2D materials and van der Waals heterostructures

TL;DR

Two-dimensional heterostructures with extended range of functionalities yields a range of possible applications, and spectrum reconstruction in graphene interacting with hBN allowed several groups to study the Hofstadter butterfly effect and topological currents in such a system.

Abstract

The physics of two-dimensional (2D) materials and heterostructures based on such crystals has been developing extremely fast. With new 2D materials, truly 2D physics has started to appear (e.g. absence of long-range order, 2D excitons, commensurate-incommensurate transition, etc). Novel heterostructure devices are also starting to appear - tunneling transistors, resonant tunneling diodes, light emitting diodes, etc. Composed from individual 2D crystals, such devices utilize the properties of those crystals to create functionalities that are not accessible to us in other heterostructures. We review the properties of novel 2D crystals and how their properties are used in new heterostructure devices.

Figures (6)

• Figure 1: Electronic properties of different classes of 2 D materials. The Fermi level is set to the zero of the energy scale. The DoS is given in states/eV per cell.
• Figure 2: Phase diagram for a 2D material with a quantum phase transition.
• Figure 3: Wet transfer and "Pick and Lift" techniques for assembly of van der Waals heterostructures. (A-F) Wet transfer technique. A 2D crystals prepared on a double sacrificial layer (A) is lifted on one of them by dissolving another (B). It is then aligned (C) and placed (D) on top of another 2D material. Upon the removal of the membrane (E) a set of contacts and mesa can be formed (F). The process could be repeated to add more layers on top. (G-O) "Pick and Lift" technique. A 2D crystals on a membrane (see (B)) is aligned (G) and then placed on top of another 2D crystal (H). Depending on the relative size of the two crystals it is then possible to lift both flakes on the same membrane (I). By repeating the process it is possible then to lift more crystals (JL ). Finally, the whole stack is placed on the crystal which will serve as the substrate (M-N) and the membrane is dissolved, exposing the whole stack (O).
• Figure 4: Morphology of the van der Waals heterostructures. (A) 1D contacts to van der Waals heterostructures. Etching mesa in van der Waals heterostructures exposes the edges of the crystals inside the stack, which allows formation of 1D contacts. Here carbon atoms are represented by blue spheres; boron - yellow; nitrogen - brown. (B-D) TEM cross-section of graphene/hBN heterostructure. Scanning TEM image (C) of a structure schematically presented on (B). In (B) atom coloring same as in (A). (D) High-angle annular dark-field image of the same stack. Scare bars - 2 nm . (E-J)AFM images of graphene transferred on other 2D crystals. Self-cleansing mechanism pushes contamination (hydrocarbons) away from graphene on hBN (E),$\mathrm{MoS}_{2}(\mathrm{~F})$ and $\mathrm{WS}_{2}(\mathrm{G})$ interfaces, forcing the contamination to gather in bubbles. Instead, on the substrates with poor adhesion to graphene, such as mica (H), BSCCO (I), $\mathrm{V}_{2} \mathrm{O}_{5}(\mathrm{~J})$, contamination is spread uniformly across the whole interface. The size of the images: $15 \mu \mathrm{~m} \times 15 \mu \mathrm{~m}$; z-scale: 4nm. ( $\mathbf{K , L}$ ) Local Young modulus for graphene on hBN for 3 □ (K) and 0 □ (L) misorientation angle. Note sharp domain walls in (L). Scale bars: 14nm. (M) Reconstructed electronic energy spectrum for graphene aligned on hBN.
• Figure 5: Electronic and optoelectronic applications of van der Waals heterostructures. (A-D) Tunnelling in graphene-hBN-graphene tunnel transistors. (A) Schematic representation of graphene tunnelling device. Here graphene electrodes are dark-purple and hBN tunnelling barrier is light-blue. The electrodes can be aligned with respect to each other. (B)$d^{2} I / d V_{b}{ }^{2}$ map of phonon-assisted tunnelling. Colour scale: yellow to red is 0 to $3.8 \cdot 10^{-5} \Omega^{-1} \mathrm{~V}^{-1}$. (C) $d I / d V$ map of resonant tunnelling due to the presence of impurities in hBN tunnel layer. Colour scale: yellow to red is 0 to $7 \cdot 10^{-8} \Omega^{-1}$. (D) $d I / d V$ map of resonant tunnelling with momentum conservation due to crystallographic alignment of two graphene electrodes. Blue colour marks the range of voltages where the negative differential conductivity is observed. Colour scale: blue to white to red is $-6 \cdot 10^{-6}$ to 0 to $6 \cdot 10^{-6} \Omega^{-1}$. (E,F) Indirect excitons in $\mathrm{MoS}_{2} / \mathrm{WSe}_{2}$ heterostructure. Photoexcited electrons from $\mathrm{WSe}_{2}$ are accumulated in $\mathrm{MoS}_{2}$. Photoexcited holes from $\mathrm{MoS}_{2}$ are accumulated in $\mathrm{WSe}_{2}$. (G) TMDC (large blue and white spheres) sandwiched between two graphene (small light-blue spheres) electrodes for photovoltaic applications. Photocarriers generated in TMDC are separated into the opposite graphene electrodes due to electric field created by external gate (not shown). The structure can be encapsulated in hBN (purple and yellow spheres). (H,I) Vertical LED heterostructures. hBN barriers increase the dwell time of the electron and hole in the TMDC, allowing their radiative recombination. Multiple quantum wells, formed by different materials, can be utilised in such structures (I). Colouring of the atoms same as in (G). (J-L) Polaritonic dispersions of graphene, hBN and graphene/hBN heterostructure.