Band structure engineering of van der Waals heterostructures using ferroelectric clamped sandwich structures

A novel strategy of band structure engineering of van der Waals heterostructure is proposed using a ferroelectric (FE) clamped sandwich structure from first principles. The validity of the strategy is demonstrated in the sandwich structure of ${\mathrm{In}}_2{\mathrm{Se}}_3$/bilayer-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ (${\mathrm{In}}_2{\mathrm{Se}}_3/\mathrm{bi}-{\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$) made by ferroelectric ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers and semiconducting bilayer (SB) ${\mathrm{CrI}}_3$. Four states with different band structures in the FE/SB/FE sandwich structure are obtained by switching the FE polarization in the top and bottom ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers. Two of the states possess spin-splitting semiconducting band structures with opposite spin channel in conduction bands which are generated from a spin-degenerated band structure of the ${\mathrm{CrI}}_3$ bilayer, resulting in an electric field controllable and nonvolatile four states spin-field effect transistor. The strategy of using FE layers to engineer band structures and generate spin-splitting semiconducting band structure in van der Waals heterostructure opens a new route in two-dimensional electronics and spintronics.

Figure 1

FE clamped sandwich structure of 2D ${\mathrm{In}}_2{\mathrm{Se}}_3$/bi-${\mathrm{CrI}}_3$/${\mathrm{In}}_2{\mathrm{Se}}_3$. The out-of-plane directions of FE polarization in ${\mathrm{In}}_2{\mathrm{Se}}_3$ layer are indicated by two thick pink arrows.

Figure 2

(a) Schematizations of four states (i.e., P1, P2, P3, and P4), (b) the corresponding band alignments, and (c) the sketches of effective charges as well as effective electric field of of ${\mathrm{In}}_2{\mathrm{Se}}_3$/bi-${\mathrm{CrI}}_3$/${\mathrm{In}}_2{\mathrm{Se}}_3$. The directions of out-of-plane polarization in the ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers are indicated by two thick pink arrows in (a). The translucent arrows represent the reversal directions of the polarization components in the ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers. The red and blue arrows in (b) represent the spin-up and spin-down channel energy level. In (c), red “$+$” and blue “−” represent the positive and negative charges which originates from the out-of-plane polarization, respectively. The cyan region and the small red arrows in P2 and P3 in (c) represent the effective built-in electric fields and their directions.

Figure 3

Projected band structures for the four states of the studied 2D ${\mathrm{In}}_2{\mathrm{Se}}_3$/bi-${\mathrm{CrI}}_3$/${\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructure. The black and gray bands represent the bands of top and bottom ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers, respectively, while the red and blue bands display the spin-up and spin-down bands of bilayer ${\mathrm{CrI}}_3$, respectively.

Figure 4

Schematic structure of the designed 2D semiconductor spin-field effect transistor based on the 2D ${\mathrm{In}}_2{\mathrm{Se}}_3$/bi-${\mathrm{CrI}}_3$/${\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructure. The source (S) and drain (D) are ferromagnetic metal. The gate voltages ${\mathrm{V}}_A$ and ${\mathrm{V}}_B$ are applied to switch the polarization of ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers and control the states of the system.