider two principal factors governing the excitonic manifold within this framework: thickness-dependent dielectric screening and structure-dependent intermolecular coupling. Thickness reduction therefore provides a direct route to perturb this excitonic Hamiltonian by modifying the dielectric environment[3]. As shown in fig:3a, polarization-resolved absorption spectroscopy via differential reflectance (DR)[46] resolved the lower and upper Davydov branches together with their vibronic progressions in exfoliated 2D Tc. The orthogonal polarization selection rules[25] of the two branches were retained (fig:3b), indicating that the basic dimeric excitonic framework survives in the 2D limit. As shown in fig:3c, however, the energy separation between the two branches, DS energy, decreased systematically with decreasing thickness. Assembly-grown crystals showed an even steeper reduction in DS energy as multilayers thinned to the monolayer regime and exhibited enhanced splitting compared to exfoliated systems. Thus, the DS energy varies with both molecular packing and crystal thickness.

We next show that the dependence of DS energy on molecular packing and thickness is consistent with the mixing model. First, the DS energy difference between exfoliated and assembly-grown crystals can be attributed to lattice contraction in the latter, as observed in diffraction patterns. Denser packing strengthens Coulombic interactions; within the dimer exciton model shown in fig:2a, the splitting between the two diabatic Frenkel exciton states (denoted as $F^{\circ}_{+}$ and $F^{\circ}_{-}$) is twice the Coulombic coupling ($J_{\mathrm{Coul}}$) between the two excitations of the two basis molecules, i.e., $2J_{\mathrm{Coul}}$ [17]. Because the leading-order term of the Coulomb coupling is dipolar, it scales inversely with the cube of the intermolecular distance ($R$). The 3.2% decrease in $R$ resulting from the contraction along $a$ and $b$ (Table 1) therefore translates into a ~10% increase in $2J_{\mathrm{Coul}}$. This results in an upshift in $F^{\circ}_{+}$ and a downshift in $F^{\circ}_{-}$. The latter downshift directly leads to a redshift of UDS because $F^{\circ}_{-}$ forms UDS without mixing with the diabatic CT states ($CT^{\circ}_{+}$ and $CT^{\circ}_{-}$) owing to symmetry [28]. The former upshift of $F^{\circ}_{+}$ also leads to a redshift of LDS provided that the Frenkel-CT mixing is sufficiently enhanced as $F^{\circ}_{+}$ becomes close to $CT^{\circ}$ states (fig:2a). The polarized DR spectra in fig:3d and fig:3e support this interpretation. All the vibronic transitions associated with both the LDS and UDS directions are redshifted in the grown crystals. Notably, the 0-0 energy difference of LDS between the two crystal types was greater than that of UDS, resulting in larger DS energies for the grown crystals (fig:3c). For 5L crystals, for example, grown crystals exhibited a splitting ~15 meV larger than that of exfoliated ones (~79 meV).

Importantly, however, both structurally distinct crystal classes exhibited the same qualitative trend of decreasing DS energy upon thinning. Notably, both the LDS and UDS 0-0 absorption energies shift to higher energies with decreasing thickness, even as their separation decreases (fig:S6). These observations strongly suggest that reduced dimensionality is a primary contributor to the thickness dependence, beyond packing variation alone. A natural microscopic origin is the evolution of dielectric screening in the few-layer limit [3]. As the surrounding polarization weakens, the CT states shown in fig:2a become destabilized. By contrast, Frenkel states are expected to be less sensitive to dimensional reduction because they are governed more strongly by the local dielectric response [47, 48] (see Supplementary Note). Therefore, with decreasing thickness, CT states are more destabilized relative to Frenkel states, thereby reducing the degree of the Frenkel-CT hybridization. Because this mixing contributes substantially to DS in acene crystals [22], weaker hybridization leads directly to a smaller splitting. Thus, the thickness-dependent DS is consistent with a progressive change in Frenkel-CT mixing as dimensionality is reduced.

Confinement-enhanced excited-state relaxation and delocalization. Beyond the absorption manifold, reduced dimensionality also strongly modifies excited-state relaxation. We tracked the lowest vibronic transition energies in absorption and emission as a function of thickness and found that both shifted to higher energies upon thinning (Fig. 4a), reflecting the general evolution of the excitonic landscape. Strikingly, however, the energy difference between them (Stokes shift) increased markedly toward the few-layer limit, rising from a small bulk-like value to approximately three times larger in the thinnest crystals.

Such behavior indicates that structural and environmental relaxation following photoexcitation becomes substantially more pronounced in ultrathin crystals, although thickness-dependent defect trapping or substrate interactions may additionally influence the measured shift. In bulk molecular solids, lattice rigidity suppresses large-amplitude nuclear reorganization. By contrast, few-layer crystals possess free surfaces, reduced out-of-plane constraint and enhanced susceptibility to substrate-induced corrugation or strain[49]. These factors can increase relaxation along low-frequency intermolecular coordinates coupled to the excited states, thereby increasing the reorganization energy. Stokes shifts of large excitonic polarons are predicted to increase as the size of one-dimensional molecular aggregates decreases due to enhanced electron-phonon coupling[50]. In this picture, the enlarged Stokes shift is consistent with enhanced relaxation along low-frequency intermolecular coordinates under reduced structural constraint. Dimensional reduction therefore controls not only exciton energies, but also the pathways by which excited states dissipate energy and reorganize the lattice.

One hallmark of collective excited states is their spatial coherence. To probe exciton delocalization, we analyzed the PL intensity ratio between the 0-0 and 0-1 vibronic transitions. In molecular aggregates, enhanced 0-0 emission is a characteristic signature of coherent excitonic states because the zero-vibration transition undergoes superradiance unlike vibronic sidebands[17]. The 0-0/0-1 ratio increased steadily as thickness decreased, approximately doubling in intermediate multilayers and rising further in the few-layer regime. Within the conventional Spano framework, in which the PL ratio serves as a spectroscopic measure of exciton coherence[17], the observed trend is consistent with progressively increasing exciton delocalization as the crystal is thinned, whereas thickness-dependent changes in vibronic coupling may also affect the absolute ratio. Notably, exfoliated and assembly-grown samples exhibited similar thickness dependence despite their different absolute transition energies, suggesting that coherence enhancement is governed primarily by dimensional confinement rather than by packing differences.

Greater delocalization in thinner crystals is consistent with stronger direct Frenkel-Frenkel Coulomb coupling under reduced screening. As the dielectric screening decreases, dipole-dipole interactions are enhanced, favoring the extension of Frenkel excitations over multiple molecules. In addition, our analysis suggests that reduced screening increases the energetic separation between the relevant diabatic Frenkel and CT states, thereby reducing their hybridization and increasing the Frenkel character of the emitting LDS, as supported by the thickness-dependent DS energy in fig:3c and the Supplementary Note. The increased Frenkel character can further favor spatial coherence, as its delocalized nature effectively reduces exciton-phonon couplings and enhances long-range Coulomb couplings. Thus, the enhanced Stokes shift and increased exciton delocalization can coexist without necessarily sharing a common microscopic origin: The former can arise from enhanced intermolecular structural relaxation, whereas the latter is consistent with stronger effective couplings due to increased Frenkel character under reduced dielectric screening.

Thickness-controlled coherence has important functional implications because exciton size influences transport[51], radiative rates[24] and multi-exciton processes such as singlet fission[38]. Together with the evolution of DS and Stokes shift, these observations show that dimensional reduction modifies intermolecular coupling, excited-state relaxation and exciton coherence through distinct microscopic processes in molecular crystals. Exfoliated 2D molecular solids therefore provide a complementary excitonic platform to inorganic 2D semiconductors, but in the regime of tightly bound and highly collective molecular excitations.

Conclusion

We demonstrated that molecular crystals can be mechanically exfoliated into structurally well-defined 2D forms suitable for probing collective excited states. Electron diffraction and polarization-resolved optical measurements confirm that crystalline order and optical anisotropy are retained upon exfoliation. Using tetracene as an important test case, we showed that reducing thickness toward the few-layer limit continuously modulates the excitonic energy landscape while largely preserving the main features of the bulk crystal structure. The structural fidelity of exfoliated crystals allows thickness-dependent effects to be examined with minimal changes in molecular packing, in contrast to the structural variations often encountered in deposited organic thin films. Out-of-plane confinement is shown to reduce the DS, substantially enhance the Stokes shift and increase the spectroscopic signatures of exciton delocalization, showing that intermolecular coupling, excited-state relaxation and coherence evolve systematically with layer number. These results identify dimensionality as an additional variable for controlling molecular excitons, alongside packing, composition and interfacial design in conventional organic semiconductors. While our analyses offer qualitatively consistent interpretations of the experimental results, further computational studies are needed for a more quantitative and definitive assessment. Other factors that have not been accounted for here, such as details of exciton-phonon couplings and the effect of interlayer exciton delocalization, require further investigation. In fact, access to thickness-defined, highly crystalline 2D molecular crystals, as demonstrated for the first time in this work, will enable systematic studies of all these important factors, with dimensional reduction as a new control variable. Furthermore, extending the protocols demonstrated here to other molecular crystals may enable systematic studies of confinement effects on singlet fission, exciton transport, polaritonic interactions and correlated excited states. Mechanical exfoliation thus extends dimensional control to molecular solids, where excitonic properties can be examined from the bulk to the few-layer and monolayer limits.

Methods

Top-down preparation of samples. Before mechanical exfoliation, quartz (qz) and sapphire (sph) slides were cleaned with piranha solution and treated with a UV-ozone (UVO) cleaner (Jaesung Eng., UVC-30). The dry-cleaned substrates were subsequently annealed at 350 °C to remove residual surface charges. Silicon wafers with 285-nm-thick $SiO_{2}$ were UVO-cleaned and annealed at 300 °C. Bulk powders of tetracene (TCI Co., > 97.0%), pentacene (TCI Co.), phenothiazine (TCI Co., > 99.9%) and diindenoperylene (Ambeed Inc., > 97.0%) were recrystallized using the physical vapor transport (PVT) method to improve purity and obtain larger crystalline domains. During PVT, Ar gas was introduced into a quartz tube containing source powders (upstream) and Si substrates in an inner tube (downstream) at a flow rate of 50–200 mL/min. The temperatures of the source and recrystallization zones were independently controlled using a three-zone furnace. The former temperature was set to ensure sublimation of source powders within a preset recrystallization period (1–10 h), whereas the latter was optimized to achieve maximal deposition within the recrystallization zone (Fig. S2). Crystalline flakes of molecular solids (typically several mm across) were grown on either the inner wall of the tube or the substrates. Typically, recrystallized crystals had flat areas that were 2–3 orders of magnitude larger than those of the as-purchased powders. Flakes with domain sizes larger than $\sim500\,\mu\mathrm{m}$ were used for mechanical exfoliation. Because of their fragility relative to inorganic layered materials such as graphite and hexagonal BN (hBN), molecular crystals required substantially milder mechanical perturbation throughout the exfoliation process.

Bottom-up preparation of samples. Few-layered Tc crystals were also prepared by assembly-assisted growth using a conventional thermal evaporator[25]. The deposition chamber was maintained below $2 \times10^{-6}$ Torr by a turbomolecular pump during deposition. Exfoliated few-layer graphene and few-nm hBN were used as assembly templates. For growth, the templates were exposed to Tc vapor at a nominal deposition rate of $0.1$–$0.5\,\mathrm{\AA}/\mathrm{s}$. The integrated flux corresponded to a nominal film thickness of 5–10 nm. The templates were maintained at 40 °C to induce ordered assembly growth.

AFM measurements. Sample thickness was determined by atomic force microscopy (AFM). Height images were acquired with an AFM system (Park Systems, XE-70) operated in non-contact mode under ambient conditions.

Electron diffraction measurements. Selected-area electron diffraction (SAED) patterns were obtained using a transmission electron microscope (JEOL, JEM-2100F) operated at an accelerating voltage of 80 kV (selected-area aperture diameter, $\sim1.2\ \mu\mathrm{m}$) at the Materials Imaging & Analysis Center of POSTECH, Republic of Korea. Diffraction signals were recorded using a CCD camera (Gatan, Orius SC200) with exposure times of 1–4 s to minimize electron-beam-induced damage. To further protect the samples from electron-beam damage, both sample types were encapsulated between single- or few-layer graphene flakes. Bottom-up samples grown on graphene were capped with graphene using the dry transfer method[26]. Top-down samples were directly exfoliated onto pre-exfoliated graphene on $\mathrm{SiO}_2/\mathrm{Si}$ substrates and immediately capped with a second graphene layer by dry transfer. To improve the yield of this double-exfoliation process, $\mathrm{SiO}_2/\mathrm{Si}$ substrates were treated with low-power air plasma for 5 min, followed by mechanical exfoliation of the first graphene layer while the substrates were maintained on a hot plate at 100 °C[52]. The graphene-sandwiched $\mathrm{T_c}$ crystals were transferred onto silicon nitride TEM grids (Norcada, NH050D2) using an ethanol-assisted wet transfer method[26]. A thin PDMS film ($\sim1$ mm thick) was attached to the sandwiched sample region, and the assembly was immersed in ethanol for 2–6 h to transfer the sample to the PDMS. The PDMS-supported sample was then dry-transferred to a silicon nitride grid pre-cleaned by $\mathrm{O}_2$ or air plasma for 10 min.

Differential reflectance and optical contrast measurements. Differential reflectance (DR) spectroscopy was used to probe the optical absorption of 2D molecular crystals supported on transparent substrates. For optically thin films supported on transparent substrates, DR (defined as $\frac{R_{\mathrm{sam}}-R_{\mathrm{sub}}}{R_{\mathrm{sub}}}$) can be approximated by $\mathrm{DR} \approx\frac{4}{n_{\mathrm{sub}}^2-1}A$[46], where $R_{\mathrm{sam}}$ and $R_{\mathrm{sub}}$ are the reflected intensities of the sample-covered and bare-substrate regions, respectively. $n_{\mathrm{sub}}$ and $A$ are the refractive index of the substrate and the absorptance of the sample, respectively. The optical contrast (OC) of the samples was used to determine their thicknesses and was defined analogously, using green-channel data extracted from optical micrographs.

Photoluminescence spectroscopy. The homebuilt photoluminescence (PL) spectroscopy setup has been described previously[25]. Briefly, a solid-state laser operated at 457.8 nm (Cobolt, Twist) was focused onto the samples to a spot size of $\sim1$ µm using a microscope objective ($40\times$, NA $= 0.6$). Backscattered PL signals were collected using a CCD camera (Princeton Instruments, PyLon) connected to a spectrometer (Princeton Instruments, SP2300). All measurements were performed under ambient conditions.

Wide-field PL imaging. PL imaging was performed using the PL spectroscopy setup described previously[25, 53]. Briefly, the linearly polarized excitation beam (457.8 nm) was focused onto the back focal plane of the objective using a plano-convex lens (focal length $= 400$ mm). The resulting wide-field excitation produced an illumination area with a FWHM of $\sim250$ µm. PL images were projected onto the CCD camera after passing through a 500–550 nm bandpass filter. The imaging area of the CCD ($100 \times100$ pixels) corresponded to a sample area of $32$ µm $\times32$ µm with the $40\times$ objective. Two PL images were sequentially acquired with horizontal and vertical excitation polarizations to extract crystallographic orientation using ratiometric polarimetry[25]. An analyzing polarizer was placed before the detector to select PL polarized parallel to the excitation polarization. The polarization-dependent sensitivity of the imaging setup was calibrated using amorphous copper oxide films as a reference for randomly polarized emission.

Density functional theory calculations. Cleavage and interlayer binding energies were calculated with the Vienna Ab Initio Simulation Package (VASP)[54] using the Perdew-Burke-Ernzerhof (PBE) functional[55], the projector augmented-wave (PAW) method[56], and the D3(BJ) dispersion correction[57, 58]. The experimental crystal structure of tetracene (CSD refcode TETCEN01)[59] was used as the initial structure and relaxed until the residual forces were below 0.01 eV Å$^{-1}$. A plane-wave cutoff energy of 750 eV was used for both bulk and slab calculations. $\Gamma$-centered k-point meshes of $5 \times4 \times2$ were used for the bulk, and $5 \times3 \times1$, $5 \times2 \times1$, $4 \times2 \times1$, and $2 \times3 \times1$ were used for the (100), (010), (001), and (110) slabs, respectively.

For each crystallographic facet, a 1L-slab model (Figure 1) was constructed with a vacuum region of 22 Å along the surface-normal direction and structurally relaxed. Cleavage energies were evaluated from the energy difference between the equilibrium and separated slab configurations, normalized by the in-plane area[39]. The vacuum spacing was verified by convergence tests.

Interlayer binding energies were additionally estimated using a 2L-slab model (fig:S1e). The binding energy was obtained from the energy difference per in-plane area between a bilayer cleaved from the bulk structure and the corresponding bilayer with increased interlayer separation, without further structural relaxation.

ASSOCIATED CONTENT

Supplementary Information is available for this paper.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]

Notes

The authors declare no conflict of interest.

ACKNOWLEDGMENTS

This work was supported by the National Research Foundation of Korea (NRF-RS-2024-00336324, NRF-RS-2024-00411134, 2021R1A6A1A10042944) and the Glocal University 30 project. This research was also supported by the Korea Basic Science Institute (National Research Facilities and Equipment Center) grant funded by the Ministry of Education (RS-2026-25539607). S.J.J. acknowledges primary support from the US Department of Energy, Office of Sciences, Office of Basic Energy Sciences (DE-SC0026114) and support from Korea Institute for Advanced Study (KIAS) through its KIAS Scholar program.

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