Magnetic topological transistor exploiting layer-selective transport

We propose a magnetic topological transistor based on ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, in which the “on” state (quantized conductance) and the “off” state (zero conductance) can be easily switched by changing the relative direction of two adjacent electric fields (parallel vs antiparallel) applied within a two-terminal junction. We explain that the proposed magnetic topological transistor relies on a novel mechanism due to the interplay of topology, magnetism, and layer degrees of freedom in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Its performance depends substantially on film thickness and type of magnetic order. We show that “on” and “off” states of the transistor are robust against disorder due to the topological nature of the surface states. Our work opens an avenue for applications of layer-selective transport based on the topological van der Waals antiferromagnet ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

Figure 1

(a) Schematic of a magnetic topological transistor based on magnetic TIs. The magnetic TI (yellow) is grown on a substrate (grey). Two independent electric fields are applied to two neighboring regions. The middle region marked by two dashed lines is free of external electric fields. The external electric field in the left region is fixed along $z$ direction. The angle $\theta$ describes the relative angle of the two independent electric fields. For case I, the electric field in the right region is parallel to that in the left region and the transistor is in the “on” state. For case II, the electric field in the right region is antiparallel to that in the left region and the transistor is in the “off” state. The purple and green colors represent the dominant surface states crossing the Fermi level at top and bottom of the sample, respectively. (b) Two-terminal conductance of the magnetic topological transistor that switches from “on” (quantized conductance) to “off” (zero conductance) as the relative direction of the electric fields changes from parallel ($\theta =0$) to antiparallel ($\theta =\pi$).

Figure 2

(a) Spectra for antiferromagnetic ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ films color-coded by the position expectation value $\langle z\rangle$ along $z$ direction in presence of opposite electric field directions. (b) Berry curvature distributions for even-layer films. Here we set $k_y=0$. The chosen parameters are adopted to the material ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ as described in Appendix pp1.

Figure 3

(a) Spectrum of even-layer 3D slab with $N_z=12$. The black and purple dashed lines represent Fermi energies at $E_F$=10, 50 meV, respectively. (b) Conductance $G$ of the magnetic topological transistor as a function of Fermi energy for different external field configurations with $N_z=12$ (even layers). The symbols $\mathrm{E}\uparrow \uparrow$ and $\mathrm{E}\uparrow \downarrow$ represent the relative directions of the electric field for left and right leads to be parallel and antiparallel, respectively. The black and purple dashed lines represent Fermi energies at $E_F$=10, 50 meV, respectively. (c) Conductance $G$ as a function of junction thickness $N_z$ with $E_F$=30 meV. The inset shows the on-off ratio $r\equiv G_{\mathrm{on}}/G_{\mathrm{off}}$ as a function of $N_z$. (d) Conductance $G$ as a function of magnetic and nonmagnetic disorder strength $W_0$ with $N_z=10$. The spin polarization of the magnetic disorder is along $z$ direction. The Fermi level is fixed at $E_F$=25 meV. Open (periodic) boundary conditions are imposed in $z\left(y\right)$ direction. The other parameters in all plots are specified in [61].

Figure 4

(a) Conductance $G$ as a function of $N_x$ for case II in Fig. 1 with $N_z=9$, 11, and 13, respectively. (b) Conductance $G$ as a function of $N_x$ for case II in Fig. 1 with $N_z=8$, 10, and 12, respectively. We choose Fermi energy $E_F$=30 meV, and other parameters are the same as in Fig. 3. (c) Illustration of the Berry curvature for top surface (purple region) and bottom surface (green region) for antiparallel configuration $\mathrm{E}\uparrow \downarrow$ for odd-layer thin films. Red arrows and blue arrows represent opposite Berry curvature. $N_x$ is the length of the middle region and $N_z$ is the thickness of the thin films. (d) Illustration of the Berry curvature for top surface and bottom surface for antiparallel configuration $\mathrm{E}\uparrow \downarrow$ for even-layer thin films.

Figure 5

(a) Spectrum and Berry curvature distribution for odd-layer film with $N_z$=9 and $V$=30 meV. The dashed line indicates the Fermi energy $E_F$. (b) The spin texture of the energy cut in (a) with $E_F$=40 meV.

Figure 6

(a) Conductance $G$ as a function of Fermi energy for odd-layer thin films with $N_y$=20 and $N_z$=13. (b) Conductance $G$ for the multimode case as a function of energy for even-layer thin films with $N_y$=50 and $N_z$=12.

Figure 7

(a) Schematic of the scattering process for the “off” state of the magnetic topological transistor with ${\mathrm{\Phi }}_t^{\pm }$ and ${\mathrm{\Phi }}_b^{\pm }$ the top and bottom right-moving and left-moving modes, respectively. $S_m$ and $S_{t/b}$ are the scattering matrices. (b)Two scattering paths for the transmission $T\left(E\right)$. Quantum interference occurs between two paths (red and blue thick lines).