Science of 2.5 dimensional materials: paradigm shift of materials science toward future social innovation

Abstract

The past decades of materials science discoveries are the basis of our present society - from the foundation of semiconductor devices to the recent development of internet of things (IoT) technologies. These materials science developments have depended mainly on control of rigid chemical bonds, such as covalent and ionic bonds, in organic molecules and polymers, inorganic crystals and thin films. The recent discovery of graphene and other two-dimensional (2D) materials offers a novel approach to synthesizing materials by controlling their weak out-of-plane van der Waals (vdW) interactions. Artificial stacks of different types of 2D materials are a novel concept in materials synthesis, with the stacks not limited by rigid chemical bonds nor by lattice constants. This offers plenty of opportunities to explore new physics, chemistry, and engineering. An often-overlooked characteristic of vdW stacks is the well-defined 2D nanospace between the layers, which provides unique physical phenomena and a rich field for synthesis of novel materials. Applying the science of intercalation compounds to 2D materials provides new insights and expectations about the use of the vdW nanospace. We call this nascent field of science '2.5 dimensional (2.5D) materials,' to acknowledge the important extra degree of freedom beyond 2D materials. 2.5D materials not only offer a new field of scientific research, but also contribute to the development of practical applications, and will lead to future social innovation. In this paper, we introduce the new scientific concept of this science of '2.5D materials' and review recent research developments based on this new scientific concept.

Keywords: 2.5 dimensional materials; 2D heterostructures; bilayer graphene; hexagonal boron nitride; intercalation; interlayer nanospace; moiré superlattice; multidimensional materials; transition metal dichalcogenide; van der Waals interaction.

Graphical abstract

Figure 1.

Trends and future directions of 2D materials research. Inset shows the number of publications about graphene, TMDCs, and hBN (the number of scientific papers whose titles contain each word was counted based on the ISI Web of Science database).

Figure 2.

Schematic showing the scientific importance of stacking 2D materials. (a) monolayer graphene, (b) BLG. When stacked with the same angle, i.e. AB-stacking, the BLG shows band gap opening in the presence of vertical electric field, which is useful for semiconductor applications. (d) When the BLG is twisted with a magic angle (~1.1°), it becomes superconducting at low temperature. Reproduced with permission from Springer Nature [10]. (e) in the interlayer 2D nanospace of the BLG, new structures or new materials can be obtained. Reproduced with permission from Wiley-VCH.

Figure 3.

Our new concept of ‘2.5D materials.’ There is a large space to develop materials science between conventional 3D bulk materials and layered 2D materials.

Figure 4.

Details of science on ‘2.5D materials.’ The research topics and purposes are displayed. The difference between the traditional materials science research and the proposed 2.5D materials research is also explained.

Figure 5.

Growth and assembly of 2D materials. SEM images of (a) single-crystal monolayer graphene grown on Cu foil and (b) in-plane heterostructure of monolayer graphene and hBN grown on Cu foil. Reproduced with permission from American Chemical Society [18] and IOP Publishing [40]. (c) STM image of monolayer MoS₂/WS₂ in-plane heterostructure. Reproduced with permission from American Chemical Society [44]. (d) SEM image of monolayer WS₂-WSe₂ in-plane superlattice. Reproduced with permission from AAAS [46]. (e) Optical microscope images of wafer-scale monolayer (left) and a three-layer (right) MoS₂ films obtained by the layer-by-layer transfer process. Reproduced with permission from Springer Nature [55]. (f) Robotic transfer system consisting of an optical microscope, stamping apparatus, and chip transfer system. (g) 29 alternating layers of graphene/hBN vertical vdW superlattice obtained by the robotic system shown in (f). Reproduced with permission from Springer Nature [8]. Scale bars are (a) 0.2 mm, (b) 5 μm, (c) 1 nm, (d) 200 nm, and (g) 20 μm.

Figure 6.

(a) Contour plots of the wave function of the lowest (left panel) and the second lowest (right panel) NFE states of an isolated graphene. The number shows the square of the wave function. Linear plots indicate the corresponding densities. Reproduced with permission from American Physical Society [62]. (b) an optimised structure of dibenzo-corannulene sandwiched by two graphene layers. Grey and pink balls denote C atoms belonging to graphene and dibenzo-corannulene, respectively, and white balls are H atoms. Reproduced with permission from American Chemical Society [63]. (c) Schematics of C₆₀-graphene co-intercalation compound (left panel) and K-doped C₆₀-graphene co-intercalation compound (right panel). Large, medium, and small balls denote C₆₀ molecules, K atoms, and C atoms, respectively. Reproduced with permission from American Physical Society [64]. (d) Isosurfaces of electron-depleted (blue) and accumulated (yellow) regions of sumanene-intercalated bilayer graphene and the charge density distribution along z-axis. Reproduced with permission from American Chemical Society [67]. (e) Geometric structure and spin density of a copolymer of phenalenyl and phenyl groups. Reproduced with permission from Elsevier [68]. (f) Geometric structure of polymerized trypticene. Reproduced with permission from the Physical Society of Japan [69]. (g) Schematics of wave functions of the edge states at k=π, 8π/9, 7π/9, and 2π/3 (left to right). Reproduced with permission from IOP Publishing [70].

Figure 7.

Intercalation in stacked 2D materials. (a) Concept of the intercalation within 2D nanospace. (b,c) Schematic and Raman spectra of monolayer, bilayer, and few-layer graphene intercalated with FeCl₃ molecules. Reproduced with permission from Wiley-VCH [75]. There are two different graphene sheets with different doping levels; G₁ and G₂ indicate lower and higher doping levels, respectively. (d) Sheet resistance change of MoCl₅-intercalated BLG stored in ambient condition. Reproduced with permission from Wiley-VCH (modified from ref. [79]). The BLG was grown by CVD method, and, by tuning the growth condition, AB- and twist-rich BLG were selectively synthesized. (e) Temperature dependence of the resistance of Ca-intercalated BLG grown on SiC. Reproduced with permission from American Chemical Society [81]. (f) Atomic models of Li ions stored in graphite (left) and BLG (right). Reproduced with permission from Springer Nature [83]. The simulation suggests higher density of Li in the BLG. (g) Illustration of Na intercalation in chemically modified graphene stacks. Reproduced with permission from AAAS [85]. Monolayer graphene sheets functionalized with 4-NBD molecules are stacked to form an electrode for the intercalation. (h) New AlCl₃ structures observed inside the interlayer space of CVD-grown BLG. Reproduced with permission from Wiley-VCH [11]. (i) Intercalation of magnetic Co ions in the interlayer of TaS₂ with the assistant of TBAC molecules. Reproduced with permission from Wiley-VCH [89]. (j) TEM images of atomic layers of Ga, In, Sn formed at the interface between graphene and SiC substrate. Right graph shows the magnetic field dependence of the superconductivity of the Ga layer. Reproduced with permission from Springer Nature [92].

Figure 8.

(a) Atomic structures of TBG with different twist angles. (b) Schematics of the Brillouin-zone (BZ) folding of TBG (10 degree), where red and blue hexagons represent the BZ of individual graphene layers, and small black hexagons are that of the moiré superlattice. (c) Band structures of low-angle TBG. Reproduced with permission from American Physical Society [98]. (d) (Top) Longitudinal resistance plotted against carrier density at different perpendicular magnetic fields from 0 T (black trace) to 480 mT (red trace). (Bottom) Color plot of longitudinal resistance measured against carrier density and temperature, showing different phases including metal, band insulator (BI), correlated state (CS) and superconducting state (SC). Reproduced with permission from Springer Nature [101]. (e) A false-colored TEM image of 30-degree TBG mapped with 12-fold Stampfli-inflation tiling. Reproduced with permission from AAAS [127].

Figure 9.

(a) Schematic of the artificial heterostructure of semiconducting monolayer (WSe₂) and magnetic material (CrI₃). Reproduced with permission from AAAS [143]. (b) Spectrum showing circularly-polarized PL from excitonic states in monolayer WSe₂, which suggests valley-Zeeman splitting induced by a magnetic proximity effect from the ferromagnetic CrI₃. Reproduced with permission from AAAS [143]. (c) Valley-Zeeman splitting induced by a magnetic proximity effect from ferromagnetic EuS. Reproduced with permission from Springer Nature [145]. (d) Schematic of vdW heterostructure of a semiconductor monolayer (MoSe₂) and a perovskite transition metal oxide ((La.₈Nd.₂)_1.2Sr_1.8Mn₂O₇) with a hBN layer. Reproduced with permission from Wiley-VCH [146]. (e) Large valley-Zeeman splitting and polarization in monolayer MoSe₂ on perovskite Mn oxide. Reproduced with permission from Wiley-VCH [146]. (f) Schematic of the atomic arrangement in the moiré superlattice formed in a heterobilayer with twist angle θ. Reproduced with permission from Springer Nature [114]. (g) Low temperature PL spectra of moiré superlattice in MoSe₂/WSe₂ heterobilayer, measured at low (blue: 20 nW) and high (dark red: 10 µw) optical power densities. Inset shows an expanded energy scale of a sharp PL spectral line, with linewidth ~100 μeV. Reproduced with permission from Springer Nature [114]. (h) 2D photoluminescence excitation (PLE) map. The two-resonance excess energies of 24 and 48 meV are indicated by the black dashed lines. Reproduced with permission from American Chemical Society [13].

Figure 10.

(a) Schematic 2D nanosheet heterostructure (left) and current on/off ratio as a function of SS (right). Reproduced with permission from Wiley-VCH [152], the references referred in the right panel can be found in this reference). (b) Ultrafast program/erase operation in MoS₂/hBN/multilayer graphene heterostructure NVM. Reproduced with permission from Springer Nature [160]. (c) SS lower than thermodynamic limitation of 60 mV/dec achieved in n-MoS₂/p⁺-MoS₂ TFET heterostructured with hBN. Reproduced with permission from American Chemical Society (modified from ref. [14]). (d) Schematic illustration of a BP/MoSe₂ heterojunction device and response of three sensors as a function of NO₂ gas concentration. Reproduced with permission from IOP Publishing [166]. (e) an all-carbon device fabricated on a flexible PEN substrate and magnified image of a 21-stage ring oscillator. Reproduced with permission from Springer Nature [171].

Figure 11.

(a) Schematic illustration of the TMDC bilayer photovoltaic device. Reproduced with permission from American Chemical Society [177]. (b) J−V curves of the device shown in (a) measured under illumination of 180, 400, 670, 1100, 1800, 4000, and 6400 W/m² (in the order of red to blue). Reproduced with permission from American Chemical Society [177]. (c) Schematic illustration of GLG. Reproduced with permission from Springer Nature [181]. (d) Schematic diagram of monolayer MoS₂ plasmonic photoFets under bias and illumination with a gate voltage. Reproduced with permission from American Chemical Society [184]. (e) Photoresponsivity of the plasmonic photoFET and bare monolayer MoS₂ photoFET as a function of illumination wavelength. The red curve shows reflection spectrum of the plasmonic nanostructures. Reproduced with permission from American Chemical Society [184].

Figure 12.

(a) Schematic of a light-emitting device sandwiching a single layer of WSe₂ between hBN barrier layers with top and bottom transparent graphene electrodes. High-resolution TEM image and energy-dispersive X-ray analysis of a cross-section of the device. Reproduced with permission from American Chemical Society [188]. (b) Electroluminescence spectra taken at different temperatures for WSe₂ and MoSe₂ light-emitting devices with hBN tunnel barriers measured with applied bias of 2 V and 1.8 V, respectively. Reproduced with permission from American Chemical Society [188]. (c) PL spectra of single-layer WSe₂, MoS₂, and WSe₂/MoS₂ hetero-bilayer. Reproduced with permission from National Academy of Sciences [189]). (d) Energy diagram of WSe₂/MoS₂ hetero-bilayer under photoexcitation. Reproduced with permission from National Academy of Sciences [189]. (e) Electroluminescence from the WSe₂/MoS₂ hetero-bilayer light-emitting device. Reproduced with permission from American Chemical Society [139]. (f) Optical image of the bilayer-WS₂/2D-PVSK (n = 4) heterostructure on a SiO₂/Si substrate. Reproduced with permission from American Chemical Society [193]). (g) Photoluminescence spectra of the bare bilayer-WS₂ (red line), the bare 2D-PVSK (n = 4) (blue), and bilayer-WS₂/2D-PVSK heterostructure (black). The excitation wavelength is 514 nm. Reproduced with permission from American Chemical Society [193].

Figure 13.

Future prospects of science of ‘2.5D materials.’