Computational design of a switchable heterostructure electrocatalyst based on a two-dimensional ferroelectric In₂Se₃ material for the hydrogen evolution reaction

Abstract

A theoretical design for an ON–OFF switchable HER catalyst using the two-dimensional ferroelectric (2D-FE) III₂VI₃ compound In₂Se₃ is reported in this paper. With vertical stacking of the basal plane of In₂Se₃ on top of the transition metal cobalt, a set of ab initio calculations reveals that the reversible polarization switching of In₂Se₃ can turn the HER activity of the heterostructure ON and OFF. The principle of HER activation/deactivation of the heterostructure is discussed in terms of the electronic structures, and the polarization-dependent modulation of electronic energy and charge transfer between In₂Se₃ and the transition metal are identified as the key factors. The distinct electron transfer mechanisms for the structures based on mono- and bilayers of In₂Se₃ are identified in terms of the different electronic connections between Co and In₂Se₃, and the structures are labelled as “direct” and “indirect” catalysts, respectively. This work provides insight into a possible pathway for designing dynamically controlled electrocatalysts based on 2D materials without introducing any chemical disorder.

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Introduction

Recent years have witnessed an exploding interest and fast development in two-dimensional ferroelectric materials (2D-FEs).^1,2 2D-FEs have reversible polarization that can be manipulated by external stimuli, even within their extremely thin atomic structures. Among many such materials, a class of two-dimensional III₂VI₃ compounds,^3,4 which is one subgroup of the two-dimensional transition metal chalcogenides (2D-TMCs), is of particular interest. Various ferroelectric two-dimensional III₂VI₃ compounds with quintuple-layer (five-atom-thick) structures have recently been proposed through simulations, of which In₂Se₃ has been the most actively studied example of 2D-FE III₂VI₃ for the last few years in both theoretical and experimental works. After the theoretical estimations on the presence of in-plane and out-of-plane ferroelectricity in ground-state α-phase In₂Se₃,^5,6 such ferroelectric behaviour was also observed experimentally.^7–9 Owing to the interesting reversible polarization switching that can be enabled by applying an electric field, various applications such as ferroelectric memory^10,11 and gas sensing¹² have been suggested. To expedite the practical applications of In₂Se₃, advances such as large-area and ultrafast synthesis have also been pursued.¹³

One compelling yet barely explored application of 2D-FE In₂Se₃ is as an electrocatalyst for which the simplest version is the hydrogen evolution reaction (HER) catalyst. Notably, recent computational studies have brilliantly demonstrated that In₂Se₃ shows reversible gas capture/release based on its polarization switching¹² and exhibits adequate built-in potential for photocatalyst applications.^14,15 This implies that In₂Se₃ can be utilized as an on/off reversible (photo-)catalyst after further manipulation of the molecular binding energies. Then, design of 2D-FE-based electrocatalyst structures with enhanced molecular adsorption and appropriate reaction energies by explicitly assessing the catalytic reaction should be the next step. In line with active researches on switchable catalysts using bulk ferroelectric materials,^16,17 the investigation of possible approaches for the utilisation of 2D-FE In₂Se₃ as a switchable electrocatalyst is a highly promising research direction. In fact, stimuli-controlled and on–off switchable electrocatalysis for on-demand hydrogen production is particularly important for efficient hydrogen generation in portable devices.^18–21 Furthermore, creative applications using on–off switchable electrocatalysts such as multiple stimuli-switchable electrocatalysis and logic gates have also been demonstrated.²²

Meanwhile, the semiconducting nature and weak molecular adsorption of the basal plane have been pointed out as the main obstacles in the use of 2D-TMCs as electrocatalysts. It is a well-known design rule that the adsorption energy of catalytic intermediates on the catalytic surface should be moderate (not too high or too low).^23,24 Therefore, boosting the molecular adsorption on the 2D-TMC surface is critical for effective utilisation of the large surface area and capability of atomic/electronic tuning^25–27 of 2D-TMCs for electrocatalyst applications. Researchers have focused on modifying the atomic/electronic structures of 2D-TMCs to enhance molecular adsorption by exposing edges and introducing atomic defects and metastable metallic phases.^28–34 Constructing heterointerfaces of 2D materials with metal substrates can be a more general approach for the systematic design of 2D-based HER catalysts without introducing chemical treatments.^27,35

This work presents the computational design of an ON–OFF switchable HER catalyst with systematic tuning of the hydrogen adsorption energy by constructing vertical heterostructures based on 2D-FE III₂VI₃ In₂Se₃ and the transition metal cobalt. Cobalt is chosen because it is a non-precious transition metal with ferromagnetic properties. Brief results with reactive and inert diamagnetic metals, Cu and Au, will also be provided for comparison. Adopting a set of density functional theory (DFT) calculations, the effect of the ferroelectric polarity of In₂Se₃ on hydrogen adsorption will be first discussed based on the electronic structures. Then, the construction of Co + In₂Se₃ vertical heterostructures will be suggested as a powerful approach to amplify the effect of polarity to modulate HER efficiency. In these heterostructures, the HER activity can be turned on and off by ferroelectrically switching the polarity of In₂Se₃. The principles behind the relationship between the polarity and HER activity will be provided in view of electronic hybridizations between Co and In₂Se₃ and manipulation of the electronic states of In₂Se₃. The distinct origins of the HER activities for Co + In₂Se₃ complexes with mono- and bilayer In₂Se₃ will also be thoroughly discussed in terms of the electron transfer mechanisms. By devising a 2D-FE In₂Se₃ heterostructure for a switchable HER catalyst, this work will pave the way for the future design of dynamically controlled electrocatalysts using III₂VI₃ and other 2D ferroelectric materials.

Computational methods

Model preparation

The ground state of the ferroelectric α-In2Se₃ has two degenerate phases, namely ferroelectric zincblende (FE-ZB′) and wurtzite (FE-WZ′) (ESI Fig. S1†). Among the two phases, FE-ZB′ was chosen to study the HER activities as in a previous report.⁶ According to the ferroelectric polarization (P) direction of In₂Se₃, which is defined by the location of the central Se atom (Se_c), upward (U) and downward (D) polarizations models were defined (Fig. 1a). The 3 × 3 supercells of FE-ZB′ were prepared to adsorb H atoms to ensure that the distance between the H atoms in the neighbouring cells was larger than 12 Å. Thus, the effect of the adsorption density was ignored in this study. Meanwhile, a four-layer hexagonal close-packed (HCP) Co metal slab along the basal (0001) plane was prepared. Then, a 5 × 5 supercell Co was generated and scaled to the 3 × 3 supercell of In₂Se₃ FE-ZB′ to construct a vertical heterostructure. The lattice misfit between 5 × 5 Co and 3 × 3 In₂Se₃ was only 1%. The details are provided in Fig. S2.†

Fig. 1 (a) The atomic structures of monolayer FE-ZB′ In₂Se₃ with upward (U) and downward (D) out-of-plane polarizations. Top views (top) and side views (bottom) visualize how the positional shift of the Se_c results in unique polarization switching. Se_s indicates the surface Se atoms that will become active sites when adsorbing H*. The yellow and green shaded areas represent the InSe and InSe₂, which are the substructures of In₂Se₃, respectively. d = 7.024 Å and P indicate the separation between the two In₂Se₃ layers and the polarization direction, respectively. (b) The projected density of states (PDOS) for U and D. The black lines and cyan-coloured areas indicate the p-orbital states of Se_c and Se_s, respectively. The orange arrow highlights the remarkable upshift of Se_s states due to the position change of Se_c. The red downward triangles indicate the position of the p-band peak for Se_s (ε_p-peak). (c) The calculated free energies of hydrogen adsorption (ΔG_H*) for different ferroelectric polarizations: U, D, and a nonpolarized phase (NP; face-centred cubic In₂Se₃, as shown in Fig. S1†). Se_a indicates an active Se_s atom where the H* is attached. (d) PDOS for the hydrogen-adsorbed U and D. The blue- and magenta-coloured areas are the p-orbital states of Se_a and s-orbital state of H*, respectively. The red arrows indicate the electronic states of Se_s that contribute to bond formations with H*.

Electronic structure calculations

All of the DFT simulations were performed to calculate the total energies and vibrational frequencies within the grid-based projector-augmented wave method as implemented in the GPAW package.³⁶ The revised Perdew–Burke–Ernzerhof (RPBE) functional was adopted as the exchange–correlation functional,³⁷ and the wavefunctions were expanded on a real space grid with a grid spacing of 0.14 Å. Fermi smearing of 0.1 eV was used, and the calculations were performed on the periodically repeated unit cells and 3 × 3 supercells of In₂Se₃ with 8 × 8 × 1 and 2 × 2 × 1 Monkhorst–Pack Brillouin zone sampling, respectively. Spin polarization was considered for all calculations. As an eigensolver, the residual minimization method–direct inversion in iterative subspace (RMM–DIIS) was utilized.^38,39 All of the structures were optimized using the conjugate-gradient method until the maximum force on any unconstrained atom was less than 0.05 eV Å⁻¹. A vacuum space of 18 Å was adopted after a series of test calculations (Fig. S3†) to avoid artificial interactions between periodic images, and the dipole correction was applied to describe the properties of the slab accurately. The effects of the calculation parameters such as the self-consistent-field convergence criterion and force-convergence criterion were thoroughly tested, and the parameters that give cost-effective yet accurate estimations on ΔG_H^* were adopted for the data generation. The details are provided in Table S1.†

Free energy calculations

ΔG_H^* is a reliable descriptor for HER activity under acidic conditions.^23,24 The free energies of the atomic hydrogen adsorptions were calculated to evaluate the HER activity as:

ΔG_H^* = ΔE_H^* + ΔE_ZPE − TΔS_H^* (1)

where ΔE_H^* is the hydrogen adsorption energy, ΔE_ZPE is the difference in the zero-point energy (E_ZPE) between the adsorbed (H*) and the gas-phase hydrogens (H₂), T is the temperature (298.15 K in this work), and ΔS_H^* is the entropy change due to adsorption. It is well known that highly efficient HER catalysts are characterized by |ΔG_H^*| ≅ 0 < 0.20 eV.⁴⁰ The hydrogen adsorption energies were computed as

ΔE_H^* = E_{sub + H} − (E_sub + 1/2E_H2), (2)

where E_{sub + H}, E_sub, and E_H2 indicate the total energies of the hydrogen-adsorbed substrate, the bare substrate, and the isolated hydrogen gas in a vacuum, respectively.

The free energy corrections (ΔE_ZPE and TΔS_H^*) were defined as:

ΔE_ZPE = E_{ZPE,1L + H^*} − (E_ZPE,1L + 0.5 × E_ZPE,H2), (3)

ΔS_H^* = S_{1L + H*} − (S_1L + 0.5 × S_H2), (4)

where 1L and 1L + H* indicate the monolayer In₂Se₃ and hydrogen-adsorbed 1L, respectively. The values of ΔE_ZPE and TΔS_H^* were explicitly computed on the basis of statistical thermodynamics from the vibrational frequencies by adopting the small displacement method based on the harmonic approximation as implemented in the ASE package⁴¹ where GPAW is plugged in as an electronic structure calculator.^42,43 The displacement amplitude of 0.015 Å was adopted.

The E_ZPE was computed by summing the vibrational frequencies over all of the normal modes ν_i,

where ħ is Planck's constant divided by 2π, i is the normal mode index, and k is the number of vibrational modes. The entropy, S, is given by⁴⁴where R is the universal gas constant, k_B is Boltzmann's constant, h is Planck's constant, N_A is Avogadro's number, and N is the number of adsorbed atoms. Eqn (5) and (6) indicate that E_ZPE and S(T) are dominated by high- and low-frequency modes, respectively. For gas-phase hydrogens, the standard state entropies are considered in most cases.⁴⁵ On the other hand, the entropy of the surface species is neglected in most studies since adsorbed hydrogen vibrates at high frequency.

However, it is important to explicitly calculate all of the relevant terms because the catalytic activities of In₂Se₃ have not been studied previously. Therefore, all of the stationary modes of monolayer In₂Se₃ (1L) with and without adsorbed hydrogen were examined in this study using eqn (3)–(6). The vibrational density of states (VDOS) for 1L, 1L + H*, and gaseous H₂ was obtained from the separate calculations without fixing any of the atoms. The details are summarized in Fig. S4 and Table S2† by showing the VDOS of 1L with/without adsorbed hydrogen and gas-phase hydrogens, and the energy correction is obtained as ΔE_ZPE − TΔS_H* = − 0.0091 + 0.0359 = 0.0268 eV. Interestingly, the infinitesimal ΔE_ZPE indicates that the hydrogen adsorbed on selenium (4p) is relatively stable compared to that on carbon (2p, 0.17 eV).⁴⁵

Results and discussion

HER activities of monolayer In₂Se₃: an indication of ferroelectricity-enabled HER control

Fig. 1a shows the atomic structures of the 1L FE-ZB′ α-In₂Se₃ with U and D polarization states. The U/D states of the polarization are achieved simply by shifting the vertical position of the Se_c atom down/up by external stimuli such as the electric field. The Se atom on the top surface is marked as Se_s and its position remains unchanged during polarization switching. Based on its quintuple-layer structure, the structure of In₂Se₃ can be further divided into two substructures, InSe and InSe₂, as indicated in Fig. 1a by the yellow and green shaded areas, respectively. Accordingly, switching from U and D modifies the configuration of In₂Se₃ from “InSe₂ (bottom) + InSe (top)” to “InSe (bottom) + InSe₂ (top)”. A step-by-step procedure of the ferroelectric switching of FE-ZB′ In₂Se₃ and the corresponding energy barrier diagram are provided in ESI Fig. S5.†

Polarization switching significantly modifies the projected density of states (PDOS) of FE-ZB′, as depicted in Fig. 1b. Unlike for transition metal catalysts, the p-orbital states of the active surface play the key role in HER on 2D-TMC.^46–48 In particular, the proximity of the valence band (VB) contribution of the Se_s p-states (the filled p-orbitals) to the Fermi energy (E_F) is of central importance. More specifically, the energetic location of the p_z-state is worth considering because the electrons should be transferred from the In₂Se₃ surface to adsorbed hydrogen by forming the bonding between Se 4p_z and H 1s to activate HER as shown in Fig. S6 and S7.†⁴⁹ To quantify the details for the location of the p_z-states of Se_s, the 4p_z-band centre (ε_pz-centre) can be introduced. ε_pz-centre represents the energetic location of the centre of 4p_z-states, analogous to the well-known d-centre:^49–51

where E and D_pz(E) are the electronic energy and PDOS for the 4p_z-orbital states of Se_s, respectively. The ε_p-centre can also be defined in the same manner but by adopting the PDOS of the averaged 4p-orbital states of Se_s, D_pz(E), in eqn (7) and the p-band peak (ε_p-peak) can be defined as the energy of the highest PDOS peak for p-Se_s below E_F. The trend of changes in values depending on the model is the same in all three of ε_pz-centra, ε_p-centre, and ε_p-peak. By definition, ε_pz-centre/ε_p-centre identifies the energetic location of the filled p_z/p-orbital of the active surface. The values are given as negative numbers by setting E_F = 0.0 eV. The closer the values are to zero, the closer the energies of the states are to E_F. Thus, ε_pz-centre will be a useful indicator for assessing ΔG_H^*. However, PDOS plots throughout this paper will be provided based on the averaged 4p-band states of the Se atoms, which include information about all the p_x, p_y, and p_z orbitals.

While the PDOS of Se_c remains unchanged, the ε_pz-centre/ε_p-centre of Se_s is −2.86/−3.26 eV in U and −1.67/−2.03 eV in D, which is an indication of a significant peak shift of ∼1.60 eV during polarization switching. This means that the electronic states of Se_c hybridize/dehybridize with those of Se_s by forming InSe₂/InSe, depending on the position in D/U. Therefore, the atomic movement of Se_c in D/U effectively turns ON/OFF the near-E_F contribution of the filled Se_s p-states, while the electronic state of Se_c itself is unchanged. Note that the spin-polarization was considered in the calculations and only the α-spin component is presented in the PDOS plot after checking that there is no significant difference between the PDOS of the two spin components.

It should be highlighted that the built-in potential within In₂Se₃ takes a key role in the polarization-dependent switching of the ε_pz-centre. The intrinsic dipole directs from the InSe₂ to InSe substructure within the In₂Se₃, as can be seen from the bond dipoles (BDs) between the two substructures (Fig. S8†). The H* adsorption on In₂Se₃ induces a negative bond dipole, which reduces/amplifies the dipole moment of 1L(D)/1L(U) (Fig. S8†). Correspondingly, the location of ε_pz-centre (and ε_p-centre) with respect to E_F is manipulated due to the polarization-dependent built-in potential (Fig. S9†). This means that the polarization-dependent local bonding environment of In₂Se₃ plays an essential role in modulating hydrogen adsorption while the built-in electric field plays a supporting role, as previously reported for a Janus MoSSe monolayer.⁵²

Owing to the manipulated locations of the filled Se_s p-states, the simple reversal of the polarization direction from U to D remarkably reduces the free energies of hydrogen adsorption (ΔG_H^*) by more than 1.0 eV, from 1.74 eV to 0.71 eV (Fig. 1c). The ΔG_H^* for models U and D are obtained using eqn (1) by attaching hydrogen (H*) onto one of the Se_s atoms (an active Se; Se_a) in the 3 × 3 supercells of monolayer In₂Se₃ (ESI Fig. S10†). The H*–Se_a bond formation on U at the InSe substructure is highly endothermic and accompanied by noticeable surface distortions. Correspondingly, the entire downward shift of the filled p-state (indicated by the red arrows) is observed upon H adsorption (Fig. 1d). On the other hand, D undergoes only a negligible surface distortion upon H adsorption on the InSe₂ substructure, and only the local valence band maximum – 1 (VBM-1) peak of p-Se_s at E_F − 2.49 eV shifts downward in Se_a (denoted by a red arrow in Fig. 1d) upon Se–H bond formation.

Note that, unfortunately, ΔG_H^* is still too large in both the U and D cases for an isolated In₂Se₃ to become a suitable HER catalyst. Similar to other 2D-TMCs,^53,54 the hydrogen adsorption will be too weak on isolated In₂Se₃. More thorough investigations into the relationship between the ferroelectric polarization and ΔG_H^* is provided in ESI Fig. S11.†D favours HER better than U, while HER is not activated in all cases even with the bilayer In₂Se₃ (2L), as will be shown in the later part of this paper.

The “direct” switchable catalyst: a case with Co + a monolayer of In₂Se₃

To exploit the polarization-dependent modulation of ΔG_H^* for turning the HER activity on and off, H* adsorption on In₂Se₃ should be amplified. Constructing vertical heterostructures with metal substrates is one effective approach in this regard, as in the cases of other 2D materials.^27,35 As a metal substrate, the transition metal Co is employed in this work. The ferromagnetism of Co can be pointed out as a key factor in ‘turning on’ the HER of In₂Se₃ upon heterostructuring, by breaking the spin degeneracy of In₂Se₃ so that its electronic states move toward E_F (Fig. S12†). By contrast, HER is not activated when adopting diamagnetic metals such as Au and Cu (Fig. S13†). Details of the metal species-dependency can be provided in the following work, and this study will focus on the design of an ON–OFF switchable HER catalyst using a Co metal slab.

By stacking monolayer In₂Se₃ on top of Co (Co + 1L), the strong effect of Co converts the electronic structure of 1L to be more favourable for H* adsorption. Fig. 2a and b respectively show the charge density differences (CDDs) of Co + 1L(D) and Co + 1L(D) + H*. The CDD of 1L vertically stacked on a Co metal slab is defined as:

Δρ_{Co + 1L} = ρ_{Co + 1L} − (ρ_Co + ρ_1L) (8)

where ρ_{Co + 1L}, ρ_Co, and ρ_1L indicate the spatial charge densities of the Co + 1L composite, Co slab, and 1L, respectively. Similarly, the CDD due to an H* adsorbed on Co + 1L is:

Δρ_{[Co + 1L] + H^*} = ρ_{[Co + 1L] + H^*} − (ρ_{Co +1L} + ρ_H), (9)

where ρ_{[Co + 1L] + H^*} and ρ_H indicate the spatial charge densities of the hydrogen-adsorbed Co + 1L and an isolated hydrogen atom, respectively. The Co–InSe interface in Co + 1L(D) undergoes a noticeable charge transfer and Δρ_{Co + 1L(D)} is easily delocalized through the Se_c atom in the middle. Consequently, the meaningful charge density difference is observed even at the top InSe₂ surface. This excessive charge (coloured in yellow) on top of the active surface will assist hydrogen adsorption as a ‘glue’ at the active surface. On the other hand, the effect of Co on the surface charge density of Se_s is negligible in the case of Co + 1L(U) (Fig. 2c). Δρ_{Co + 1L(U)} is localized at the Co–InSe₂ interface so that the hydrogen adsorption on Co + 1L(U) benefits less from the charge transfer between Co and In₂Se₃ (Fig. 2d).

Fig. 2 Charge density differences and PDOS plots for (a) Co + 1L(D), (b) Co + 1L(D) + H*, (c) Co + 1L(U), and (d) Co + 1L(U) + H*. The green and yellow shaded areas indicate InSe₂ and InSe substructures within In₂Se₃, respectively. The isovalue is 0.001 e Å⁻³, while the yellow and cyan colours represent positive and negative values, respectively. The cyan, black, and blue areas in the PDOS indicate the p-orbital states of Se_s, Se_c, and Se_i, respectively. The brown shaded areas and orange dashed lines indicate the d-orbital states of Co_i and Co_b, respectively. The red and orange downward triangles indicate the position of the p-band peaks for Se_s (ε_p-peak) and Se_c, respectively.

The corresponding PDOS plots shown on the right hand sides of Fig. 2a–d more closely reveal the origin of the catalytic activities. Since the ferromagnetic properties of Co induce the spin splitting of In₂Se₃ (Fig. S12†), α and β spins are shown in the positive and negative DOS regions, respectively. The Se atoms at the Co–In₂Se₃ interface (Se_i) strongly hybridize with the interface Co atoms (Co_i), both for Co + 1L(U) and Co + 1L(D) (Fig. 2a and c). Furthermore, Se_c and Se_s become slightly metallic owing to having a finite value in the bandgap region of In₂Se₃ (Fig. S12 and S14†). Having a synergistic effect with strain caused by chemical bonding, this promotes charge transfer from the electron reservoir Co to the In₂Se₃ active surface. This is consistent with the recent studies demonstrating that the synergistic effects of local bonding and charge transfer related to surface states can tune the adsorption properties of the surfaces.^55,56 Such adjustments of the surface adsorption characteristics can even control the growth modes of the thin film and the stability of the catalyst.

Meanwhile, the intrinsic built-in potential of In₂Se₃ (Fig. S15†) polarization-dependently modifies the potential energies of the active surface when adsorbed on Co. Therefore, the occupied p-orbital states of Se_c in Co + 1L(D) are located near E_F, while those of Co + 1L(U) are located far below E_F (the orange downward triangles in Fig. 2a and c). Recalling that the Co + 1L(U) can be divided into Co–InSe₂ and InSe, while Co + 1L(D) consists of Co–InSe and InSe₂, Se_c is selectively hybridized with Se_s/Se_i for Co + 1L(U)/Co + 1L(U). Thus, the filled p-Se_s state in Co + 1L(U) is located even further away, while it comes closer to E_F and coincides with that of Se_c in Co + 1L(D) (marked by the red downward triangles). Correspondingly, the ε_pz-centre/ε_p-centre of Se_s is −3.15/−3.58 eV in Co + 1L(U), and the values significantly shift closer to zero (E_F) in Co + 1L(D) by having −1.58/−1.97 eV. The values are given for the α-spin state that is located closer to E_F than its β-spin counterpart.

The upward shift of ε_pz-centre/ε_p-centre assists the electron transfer from Co to In₂Se₃ in Co + 1L(D) and this promotes H* adsorption through the hybridization of the Se_a-p and H-s orbitals (Fig. 2b and d). Eventually, polarization switching turns HER activity “ON” and “OFF”, by showing ΔG_H^* for Co+1L(D) = 0.079 eV < 0.2 eV, while having ΔG_H^* for Co+1L(U) = 0.49 eV > 0.2 eV. Note that the ΔG_H^* values are provided after finding an active site among various Se_s (Fig. S16†). Each Se_s gives a slightly different ΔG_H^* due to the difference in the local structures but shows ΔG_H^* < 0.2 eV for Co + 1L(D) in all cases. Because the Co metal slab directly modulates the activity of the In₂Se₃ based on strong chemical bonding, Co + 1L(D) can be categorized as a “direct catalyst”.

The “indirect” switchable catalyst: a case with Co + a bilayer of In₂Se₃

The effect of the Co substrate can be further investigated by stacking one more In₂Se₃ on top of Co + 1L, creating Co + 2L. Since Co + 1L(D) has been identified as an effective metal in the previous section, it is informative to consider Co + 2L(D) as a composite of an active layer 1L(D) and an effective metallic substrate Co + 1L(D). Fig. 3a illustrates the CDD between the substrate Co + 1L(D) and the active material 1L(D), where Δρ_{[Co + 1L] + 1L} is obtained using eqn (8) but replacing Co with Co + 1L. Due to the introduction of the Co substrate, the CDD between the two 1L(D)s in Co + 2L(D) is significantly amplified compared to the case of 2L(D) without Co (Fig. S17†). Correspondingly, the physical interlayer distance (d) between the 1L layers was noticeably reduced by 0.5 Å from 3.93 Å to 3.43 Å when introducing Co (Fig. 3a and S17†). Furthermore, the excess charge (the red arrow) is observed at the top of Se_s within the Co + 2L(D), and this will act again as a ‘glue’ for assisting hydrogen attachment (Fig. 3a). On the contrary, the charge deficiency (the blue arrow) shown at the top of Se_s for Co + 2L(U) implies that the hydrogen adsorption will be less favoured (Fig. 3c).

Fig. 3 Atomic models (left) and the PDOS (right) for (a) Co + 2L(D), (b) Co + 2L(D) + H*, (c) Co + 2L(U), and (d) Co + 2L(U) + H*. For the models without H*, CDDs between the two In₂Se₃ layers are overlaid with the atomic models. The isovalue is 0.0002 e/ų, while the yellow and cyan colours represent positive (excessive electrons) and negative (deficient electrons) values, respectively. d = 3.43 Å indicates an interlayer distance between the 1L layers within Co + 2L(D). Red/blue arrows indicate the excessive/deficient charge at the active surface of Co + 2L(D)/Co + 2L(U). The types of atoms in the models are indicated by coloured arrows, and the same colours are used to represent the PDOS: cyan, black, orange, green, blue, and magenta represent Se_s, Se_c, Se_u, Se_l, Se_a, and H*, respectively. In plotting the PDOS, p-orbitals for Se and s-orbitals for H are used. The blue downward triangles indicate the energy location of the local VBM-1 for Se_s and Se_l. The red downward triangle represents the position of the p-band peak for Se_s (ε_p-peak).

Focusing on PDOS, the local VBM-1 p-states of the outer surface atoms in the lower (Se_l) and upper (Se_s) In₂Se₃ layers coincide entirely in terms of electronic energy, as indicated by the blue downward triangles. Due to the charge transfer between Co and the first In₂Se₃, the electron tunnelling channel opens up across the two In₂Se₃ layers. Then, a well-connected electron transport channel near E_F evolves from the substrate to the active layer, efficiently supplying electrons for the HER. Note that the effect of the Co substrate is now weaker than that in the above-mentioned Co + 1L case and the induced metallicity and strain on the active surface are absent.

ε _pz-centre/ε_p-centre for Co + 2L(D) is −1.28/−1.62 eV and ΔG_H^* is obtained as 0.111 eV in the “HER-ON” state. Such channel-opening results from the charge transfer between Co and In₂Se₃, which is not observed in 2L(D) (Fig. S17†). The corresponding potential energy profiles are provided in Fig. S18.† When a hydrogen is attached, the electronic state of the upper In₂Se₃ layer (Se_s, Se_c, and Se_u) shifts downward, while that of the lower In₂Se₃ layer (Se_l) remains unchanged (Fig. 3b). With the hydrogen desorption, the tunnelling channel from the Co to the top 1L(D) opens up again (Fig. 3a). The electron tunnelling channel in Co + 2L(U) is similarly connected from Co + 1L(U) to the top 1L(U) but the filled p-Se_s states are located far below E_F (Fig. 3c and d). ε_pz-centre/ε_p-centre is −3.33/−3.75 eV for Co + 2L(U) with ΔG_H^* = 1.665 eV in “HER-OFF”. Thus, ON/OFF switchable HER is again achieved with Co + 2L. Since the Co metal slab indirectly modulates the activity of the In₂Se₃ based on weak physisorption (the van der Waals interaction between the two In₂Se₃ without induced metallicity and strain) and tunnelling, Co + 2L(D) is labelled as an “indirect catalyst”.

The descriptors for HER-ON/OFF states

Fig. 4a provides a schematic diagram that summarizes the HER activities of the models introduced throughout this work and Fig. 4b and c visualize the evaluations of the ON/OFF states for HER based on ΔG_H^*. Prior to their incorporation in the heterostructure, monolayer In₂Se₃, bilayer In₂Se₃, and the bare metal Co are all inactive materials for HER. Upon stacking monolayer In₂Se₃ on top of Co (Fig. 4b), the ΔG_H^* of Co + 1L(U) and Co + 1L(D) is 0.49 eV (>0.20 eV) and 0.082 eV (<0.20 eV), respectively. This identifies Co + 1L(U) as “HER-OFF” and Co + 1L(D) as “HER-ON” states. Therefore, the HER activities of 1L stacked on Co can be turned “ON” and “OFF” simply by controlling its polarity to D and U using external stimuli. Furthermore, the switchable HER activity can be observed even when stacking bilayer In₂Se₃ on the Co slab (Fig. 4c). After adsorbing one more In₂Se₃ layer on top of Co + 1L through van der Waals interactions, Co + 2L(D) and Co + 2L(U) are also respectively assigned as “HER-ON” and “HER-OFF”. The ΔG_H^* values of Co + 2L(D) and Co + 2L(U) are 0.11 eV < 0.20 eV and 1.67 eV > 0.20 eV, respectively.

Fig. 4 (a) A schematic diagram of HER based on In₂Se₃ FE-ZB′ and Co. First, neither Co nor 1L is a suitable HER catalyst for opposite reasons: while hydrogens adsorb too strongly on a bare Co metal surface, they are unlikely to adsorb on an isolated In₂Se₃ regardless of the polarity (U or D). Second, Co metal surfaces that are decorated by D state-In₂Se₃ of either 1L or 2L are good HER catalysts. The atomic-level origin for these HER activities is distinct for monolayer and bilayer In₂Se₃, which are identified as “direct” and “indirect”, respectively. A free energy diagram for HER at zero potential on various Co–In₂Se₃ heterostructures with (b) 1L and (c) 2L. The red, blue, green, magenta, and black lines indicate 1L/2L(U), 1L/2L(D), Co + 1L/2L(U), Co + 1L/2L(D), and bare Co cases, respectively. The grey shaded area indicates the condition where |ΔG_H^*| < 0.20 eV.

The origins of ON–OFF switching can be systematically analysed based on Table 1, providing the ΔG_H^* and ON/OFF status of the models in Fig. 4 with proper descriptors. First, the effect of ferroelectric switching is indicated by ε_pz-centre and ε_p-centre. For all of the models, the values are closer to zero (the filled p-Se_s are closer to E_F) in D than U and modulating the structure from U to D significantly reduces ΔG_H^*. Since U and D in each model are basically the same material with different ferroelectric states, ε_pz-centre, ε_p-centre, and ε_p-peak are intuitive descriptors for comparing the HER efficiencies of U and D. However, ε_pz-centre/ε_p-centre/ε_p-peak cannot be the only parameters for HER efficiency when it comes to the comparison of two distinct materials since the evaluation of HER efficiency basically contains the precise assessment of hydrogen adsorption energies. For example, as the stiffness or stability of In₂Se₃ changes with the thickness, the hydrogen adsorption energy will also change with the number of In₂Se₃ layers. While 2L(D) shows a higher εs and smaller ΔG_H^* than its 1L(D) counterpart, the assessment of thickness-dependent HER activity cannot be discussed simply on the basis of ε_pz-centre/ε_p-centre/ε_p-peak when the In₂Se₃ becomes thicker.

Table 1 Calculated ΔG_H^* and evaluation of HER ON/OFF states for all the models with different polarizations (P) of D/U considered in this work, together with ε_pz-centre, ε_p-centre, and ε_p-peak for α/β spin and the effect of the Co slab. For the cases without Co, only the α spin is considered

Model	P	ΔGH^* [eV]	ON/OFF^a	ε pz-centre (α/β) [eV]	ε p-centre (α/β) [eV]	ε p-peak (α/β) [eV]	Co effect^b
a ‘ON’ if |ΔGH^*| < 0.20 eV, ‘OFF’ if not. b ‘Strong’ if the active In2Se3 is directly attached on Co, ‘weak’ if the active In2Se3 is influenced by but not directly attached to Co, ‘None’ if there is no Co in the atomic model.
Co + 1L	D	0.082	ON	−1.58/−1.78	−1.97/−2.16	−0.91/−1.14	Strong
	U	0.490	OFF	−3.15/−3.32	−3.58/−3.64	−3.17/−3.27
Co + 2L	D	0.111	ON	−1.28/−1.45	−1.62/−1.79	−0.47/−0.65	Weak
	U	1.665	OFF	−3.33/−3.48	−3.75/−3.91	−3.00/−3.19
1L	D	0.710	OFF	−1.67	−2.03	−0.87	None
	U	1.740		−2.86	−3.26	−2.48
2L	D	0.448		−1.35	−1.71	−0.55
	U	1.745		−3.23	−3.63	−2.85

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Meanwhile, the Co metal slab significantly modifies the electronic structure of In₂Se₃. Co acts as an electron reservoir and provides an electron transfer channel to activate In₂Se₃. This is particularly enabled by the ferromagnetism of Co because Co-induced spin decomposition on In₂Se₃ attracts α spin to shift closer to E_F as a major charge transfer channel. If In₂Se₃ undergoes the ‘strong’ Co effect, the nature of In₂Se₃ will be modified through applied strain and slight metallization due to the Co–In₂Se₃ hybridizations. Even if the In₂Se₃ undergoes only a ‘weak’ Co effect, the electrons will be efficiently supplied to the active surface while the electronic structure of In₂Se₃ remains intact.

Achieving ON and OFF states of HER can be understood as manipulating the synergy of the ferroelectric switching of In₂Se₃ and the ferromagnetic Co effects. In the absence of Co (few-layer In₂Se₃ with no Co effect), ΔG_H^* for D is always more favourable for HER than its U counterpart as can be anticipated in the previous report¹² but always stays “OFF” for all cases. When Co is introduced without metalizing In₂Se₃ or hybridizations (Co + 2L with a ‘weak’ Co effect), the electrons are transferred to the active surface through tunnelling to promote hydrogen adsorption. ΔG_H^* is reduced both in D and U so that the ON(D)–OFF(U) states of HER are achieved. Co + 2L(D) has been labelled as an ‘indirect’ catalyst in this paper. For ‘strong’ Co effects with interfacial strain, induced metallicity, and hybridizations on In₂Se₃ (Co + 1L), ΔG_H^* is further reduced by direct charge transfer. Then, ON(D)–OFF(U) states of HER are again achieved. Having a ΔG_H^* of almost zero, Co + 1L(D) can be understood as a more efficient catalyst than Co + 2L(D) and labelled as a ‘direct’ catalyst.

Conclusions

In summary, this theoretical work provides a brief concept design and insight into the construction of a dynamic catalyst based on a 2D-FE material-transition metal complex. The main points in this work can be summarized as follows:

• A theoretical design of a 2D material-based heterostructure for a switchable catalyst.

• A theoretical formulation on how the ferroelectric modulation of the 2D material gives rise to an active/inactive HER surface through coupling with a non-noble metal substrate, without introducing chemical modifications.

Owing to the unique quintuple structure and intrinsic ferroelectricity of the III₂VI₃ compound, the stacking of In₂Se₃ onto the ferromagnetic transition metal Co slab enables control over the hydrogen adsorption onto In₂Se₃, thereby switching the HER on and off. The underlying principle is the polarization-dependent control of the electron supply from Co to In₂Se₃, which is based on the synergy of ferroelectric switching of In₂Se₃ and the effect of ferromagnetic metal Co. Correspondingly, the “direct” and “indirect” catalysts are defined in terms of the bonding nature of the electron supply paths from Co to In₂Se₃ (either chemical bonding at Co + 1L In₂Se₃ or tunnelling through physical bonding at Co + 2L In₂Se₃).

For the design of switchable electrocatalysts based on 2D-FE III₂VI₃ heterostructures, this work mainly focuses on the principles of catalytic activities of the heterostructure through theoretical discussions by taking In₂Se₃ as an example III₂VI₃ material. For the viability of ON–OFF conversion, the controllability of the polarization energy barrier of In₂Se₃ in response to external stimuli without (Fig. S19†) and with (Fig. S20 and S21†) the presence of a Co slab was also briefly investigated. The energy barrier for D–U conversion in a neutral system implies the reasonable stability of the structure. The barrier can be significantly reduced by applying an electric field or net charge. It is important to recall that a switchable non-volatile memory based on the polarization conversion of few-layer In₂Se₃ (∼2.6 nm) was realized experimentally by applying a gate bias on top of a metallic gate.¹⁰ Consistent with the experimental achievement, the backgate voltage that gives the net charge on the system can modulate the energy barrier between D and U even when the In₂Se₃ is adsorbed on the Co substrate (Fig. S20 and S21†). While brief indications of the viability of the ON–OFF conversion are provided, the next step will be to theoretically expand and experimentally realize this brief idea. Thorough theoretical discussions on the thickness-dependent ΔG_H^* of ferroelectric In₂Se₃, metal species-dependent HER activity of the metal-In₂Se₃ heterostructure and ON–OFF conversion dynamics within the non-equilibrium external stimuli will be pursued in the following studies. In this effort, the design principle and theoretical analysis provided in this work will offer key guidances for the experimental development of switchable electrocatalysts based on 2D-FE III₂VI₃ heterostructures in the future.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

All the simulation data in this work were generated and analysed with the active use of the NURION (KISTI-5) high-performance computing resources supported by the Korea Institute of Science and Technology Information (KISTI) (KSC-2019-CRE-0199 & KSC-2020-CRE-0300). This work was carried out under the financial support from the institutional R&D program of KISTI (K-21-L02-C10) and the National R&D program of the National Research Foundation (NRF) (NRF-2020R1F1A1075573) funded by the Ministry of Science and ICT of Korea. I would like to thank my dear friend Min Jong Noh for all of the support and valuable discussions regarding this research.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ta09738a

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