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Ferroelectricity, Antiferroelectricity and Ultrathin 2D Electron/Hole Gas in Multifunctional Monolayer MXene Anand Chandrasekaran, Avanish Mishra, and Abhishek Kumar Singh Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b01035 • Publication Date (Web): 04 Apr 2017 Downloaded from http://pubs.acs.org on April 5, 2017

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Ferroelectricity, Antiferroelectricity and Ultrathin 2D Electron/Hole Gas in Multifunctional Monolayer MXene Anand Chandrasekaran, Avanish Mishra, and Abhishek Kumar Singh∗ Materials Research Centre, Indian Institute of Science, Bangalore 560012, India E-mail: [email protected] Abstract Presence of ferroelectric polarization in 2D materials is extremely rare due to the effect of the surface depolarizing field. Here, we use first-principles calculations to show the largest out-of-plane polarization observed in a monolayer in functionalized MXenes (Sc2 CO2 ). The switching of polarization in this new class of ferroelectric materials occurs through an previously unknown intermediate antiferroelectric structure thus establishing three states for applications in low-dimensional non-volatile memory. We show that the armchair domain-interface acts as an 1D metallic nanowire separating two insulating domains. In the case of the van-der-Waals bilayer we observe, interestingly, the presence of an ultrathin 2D electron/hole gas (2DEG) on the top/bottom layers, respectively, due to the redistrubution of charge carriers. The 2DEG is nondegenerate due to spin-orbit-coupling, thus paving the way for spin-orbitronic devices. The coexistence of ferroelectricity, antiferroelectricity, 2DEG and spin-orbit splitting in this system suggests that such 2D polar materials possess high potential for device application in a multitude of fields ranging from nanoelectronics to photovoltaics.

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Keywords Ferroelectric, 2D electron gas, polarization-discontinuity, MXene, spin-orbit coupling Polarization in non-centrosymmetric material is of great technological importance due to a variety of phenomena such as ferroelectricity, piezoelectricity and pyroelectricity. Ferroelectric materials possess a spontaneous electric polarization that can be reversed through the application of an external electric field. Oxides, such as lead zirconate titanate (PZT), are technologically indispensable for their excellent dielectric and piezoelectric properties. Currently they are also being used in non-volatile memory devices in the form of ferroelectric random access memory (FeRAM). However, more recently, ferroelectric oxides have attracted much interest due to observation of strongly charged domain walls 1 which show the presence of a 2DEG. The origin of the 2DEG is due to development of a polarization discontinuity at the interface and was first observed in lanthanum aluminate/strontium titanate (LAO/STO) interfaces. 2 2DEGs at polar interfaces have shown fascinating properties ranging from superconductivity 3 to giant Seebeck coefficients for thermoelectrics. 4 In contrast to polar oxides, the observation of ferroelectricity in 2D layered materials is extremely rare. While the presence of in-plane polarization is relatively common, 5–8 the presence of strong and stable out-of-plane ferroelectric polarization in monolayers is yet to be reported. The biggest challenge for the stabilization of out-of-plane polarization in ultrathin materials is the presence of the depolarizing field at the surface. 9 For zero external electric field, traditional ferroelectrics generally show the presence of polarization only for films of thickness greater than 7 unit-cells. 10 More recently, ferroelectricity has been found in HfO2 11,12 for films of thickness less than 10nm. Even so, it will be exceedingly difficult to integrate traditional oxide ferroelectrics with next-generation sub-nanometer level electronic devices. The search for new classes of low-dimensional ferroelectrics is therefore vital for accelerating design of nanoelectronic devices. In this letter we report the presence of both in-plane and out-of-plane polarization in monolayer oxygen-functionalized scandium carbide MXene (Sc2 CO2 ). This material has 2


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an out-of-plane polarization of 1.60 µC/cm2 , which is the highest reported so far for a monolayer. This polarization is switchable through an intermediate antiferroelectric state thus giving rise to a new class of atomistically thin ferroelectric materials. As a natural consequence of the strong out-of-plane polarization, we observe, for the first time, a 2DEG in an ultrathin van-der-Waals bilayer. Layered transition metal carbides and nitrides (MXenes) are a relatively recent family of 2D materials. 13,14 These materials are derived from their corresponding layered hexagonal MAX phases; M is an early transition metal, A is a group IIIA or IVA element and X is carbon or nitrogen. The M-X layers, which are bonded to the A layers by metallic bonds, need to be etched out using an appropriate chemical reagent 15 and separated using sonication. Monolayer MXenes such as Ti2 C, Ti3 C2 , Nb2 C, V2 C, (Ti0.5 ,Nb0.5 )2 C, Ti3 CN, Ta4 C3 have already been synthesized 13,16–18 while a host of other MXene/MAX phases have been predicted. 19 MXenes have attracted much interest in the field of energy materials, 20 especially as possible electrodes for supercapacitors 21 and for Li+ , Na+ and K+ -ion batteries. 22 Their recently discovered thermoelectric 23,24 and optoelectronic properties 25,26 show promise for future applications. Moreover, certain oxygen-functionalized MXenes have been demonstrated to be wide band-gap topological insulators 27 thus opening up possibilities in the field of nanoelectronics as well. 28,29 As an initial step we sought to understand the various structures of oxygen-functionalized MXene. Existing reports 30,31 indicate three possible structures for any functionalized MXene. The configurations are labeled as carbon-top, metal-top and mixed-configuration based on the relative position of the oxygen atoms with respect to the bare MXene. In the case of the carbon-top structure, the oxygen atoms are located on top of the carbon sublattice on both sides of the monolayer as shown in Fig. 1a. Similarly, the metal-top has the oxygen atoms placed above the transition metal sites on both sides of the monolayer (Fig. S1). The mixed-configuration has the oxygen atoms located on top of the carbon sites on one side and on the other side the oxygen atoms are on top of the metal atoms as depicted in

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depicted in Fig. 2b. This bonding between the two oxygen and carbon atoms is characterized by p-orbital hybridization between the two atoms (Fig. S3). This is reminiscent of the covalent interactions in lead-based perovskites which give rise to their exceptionally large ferroelectric displacements. 33 This overlap is also present in the case of the non-centrosymmetric carbon-top structure; however, due to the alternate arrangement of dipoles the net out-ofplane polarization is zero thus exhibiting an antiferroelectric nature. To our knowledge, there exists only one other prediction of antiferroelectricity in a 2D material. 34 In the case of the symmetric carbon-top structure the carbon atom is located in the middle of the two scandium planes and there is no charge density overlap between the carbon and oxygen planes as depicted in Fig. 2a. Having established the presence of low-energy dynamically stable ferroelectric and antiferroelectric configurations, it is of interest to investigate the mechanism of polarization reversal in these systems. The polarization switching process, caused by a displacive transformation, is analyzed in detail using the nudged elastic band method (NEB) 35 as described in Fig. 3. The energy barrier for switching of polarization from the polar to non-polar configuration is 0.52 eV per formula unit and proceeds via a multi-step process of oxygen atom displacements as depicted in the animiation provided in the supporting information. In comparison, the energy barrier for the switching of the well known perovskite ferroelectric LiNbO3 36 is 0.26 eV. In reality the actual barrier is likely to be lowered in the Sc2 CO2 monolayer due to domain-wall/vacancy assisted migration of oxygen atoms. By following the polarization transformation process we verified that the Pz value of 1.60 µC/cm2 for the polar configurations is indeed with respect to the non-polar phase. This is especially important since the absolute value of polarization is not a well-defined quantity 37 and only changes in polarization can be calculated as a bulk property. A density of states calculation is performed for every image on the path to confirm that there is no metallic transition at any point during the transition thus ensuring the possibility of polarization reversal and also the validity of the Berry phase calculations.

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Figure 3: Nudged elastic band calculation for polarization reversal from +Pz ferroelectric state (F) to -Pz ferroelectric state. The transformation proceeds through an intermediate antiferroelectric configuration denoted by AF. NEB calculations were performed using the ground-state lattice parameters of the ferroelectric configuration, therefore both the antiferroelectric and ferroelectric appear to be almost isoenergetic. However the fully-relaxed antiferroelectric configuration is the ground state. The in-plane polarization depends on the length of the vacuum layer hence it is more appropriate to report this quantity in terms of the dipole moment per unit area (Px ). Here the x direction denotes the arm chair direction. The magnitude of the in-place polarization of the polar configuration is 1.76×10−10 C/m2 ; similar to that reported for SnSe monolayer by Wu and Zeng. 7 It is important to note that due to the simultaneous change in both Pz and Px one may, for the first time, control the in-plane polarization through the variation of an out-of-plane electric field. This opens up a host of interesting applications through which domains of different polarizations can be ’written’ using an atomistic tool like a piezoresponse force microscopy (PFM) 38 or atomic-force microscopy (AFM). As such, we looked into the properties of the 1D interfaces separating “domains” within

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one single monolayer of this 2D material. Our supercell is 12 unit cells wide, with 6 unit-cells in the +Pz polarized state and the other 6 unit-cells in the -Pz polarized state. The two bulk regions were separated by an interface along the arm-chair direction so as to avoid in-plane polarization discontinuity. As depicted in Fig. 4, we observed an area of local metallicity located at the interface while the rest of the supercell remained insulating. From a projected density of states calculation we inferred that the metallic properties of the interface arise from the presence of defect states within the band-gap of the system. The defects are caused by the mismatch in the oxygen sub-lattice arrangement across the interface. Due to this, the energy of this interface is much higher compared to conventional domain walls in ferroelectrics. 39–41 However, they resemble closely the high-energy charged domain walls that have recently attracted much interest in the field of ferroelectric oxides. 1,42 Such walls do not satisfy the electrostatic conditions for a neutral interface but are still experimentally seen in certain materials. 1,43 For example, in the classical ferroelectric BaTiO3 , 1 charged domain walls show the presence of a 2DEG system similar to that observed in LAO/STO interfaces. 2 In order to investigate an analogous phenomenon in 2D materials, we looked at the property of bilayer Sc2 CO2 consisting of 2 stacked polar monolayers as shown in Fig. 5a. Atomic positions were relaxed (including van der Waals interaction), revealing a strong binding energy of 0.18 eV per formula unit between the two layers. (change) Calculations also showed that this ferroelectric stacking of the bilayer was 0.27 eV more favorable compared to an antiferroelectric coupling (Fig. S4). Surprisingly, the density of states calculation for this bilayer revealed no band-gap and pointed at a metallic nature. This is in stark contrast to the band gap of 1.91 eV observed for monolayer Sc2 CO2 . In order to understand the atomistic origin of this behavior we performed a projected density of states calculation to capture the contribution from individual atomic orbitals. Fig. 5b separates the total projected density of states contributions coming from the top and bottom Sc2 CO2 layers. The Fermi level is set to 0 and is depicted by the dashed red line in Fig. 5. Very interestingly the Fermi level

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polarization in the bulk and the unit vector normal to the surface, respectively. In the case of the bilayer, the polarization discontinuity (and the incipient potential difference) is sufficient to cause significant band bending thus resulting in the redistribution of free charge carriers across the material; i.e., the electrons from the valence band in the bottom layer start to occupy the conduction band in the top layer. Recently, Gibertini et al. 46 showed that the free charge carrier density at the surface asymptotically approaches the bound charge density with increasing number of polar unit-cells. Therefore, in this system, it is easy to tune the free charge carrier density at the Fermi layer simply by stacking more layers of Sc2 CO2 (Fig. S5). The critical thickness for the 2DEG at LAO/STO interfaces is 4 unit-cells 44 while in the present case a bilayer suffices to induce an insulator-to-2DEG transition. The reason for this is two fold; firstly, the band-gap of this system is lower than traditional oxide ferroics and secondly, the presence of the large out-of-plane polarization due to the strong covalent interaction between carbon and oxygen sublattices facilitates the development of the necessary potential difference. The potential difference across the monolayer is 1.8 eV(Fig. S6) and as expected the potential difference across the bilayer is 3.6 eV (double that of the monolayer). Since the development of the 2DEG is sensitive to the width of the band-gap it is important to understand the limitations of PBE in predicting the insulator-to-2DEG transition. Using HSE06, 47 we calculated the band-gap of Sc2 CO2 monolayer to be 2.92 eV while the band-gap of the bilayer was 0.38 eV (Fig. S7). HSE06 calculations revealed the insulatorto-2DEG transition to occur for the trilayer. However, the experimental band-gap may still differ significantly from calculated HSE06 values and hence it cannot be determined with certainty whether the closing of the band-gap occurs first in the bilayer or trilayer. Moreover, in case there exists a small band-gap in the bilayer (as found in HSE06), it can be closed through the application of an external electric field or strain. The band structure of the bilayer is shown in Fig. 5c and it demonstrates the presence of the 2D hole gas at the Γ point and the 2D electron gas between the Γ and M points.

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The projected density of states revealed that conduction band contribution to the electron gas arises solely from the Sc 4d bands in the top layer (denoted by Sc* in Fig. 5a). The valence band contribution to the hole gas, on the other hand, arises mainly from the carbon p bands in the bottom layer(denoted by C* in Fig. 5a). Interestingly, including spin-orbitcoupling effects (SOC) results in the splitting of the conduction bands close the Fermi level as depicted in Fig. 5d. The maximum splitting between the bands (∆SOC ) is 16 meV. Due to the difference in the Fermi level overlap between these two split bands, there exists two electron gases with different densities rather than one degenerate electron gas. The origin of the conduction band splitting can be understood in terms of the interaction of the Sc 4d bands with the symmetry-breaking electric field perpendicular to the interface (arising from the out-of-plane polarization Pz ). Similar phenomena has been reported in InAs/AlSb quantum wells 48 and LAO/STO interfaces 49 and experimentalists are drawing ever closer to the realization of gate-controlled spin splitting 44,50 for application in spintronics. For example, Lesne et al. 44 recently demonstrated that the two inequivalent Fermi surfaces in 2DEGs may be shifted using spin pumping resulting in a transverse charge current through the so-called inverse Edelstein effect. Electron-hole bilayers have been predicted to undergo a transition from a weakly coupled two-dimensional system to a strongly coupled exciton system as the width of the bilayer is reduced. 51 This Sc2 CO2 system has a distance of 6.7 ˚ A between the top Sc-centered electron gas layer and the bottom carbon centered hole gas layer. To our knowledge this is the thinnest reported electron-hole bilayer 52,53 thus making this material the ideal system to study phenomena such as Coulomb-drag and investigate Bose-Einstein condensation of excitons at zero magnetic field. 51 A complete understanding of ferroelectricity in these class of materials can be obtained by looking at the polarization of bulk oxygen functionalized Sc2 CO2 . Interestingly, bulk Sc2 CO2 has an extremely high polarization of 57 µC/cm2 . This polarization is even higher than the traditional ferroelectric BaTiO3 , which has a spontaneous polarization of 30 µC/cm2 in its

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tetragonal phase. 54 Thus, the polarization of this system can be tuned over a exceptionally wide range just by changing the number of layers. We mention that the boundary conditions of the bulk and monolayer calculations are different. 9 Due to the vacuum, calculations on the monolayer represent ferroelectric polarization in the presence of a depolarizing field. On the other hand, in the case of bulk Sc2 CO2 , due to periodic boundary conditions, there is no depolarizing field and this results in a much larger polarization. The monolayer also shows extremely different Born effective charges (Table S1) compared to the bulk due to the strong effects of interlayer ferroelectric coupling. Such large differences of Born effective charges between monolayer and bulk have also been reported earlier in the case of V2 O5 . 55 We also show, in Fig. S8, that the “ferroelectric displacement” of the central carbon atom in these layered slabs asymptotically approaches that of bulk as the number of layers is increased. The operation of a ferroelectric device usually involves the utilization of two metal electrodes that result in a vanishing depolarizing field across the ferroelectric (due to charge compensation by the metals). Therefore we may conclude that the spontaneous polarization of monolayer Sc2 CO2 is likely to be much higher than 1.6 µC/cm2 under operating conditions due the presence of conductive electrodes. With regard to the experimental feasibility of synthesizing Sc2 CO2 monolayer; the formation of a scandium MAX phase such as Sc2 AlC 56 and Sc2 InC 57 has already been reported. Such phases would then have to be exfoliated using a suitable etchant under oxygen rich atmosphere to produce the oxygen functionalized MXene, which eventually happens, spontaneously. A theoretical thermodynamic study on MXenes clearly shows that it is possible to synthesize the Sc2 C based MXene materials. 58 Studies have shown that a fully oxygenfunctionalized MXene is thermodynamically the most favored state rather than a partially functionalized MXene 59 thus facilitating the formation of the ferroelectric Sc2 CO2 monolayer. Moreover, the phonon dispersion of both the ferroelectric and antiferroelectric Sc2 CO2 monolayer does not show the presence of any negative phonon frequencies (Fig. S2), thus verifying the dynamical stability of this system. Although a variety of other MXenes also

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show dynamical stability of the polar configuration, 32 only Group III transition metal MXenes possess the ground-state structure corresponding to the polar structure. Our choice of Sc2 CO2 is thus justified because of the combined thermodynamic and dynamical stability along with the presence of the largest band-gap amongst functionalized MXenes. (a)

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M Figure 5: (a) Schematic of bilayer Sc2 CO2 . The direction of the out of plane polarization, Pz , is shown by the black arrow. The electron gas is centered on the Sc* atom while the hole gas is centered on the C* atom. (b) The projected density of states of the top and bottom layers. The formation of the 2DEG in the top layer is evident from the intersection of the Fermi level (dashed red line) with the conduction band. Similarly, the hole gas in the bottom layer is formed due to the intersection of the Fermi level with the valence band. (c) Band structure of the bilayer. (d) Close-up of the overlap of the Fermi level with the valence and conduction bands. The conduction band splits close to the Fermi level due to spin-orbit coupling. In conclusion, we have established the presence of switchable polarization in 2D monolayer Sc2 CO2 due to presence of dynamically stable ferroelectric and antiferroelectric structures. The energy barrier for switching is sufficiently high to ensure the presence of three distinct 13


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states (+Pz ,0,-Pz ) for non-volatile memory applications even at room temperature. 7 There already exist methods for imprint lithography using an electric field; 60 by utilizing a template which consists of conductive/non-conductive portions it would be possible to use an electric field to produce complex 1D electrical circuitry and non-volatile memory states for large-scale commercial applications. To our knowledge, this is the first report of a 2DEG in ultrathin van-der-Waals bilayer material. Usually the formation of a 2DEG in complex oxides requires careful preparation using molecular beam epitaxy whereas in our case it can be produced by the simple stacking of polar 2D materials. The bilayer is automatically formed due to the large binding energy and the electron gas manifests on an atomically flat surface without any dangling bonds or defects. Another important observation is that the band-gap of Sc2 CO2 as revealed by the HSE06 calculations (2.92 eV) is within the visible spectra range. In the case of multilayer Sc2 CO2 , light which is incident on the insulating bulk of the material will result in the absorption of a photon and the creation of an electron-hole pair. However, due to the inbuilt electric field, the electron and hole are separated and transported to opposite surfaces of the multilayer which are conductive in nature. This material is thus an ideal candidate for novel polarization-driven photovoltaic devices that have been proposed very recently. 46 Through the amalgamation of the existing fields of 2D materials, ferroelectricity, antiferroelectricity, spintronics and 2DEGs, these class of ultrathin materials represent a giant leap in the field of low-dimensional nanoelectronics. It is very likely that there exists a plethora of 2D materials showing ferroic properties and a high-throughput search of monolayers and functionalized monolayers would likely pave the way for next-generation materials design and discovery.

DFT Calculation details. We used density functional theory with the Perdew–Burke– Ernzerhof (PBE) exchange-correlation approximation using ultrasoft pseudopotentials 61 and plane waves, as implemented in the Quantum-ESPRESSO distribution. 62 An effective MonkhorstPack k-point mesh of 12 × 12× 1 per five-atom cell, a plane-wave cutoff of 60 Ry,and a charge

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density cutoff of 600 Ry are utilized. The plane-wave cutoff is chosen to converge the forces on atoms to 10-4 Ry/bohr. A vacuum layer of 20˚ A is used in the supercell to separate the monolayers. The vacuum spacing and k-points mesh are chosen to converge the total energy to 1 meV per formula unit. Atomic positions were optimized until the forces were less than 10-4 Ry/atom. The equilibrium lattice parameters and angles were obtained by allowing the stress tensor to go to zero. The density of states and projected density of states are performed on an extended k-mesh of 16×16×2. The polarization is calculated using the Berry phase approach 37,63 as implemented in the Quantum-ESPRESSO distribution. The structures of multilayer Sc2 CO2 are optimized using the long-range dispersion correction as given by Grimme. 64 In the case of the 1D domain interface, we relaxed the atoms in the vicinity of the interface to a threshold of 10−4 Ry/bohr while keeping the bulk atomic positions fixed. The Heyd-Scuseria-Ernzerhof functional (HSE06) 47 calculation for the monolayer ground state of Sc2 CO2 band-gap was specifically performed using the Vienna Ab-initio Simulation Package (VASP). 65,66 Projector augmented pseudopotentials 67 were used for the electronion interactions. One-fourth of the PBE exchange is replaced by the Hartree-Fock exact exchange and the full PBE correlation energy is included.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: XX. Model structure of metal-top Sc2 CO2 , phonon dispersion for ferroelectric and antiferroelectric monolayer, the projected density of states showing hybridization between carbon and oxygen, the relative energies of ferroelectric and antiferroelectric coupling of the bilayer, projected density of states for the trilayer, average planar electrostatic potential, HSE06 band structure for mono and bilayer, Born effective charge tensor for bulk and monolayer, ferroelectric displacement plot for different slab thickness.

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AUTHOR INFORMATION Corresponding Author ∗ Email: [email protected] Notes The authors declare no competing financial interests.

Acknowledgement We acknowledge the Materials Research Centre and Supercomputer Education and Research Centre of Indian Institute of Science, for providing computing facilities for the completion of this work. All the authors acknowledge the support from DST Nanomission.

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Ferroelectricity, Antiferroelectricity, and Ultrathin ... - ACS Publications

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