The thick red (thin blue) arrow corresponds to the spin-up (spin-down) current. (d) Local current density distribution of multichannel germanene transistor in the on state with λ E = 0 and ε = 10 meV, and with central region size N x = 40 and N y = 24. (c) Drain current I D of the multichannel normal germanene FET as a function of λ E with bias voltages of V D S = 10, 30, and 50 mV. Inset shows the corresponding on-state local current density distribution with λ E = 0 and the energy ε = 10 meV. (b) Drain current I D of the dual-channel normal germanene FET versus λ E with bias voltages of V D S = 10, 30, and 50 mV. (a) Drain current I D of the multichannel ferromagnetic germanene FET as a function of electric-field-induced staggered potential λ E with different values of the bias voltage V D S. Each magnetic insulator layer is divided into two parts, and the magnetization of the magnetic insulator is indicated by the red arrows in the dark region and blue arrows in the light region. (b) Side schematic of the germanene and magnetic insulator layers.

A pair of top and bottom gates are used to provide an electric field perpendicular to the germanene. The removed Ge atoms are represented by light gray spheres, and four Ge atoms removed along the y axis on the leftmost side are marked with red numbers. Some Ge atoms in the germanene sheet with N x = 18 and N y = 4 are removed. The number of unit cells in the x-axis direction and atom sites (black and light gray spheres) in per unit cell are N x = 18 and N y = 24, respectively. The Ge atoms (represented by the black spheres) form a buckled germanene layer, and the unit cell of the germanene is marked by red spheres ( A sites) and green spheres ( B sites). (a) Schematic cross-section view of the ferromagnetic germanene FET, in which the central device is decomposed into seven layers. All the results indicate that the proposed ferromagnetic germanene FET is a promising candidate for ultra-low-power dissipation topological devices. With the moderate increase in the exchange field, the switching mechanism is not changed, but the threshold electric field and breakdown voltage of the FET can be, respectively, reduced and enhanced significantly. In the low electric field conditions, the switching-off mechanism is due to spin blocking caused by the edge-state mismatch, while for relatively high electric field cases, both the edge-state mismatch and energy-valley mismatch are utilized. The ferromagnetic germanene FET can be turned off just by adjusting the electric field. Under the coaction of electric induced staggered potential and staggered exchange field, both the 100 % spin-polarized edge states and valleys can be achieved. The proposed multichannel ferromagnetic germanene transistor has a twice on-state current and half subthreshold swing than that of traditional germanene FETs. The results reveal that new edge channels can be formed by removing some Ge atoms along the x axis of the device.

The electron transport properties of the topological transistor are investigated through the nonequilibrium Green’s function method. Based on ferromagnetic germanene, we theoretically propose a multichannel depletion-type field-effect transistor (FET) operated by a vertical electric field.

Field effect transistor