Nanodevices engineering and spin transport properties of MnBi2Te4 monolayer

Two-dimensional (2D) magnetic materials are essential for the development of the next-generation spintronic technologies. Recently, layered van der Waals (vdW) compound MnBi2Te4 (MBT) has attracted great interest, and its 2D structure has been reported to host coexisting magnetism and topology. Here, we design several conceptual nanodevices based on MBT monolayer (MBT-ML) and reveal their spin-dependent transport properties by means of the first-principles calculations. The pn-junction diodes and sub-3-nm pin-junction field-effect transistors (FETs) show a strong rectifying effect and a spin filtering effect, with an ideality factor n close to 1 even at a reasonably high temperature. In addition, the pip- and nin-junction FETs give an interesting negative differential resistive (NDR) effect. The gate voltages can tune currents through these FETs in a large range. Furthermore, the MBT-ML has a strong response to light. Our results uncover the multifunctional nature of MBT-ML, pave the road for its applications in diverse next-generation semiconductor spin electric devices.


INTRODUCTION
The discovery of magnetic van der Waals (vdW) layered materials has inspired tremendous research interest recently as they provide new opportunities for the development of magnetic nanodevices. Scientists have utilized their spin degree of freedom to demonstrate exotic phenomena and devoted significant efforts to fabricate vdW ultrathin films down to the monolayer (ML) limit. It has been reported that the magnetic properties of vdW layered materials change significantly as their thickness reduces to atomically thin, and many of 2D vdW monolayers appear to be promising for spintronics applications. 1,2 In particular, enormous opportunities arise as a consequence of reduced dimensionality, which allows gating capabilities to tune their physical properties in a large range. Therefore, searching for functional 2D magnetic monolayers and designing conceptual nanodevices are extremely active and may forcefully drive the new technological development.
Here, we propose several conceptual MBT-based nanodevices and investigate their spin-dependent transport properties with the first-principles approach. We first construct pn-junction diodes with a MBT-ML and demonstrate its spin-dependent transport function.
This incites us to build up several MBT-ML field-effect transistors that can be used for the design of spin logic circuits and storage units. We further propose MBT-based phototransistors and show the potential utilizations of MBT-ML in photoelectric nanodevices. with previous work. 35,36 MBT-ML was prepared on the Si (111) substrate in a so-called SL-by-SL manner by alternative growing quintuple-layer of Bi2Te3 and bilayer of MnTe in molecular beam epitaxy. 33 The dynamic stability of the free-standing MBT-ML is confirmed by its phonon spectrum (Fig. 1b), which has no imaginary phonon modes. According to the projected phonon density of states (Ph-DOS) in Fig. 1b  The cone-shaped conduction-band near the Γ point (Fig. 1g, i) suggests mostly isotropic effective mass around the Γ point. They are 0.10 and 0.13 me (me is the free electron mass) for the spin-up and -down states, corresponding to Fermi velocities of 6.5 × 10 5 and 4.0 ×10 5 m/s, respectively, which is close to those of graphene and silicene. 37 The MBT-ML hence has higher carrier mobility and larger transmission possibility in the spin-up channel, and a spin-polarized electronic transport behavior is expected. Besides, both the energy dispersions and effective mass become anisotropic away from Γ point, such as between the x axis (along 6 zigzag direction) and y axis (along armchair direction) shown in Fig. 1a, which should lead to anisotropic transport properties along these two directions like many other 2D materials. 6,[38][39][40] Note that the bandgap becomes smaller (see Supplementary Fig. 1a) as considering the spin-orbit coupling (SOC), consistent with the previous report. 41 This suggests that the semiconductor nanodevices based on the MBT-ML is easily achieved when the SOC is included. In the following, we design several conceptual nanodevices of MBT-ML and mainly focus on its spin-polarized transport behaviors without SOC, which qualitatively retains its electronic transport properties based on a test (see Supplementary Fig. 1b).

Spin Transport Properties and PN-Junction Diodes of MnBi2Te4 Monolayer. A
pn-junction diode of MBT-ML ( Fig. 2a) is first constructed by using the method of electrostatic doping with p-and n-type atomic compensation charges, 42 which has been used for various nanodevices modeling. 39,[43][44][45] According to the atomic lattice structures (Fig. 1a), there exist two types of MBT-ML diode structures, i.e., Z-type (along the x axis, zigzag at edges) and A-type (along the y axis, armchair along the edges). We consider three levels of doping densities of p-and n-type carriers, i.e., 3 × 10 12 cm -2 (low), 3 × 10 13 cm -2 (medium),  Each spin-resolved I-V curve of the Z-type pn-junction diode of MBT-ML (Fig. 2b) shows a strong unidirectional transport feature, with a high rectifying ratio up to 10 7 as shown  tunneling under a reverse bias, such as -0.8 V (Fig. 2f). In contrast, the electron transmission retains zero under a forward bias due to the band alignment as depicted in Fig. 2g.
Furthermore, the PLDOS of spin-up state has smaller gap between valence and conduction band than spin-down state, thus the transmission of spin-up state can do better (Fig. 2f).
Within the BW, strong transmission occurs near the Γ point (Fig. 2h). For the spin-up states, transmission coefficients remain high over the whole Brillouin zone, i.e., from Γ to Y (-Y).
The transmission becomes zero close to Y (-Y) for the spin-down states. This causes the much reduced transmission for the spin-down states under a reverse bias and appearance of a spin-polarized behavior. These factors result in the strong rectifying and spin filtering effects of the Z-type pn-junction diode of MBT-ML. Note that the similar rectifying effect persists as the SOC is included in band and transport calculations (see Supplementary Fig. 1b). Therefore, the concepts we discussed above holds in actual MBT diodes, providing that the reduction of spin mean free path by SOC is insignificant because of the small size of pn-junction. The total current and differential conductance (dI/dV) density of the Z-type pn-junction diode of MBT-ML are 752 mA/mm (Fig. 2b) and 3 S/mm (Fig. 3a) at -0.8 V, respectively.
The dI/dV curve also shows a spin-polarized behavior, particularly strong under a low bias below −0.2V. The tunneling current mostly appears within the BW, according to the spectral currents shown in Fig. 3b, c. Note that the low doping concentration decreases the current density a little and retains the spin filtering and rectifying effects, while the high doping concentration significantly increases the current density (see Supplementary Fig. 2). The A-type pn-junction diode of MBT-ML shows similar rectifying and spin filtering effects with the same mechanisms (see Supplementary Fig. 3, 4) to its Z-type diode. The current along the A direction is slightly smaller than that along the Z direction due to larger carrier effective mass along A direction, implying its weak anisotropy ratio (1.3). 40 Furthermore, the I−V characteristics of the pn-junction diodes of MBT-ML can be described by 42 where q and T are the elementary charge and temperature respectively, I0 indicates the saturation current, and n is the so-called ideality factor that is an important parameter to assess how much the pn-junction resembles an ideal diode (n = 1). One can extract the value of the ideality factor from the slope of a log-plot of I/(1 − e −qVb/kBT ) against Vb. As a result, both the ideality factors of both Z-and A-type pn-junction diodes of MBT-ML are 1.1 (close to the ideal case) at room temperature (Fig. 3d), and can retain a high value up to 500 K (Fig. 3e).
(3) Figure 4b shows the I−V curves of the Z-type pin-junction FET of MBT-ML under zero gate voltage. Compared with the pn-junction diode of MBT-ML, the Z-type pin-junction FET of MBT-ML shows the same spin filtering and perfect rectifying effects with the same transport mechanisms (see Supplementary Fig. 5), although its current density is slightly suppressed due to the semiconductor nature of the central intrinsic region. Strikingly, when a positive or negative gate voltage is applied, the current density is dramatically enhanced (Figure 4c,d), demonstrating an excellent field-effect behavior.
According to the goals of the ITRS 2015 edition, 48  All of their current densities increase monotonically as the gate voltage increases, and achieve the off-state at Vg = 0.5 V. The corresponding on/off ratios at room temperature for HP(LP) are 24 (16), 43 (28), and 61 (40), respectively. The on/off ratios remain constant up to 400 K (Fig. 4f), and may further increase to achieve the three goals in 2024, 2027, and 2030.
The A-type pin-junction FET of MBT-ML shows the same field-effect properties to its Z-type counterpart and has even larger on/off ratios (see Supplementary Fig. 6,7). Besides, we also construct and investigate two other types of MBT-ML FETs, i.e., pip-and nin-junction FETs (see Supplementary Fig. 8:13). Each of them shows an interesting negative differential resistive (NDR) effect 49 and a spin filtering effect with larger polarization ratios. Figure 5 schematically illustrates their NDR mechanisms and the rectifying mechanism of the pin-junction FET that is consistent with the previously discussed pn-junction diode. For the pip-junction FET, its VB is adjacent to the EF and plays a critical role in the NDR behavior.
Very differently, for the case of nin-junction FET, its CB adjoins to the EF and dominates the electron transport.

Fig. 5 Rectifying and NDR mechanisms of the transistors of MnBi2Te4 monolayer. a
Rectifying mechanism of pin-junction FETs of MnBi2Te4 monolayer. b NDR mechanism of pip-junction FETs of MBT-ML. c NDR mechanism of nin-junction FETs of MBT-ML. Green shadow is the bias window.  and  refer to the strong and weak transport, and  indicates the prohibited transport.
Phototransistors of MnBi2Te4 Monolayer. We further investigate the photoelectric performance of MBT-ML and its potential applications in spin-photonics. The optical-conductivity σ (|real| part) is found to be almost unchanged as different functionals are used in our calculations, i.e., spin-polarized generalized gradient approximation 50 and local density approximation. 51 The photoconduction process is opened as the photon energy is higher than the energy gap of MBT-ML (Fig. 1c,d). It has a broad σ peak in the whole visible region (Fig. 6a) for both the spin-up and -down states, and it is therefore promising for developing photovoltaic devices within the AM1.5 standard. 52 Whereafter, a phototransistor based on the pin-junction of MBT-ML is designed (Fig. 6b) and its photoelectric transport properties under illumination are unveiled, as well as the regulation effect from the gate electrode. In this work, linearly polarized light is considered and the incident photon energy is set from 0 to 5 eV. The first-order correction to the photo-generated current into electrode α = D/S due to absorption of photons with frequency ω is given by 44,53 , The total photocurrent is obtained by Iph = ID − IS. More details about the photocurrent are provided in the Supplementary D1. Under zero bias (without power), the Z-type pin-junction phototransistor of MBT-ML has a good photo response in the visible region due to its large σ in that region, and its total photocurrent is as high as 22 mA/mm 2 (Fig. 6c), much larger than a silicon solar-cell device. 44 In addition, the spin-up photocurrents have a larger proportion and a stronger peak in yellow light region, demonstrating its key role in photoelectric sensors. Generally, a gate electrode can be employed to tune the optical response of a phototransistor. 54,55 The applied gate voltages significantly influence the photoelectric performance of the Z-type pin-junction MBT-ML phototransistor. For instance, it is easy to generate a strong photocurrent peak under low gate voltages (Fig. 6d), while high gate voltages lower its photoelectric performance and should be avoided in a photovoltaic device.
Therefore, the Z-type pin-junction phototransistors of MBT-ML can be utilized as photovoltaic devices or photoelectric sensors for detecting yellow light. For the A-type pin-junction phototransistor of MBT-ML, whose spin-down state plays a key role, it generates a peak in the yellow (for spin-up state) and the blue light (for spin-down state), respectively.
The total photocurrent amplitude is half of the Z-type phototransistor (see Supplementary Fig.   14). Last, the photoelectric performances of other types of MBT-ML (i.e., pip-and nin-junction) are lower than its pin-junction phototransistors (see Supplementary Fig. 15:18), and they may be overshadowed in photovoltaic devices.
In summary, we have designed various conceptual nanodevices based on the MnBi2Te4 monolayer (listed in Table I)

METHODS
All the first-principles self-consistent calculations are performed by the density-functional theory combined with non-equilibrium Green's function method using the Atomistix Toolkit code. [56][57][58] The Norm-Conserving pseudopotentials, 59 linear combinations of atomic orbitals basis sets, and the spin-polarized Perdew-Burke-Ernzerhof exchange-correlation functional at the level of generalized gradient approximation (GGA) are used. 50,60 The GGA+U method is employed to describe the localized 3d orbitals of Mn atoms and U = 4 eV is adopted according to previous tests. 41 A real-space grid density mesh cut-off of 100 Ha is used. The Monkhorst-Pack k-point grids 1 × 5 × 200 and 1 × 9 × 150 are used to sample the Brillouin zone for the electrodes of Z-type and A-type MBT-ML devices, respectively. The total energy tolerance and residual force on each atom are less than 10 −6 eV and 0.001 eV/Å in the structural relaxation of both lattice constants and atomic positions, respectively.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.