Suppression of magnetoresistance in PtSe₂ microflakes with antidot arrays

Platinum diselenide (PtSe₂) is a recently discovered two-dimensional (2D) transition metal dichalcogenide [1, 2], its exotic spin texture gives an application opportunity in electrically tunable spintronics [3]. The high electron mobility and air-stability of few-layer PtSe₂ devices have aroused great research interest for nanoscale electronic applications [4, 5], such as gas sensing [6, 7] and catalytics [8]. Moreover, the bulk PtSe₂ is theoretically predicted as a candidate of the type-II Dirac semimetal [9]. The anisotropic three-dimensional Dirac cones with the Dirac cone highly tilted along the k_z direction in the Brillouin zone are experimentally observed by using angle-resolved photoemission spectroscopy [10]. Therefore, the electrical transport study of PtSe₂ devices is very important not only for fundamental physics, but also for future applications in electronics and catalysis.

Magnetoresistance (MR) is a key property to examine the electron transport mechanisms in materials and devices, and is also applied in variety areas, such as magnetic field sensing and magnetic storage [11–13]. For a nonmagnetic material, its MR has the attractive features such as no magnetic hysteresis and high MR value, making it has potential application in magnetoelectronics devices [14–16]. However, in some cases, for example, to measure the temperature, or gas concentration, or humidity in a magnetic field environment, the MR of sensitive materials will lead to a measurement error [17–19]. The high MR value and the large measurement error. Therefore, the suppression of MR is useful for the sensor applications in the magnetic field environments.

In this work, we report on the suppression of MR in PtSe₂ microflakes by introducing the antidot arrays (AAs). AA is a fascinating artificial microstructure, which is consists of an array of holes in a film. The anomalous quantum transport properties of AAs, fabricated on the semiconductor heterostructures, graphene, topological insulators, etc, have been widely investigated previously [20–27]. Here, the AAs were fabricated on the PtSe₂ microflakes. We compared the magnetotransport behaviors of PtSe₂ microflakes before and after milling of AAs. The notable suppression of MR was observed while the AAs are milled in the PtSe₂ microflakes. Our work gave an evidence of MR suppression by introducing AAs in the materials/devices, which may be useful for the PtSe₂-based sensor applications to immure magnetic field.

The high-quality PtSe₂ bulk crystals were purchased from the commercial company (HQ Graphene, the Netherlands). By using a mechanical exfoliated method, the thin PtSe₂ microflakes were transferred onto the silicon substrate covered by 300 nm silica. The Ti/Au (10 nm/150 nm) electrodes were patterned onto the microflakes by a series of processes including the photolithography, electron beam evaporation deposition and lift-off technology. The thickness of the samples was determined by atomic force microscopy. The AA patterns were etched in the PtSe₂ microflakes via focused ion beam (FIB) direct writing technology. The electrical transport properties of the PtSe₂ devices were measured in a quantum design physical property measurement system.

Figure 1(a) shows a PtSe₂ device which prepared the six-probe Hall-type electrodes (denoted as S1). The thickness of S1 is around t = 98 nm. Its length (L, the distance between the two voltage probes) and width (W) are both 10 μm. A periodic distributed AA pattern was etched in this PtSe₂ microflakes (figure 1(b)). The average diameter of the antidots was around d = 0.9 μm. As we know, the lattice damages could be occurred by the Ga ion implantation of FIB technology. The serious damages could alter the crystal structure of PtSe₂ materials. To overcome this disadvantage, we kept the ratio d/a = 0.5 (a is the center-to-center distance between the adjacent antidots) in our experiments. In such case, the PtSe₂ materials can not be completely damaged after AA fabrication [28]. Figure 1(c) shows the Raman spectrums of the PtSe₂ device before and after AA milling. The Raman peaks at 175 and 205 cm⁻¹ are belong to the E_g and A_1g modes of PtSe₂ crystal. The notable Raman modes are both observed in PtSe₂ device with and without AAs, this result demonstrated that the PtSe₂ crystal structure is not changed after FIB machining.

Zoom In Zoom Out Reset image size

Figure 1(d) displays the temperature dependence of resistance of sample S1 with and without AAs. We can see that, after etching AAs, the device's resistance increased compared with the pristine microflake. For sample S1 at T = 2 K, we could obtain that ${R}_{{\rm{A}}{\rm{A}}}=44.76\,{\rm{\Omega }},$ ${R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}=0.54\,{\rm{\Omega }}$ and ${R}_{{\rm{A}}{\rm{A}}}/{R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}=83.$ Furthermore, we could obtain the bulk resistivity ${\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\,={R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\times Wt/L=0.053\,\mu {\rm{\Omega }}\,{\rm{m}}$ for the pristine sample. While the AAs were etched in the PtSe₂ microflake, the effective volume of materials ${V}^{\star }$ can be estimated by ${V}^{\star }\,=L{W}^{\star }t=LWt-N\times {(\pi {d}^{2}/4)}^{2}t,$ where N is the total number of antidots. Then, we could obtain the bulk resistivity of flakes with AAs ${\rho }_{{\rm{A}}{\rm{A}}}={R}_{{\rm{A}}{\rm{A}}}\times {W}^{\star }t/L=1.597\,\mu {\rm{\Omega }}\,{\rm{m}},$ and ${\rho }_{{\rm{A}}{\rm{A}}}/{\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}=30.$ If we suppose that any resistance increase in PtSe₂ microflakes would result from a reduction of the flake's cross-sectional area for the current path, then we should observe that ${\rho }_{{\rm{A}}{\rm{A}}}/{\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\sim 1.$ Obviously, this assumption is conflict to the experimental results, the detailed reasons should be further investigated.

Hall resistance of PtSe₂ microflakes was also measured. Figure 1(e) presents the ${R}_{xy}-B$ curves of sample S1 with and without AAs at T = 2 K. Then, we could extract the electron concentration ${n}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\sim 0.96\times {10}^{21}\,{{\rm{cm}}}^{-3}$ and ${n}_{{\rm{A}}{\rm{A}}}\,=1.54\times {10}^{21}\,{{\rm{cm}}}^{-3}$ for S1 without and with AAs respectively. By repeating the above sequence, we could obtain the relevant parameters for S1 at T = 300 K, and the results have been listed in table 1. We can see that ${n}_{{\rm{A}}{\rm{A}}}/{n}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\sim 1$ in the studied temperature range. We expect that the electron effective mass ${m}^{\star }$ is nearly unchanged in PtSe₂ microflakes while introducing AAs, that is, ${m}_{{\rm{A}}{\rm{A}}}^{\star }/{m}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}^{\star }\sim 1.$ According to $\rho ={m}^{\star }/(n{e}^{2}\tau ),$ where e is the electron charge and τ is the elastic scattering time, we found that ${\rho }_{{\rm{A}}{\rm{A}}}/{\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}\approx {\tau }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}/{\tau }_{{\rm{A}}{\rm{A}}}.$ Therefore, the significant increase of the bulk resistivity is originated from the enhanced electron scattering rate (1/τ) introduced by the AAs. As shown in figure 1(f), there are displayed two types of electron diffusion paths in the nanostructured flakes. The path ① presents the carriers transport in the bulk materials without the electron–antidot interactions (corresponding scattering time denoted as τ₁). If the electron–antidot scattering time τ_ea is take into account (the path ②), the total electron scattering rate can be expressed as ${\tau }^{-1}={\tau }_{1}^{-1}+{\tau }_{{\rm{e}}{\rm{a}}}^{-1}.$ Obviously, the electron scattering rate is enhanced while appearing AAs in PtSe₂ flakes.

Table 1.  Parameters of sample S1.

	R (Ω)			ρ (μΩ m)			n (1021 cm−3)
T (K)	w/o AA	AA	$\displaystyle \frac{{R}_{{\rm{A}}{\rm{A}}}}{{R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}}$	w/o AA	AA	$\displaystyle \frac{{\rho }_{{\rm{A}}{\rm{A}}}}{{\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}}$	w/o AA	AA	$\displaystyle \frac{{n}_{{\rm{A}}{\rm{A}}}}{{n}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}}$
2	0.54	44.76	83	0.053	1.597	30	∼0.96	1.54	∼1.6
300	3.53	91.72	26	0.346	3.272	9.5	7.78	8.73	1.1

Figure 2 displays the MR curves of sample S1 with and without AAs. We can see that the MR values of PtSe₂ microflakes with AAs are greatly suppressed comparing to that of the pristine PtSe₂ microflakes (figures 2(a), (b)). For example, MR = 121% and 8% for S1 without and with AAs respectively, at T = 2 K, where MR = [R(B) − R(0)]/R(0) × 100%. If we define ${C}_{{\rm{M}}{\rm{R}}}={\rm{M}}{{\rm{R}}}_{{\rm{A}}{\rm{A}}}/{\rm{M}}{{\rm{R}}}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}},$ we could obtain ${C}_{{\rm{M}}{\rm{R}}}^{-1}=15$ for S1 at T = 2 K. With the temperature increasing, the MR is weakened both PtSe₂ microflakes with and without AAs (figures 2(c), (d)). Nevertheless, the MR of AA device is always suppressed in the studied temperature range compared to the pristine device. The suppressing factor ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ is decreased with temperature increasing. The insets of figures 2(c), (d) show the Kohler plot of the MR data of S1 with and without AAs. The MR curves gradually deviated from the universal curve with the temperature increasing, which suggests that the multiple electron scattering processes are dominate in the PtSe₂ microflakes with and without AAs.

Zoom In Zoom Out Reset image size

As we know, the commensurability effect of MR is usually observed in a strong spatially modulated potential [20, 22, 29], which is associated with the commensurate orbits encircling a specific number of antidots. Obviously, the high carrier mobility of materials is necessary to observe the commensurability oscillations. Furthermore, the resistance peak position, corresponding orbits around 1 antidot, can be estimated as ${B}_{1}=2\hslash \sqrt{2\pi {n}_{s}}/ea\approx 18\,{\rm{T}}$ for our PtSe₂ microflakes, where $\hslash$ is the Planck constant and n_s is the 2D carrier density. We can see that B₁ is outside of the magnetic field range in this work. And taking into account the low mobility of our PtSe₂ microflakes (μ ∼ 0.1 m² V⁻¹ s⁻¹), the commensurability transport is therefore absent.

Figure 3 shows the transport properties of other PtSe₂ devices, the suppressed MR by introducing AAs is further confirmed. Here, three types of AA are prepared in the PtSe₂ microflakes. The first type is the periodic distributed AA (sample S2, figure 3(a)). The second type is the quasi-random distributed AA (sample S3, figure 3(d)), in which the every antidot is randomly distributed in the every sub-area while the entire area is periodically divided into N × M sub-areas. The third type is the random distributed AA (sample S4, figure 3(g)), where the antidots are randomly distributed in the entire area. By analyzing the experimental results of S2–S4, the main theses discussed above are confirmed, that is, comparing to the pristine samples, (i) the electron scattering rate is enhanced while introducing AAs, which leads to the increment of resistance for samples with AAs; (ii) the MR is suppressed for all samples while introducing AAs. One interesting phenomenon is that the resistance upturns with decreasing temperatures at T < 50 K for S3 with AAs (figure 3(e)). Moreover, a weakly MR dip around zero-field can be identified for the nanostructured sample S3 (the inset of figure 3(f)). These results may be originated from the weak antilocalization effect due to the quantum confinement effect [28].

Zoom In Zoom Out Reset image size

In figure 4(a), we have given a summary of resistance ratio ${C}_{R}={R}_{{\rm{A}}{\rm{A}}}/{R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}$ as a function of temperature for S1–S4. We can clearly see that ${C}_{R}$ is gradually decreased with increasing temperature. According to above discussions, we have known that the resistance increments of PtSe₂ microflakes with AAs are resulted from the scattering rate (1/τ_ea) enhancement of electron–antidot scattering. If we denoted the resistivity of pristine PtSe₂ microflakes as ${\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}={m}^{\star }/(n{e}^{2}{\tau }_{1}),$ where τ₁ is the electron scattering time including electron–impurity, electron–electron, electron–phonon interactions, and so on. Then, the resistivity of PtSe₂ microflakes with AAs can be written as ${\rho }_{{\rm{A}}{\rm{A}}}=\displaystyle \frac{{m}^{\star }}{n{{e}}^{2}}({\tau }_{1}^{-1}+{\tau }_{{\rm{e}}{\rm{a}}}^{-1}).$ Finally, we obtained that

$$\begin{eqnarray}&&{C}_{R}=\displaystyle \frac{{R}_{{\rm{A}}{\rm{A}}}}{{R}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}}\propto \displaystyle \frac{{\rho }_{{\rm{A}}{\rm{A}}}}{{\rho }_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}}=1+\displaystyle \frac{{\tau }_{{\rm{e}}{\rm{a}}}^{-1}}{{\tau }_{1}^{-1}}.\end{eqnarray} \tag{ 1 }$$

Obviously, ${\tau }_{1}^{-1}$ is increases with increasing temperature and ${\tau }_{{\rm{e}}{\rm{a}}}^{-1}$ is nearly independent to the temperature. Therefore, we observed that ${C}_{R}$ is decreases with increasing temperature.

Zoom In Zoom Out Reset image size

Figure 4(b) plotted the MR ratio ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ as a function of temperature for S1–S4. At the beginning, we tried to understand the physical mechanisms behind the suppressed MR with AAs. The classical orbital MR theory [30] gives that ${\rm{M}}{\rm{R}}\approx {(\mu B)}^{2},$ where $\mu =e\tau /{m}^{\star }$ is the electron mobility. After a few steps simple calculations, we could obtain that

$$\begin{eqnarray}&&{C}_{{\rm{M}}{\rm{R}}}^{-1}={\left(1+\displaystyle \frac{{\tau }_{{\rm{e}}{\rm{a}}}^{-1}}{{\tau }_{1}^{-1}}\right)}^{2}.\end{eqnarray} \tag{ 2 }$$

That is, ${C}_{{\rm{M}}{\rm{R}}}^{-1}\propto {C}_{R}^{2}.$ As shown in figure 4(b) for T = 2 K, we can see that ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ is increases with increasing ${C}_{R}$ for S1, S2 and S4, but S3 is outside with this rule. This may be originated from the quantum interference (weak antilocalization) effect in S3. Let us concentrate on the data at T = 30 K, where the quantum interference effect is weakened in S3, we can see that the scaling law of ${C}_{{\rm{M}}{\rm{R}}}^{-1}\propto {C}_{{R}}^{2}$ is nearly satisfied. Furthermore, please see the inset of figure 4(b), where ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ has been plotted as a function of ${C}_{R}^{2}$ for sample S1. The linear relationship between ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ and ${C}_{R}^{2}$ demonstrates the accuracy of equation (2). Next, according to ${C}_{{\rm{M}}{\rm{R}}}^{-1}\propto {C}_{R}^{2},$ the ${C}_{{\rm{M}}{\rm{R}}}^{-1}(T)$ behaviors can be interpreted by the ${C}_{R}(T)$ data. That is, ${C}_{{\rm{M}}{\rm{R}}}^{-1}\,({C}_{R})$ is decreases with increasing temperature. Finally, we could notice that ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ is increases with increasing temperature for $T\lesssim 30\,{\rm{K}}$ in samples S2–S4. Obviously, this contradicts with the predictions of ${C}_{{\rm{M}}{\rm{R}}}^{-1}\propto {C}_{R}^{2}.$ In our previous work [31], we have reported the anomalous magnetotransport properties of PtSe₂ microflakes, that is, the MR value increases with increasing temperature at low-temperature regime. We could expect that the low-temperature ${C}_{{\rm{M}}{\rm{R}}}^{-1}$ is dominated by ${\rm{M}}{{\rm{R}}}_{\displaystyle \frac{w}{o}{\rm{A}}{\rm{A}}}$ due to the ${\rm{M}}{{\rm{R}}}_{{\rm{A}}{\rm{A}}}$ is suppressed by AAs. We therefore observed the anomalous behaviors of ${C}_{{\rm{M}}{\rm{R}}}^{-1}(T)$ at low-temperature regime.

In conclusion, we reported the magnetotransport properties of PtSe₂ microflakes with and without AAs. Comparing with the pristine PtSe₂ devices (without AAs), the enhanced resistivity and suppressed MR are observed in the PtSe₂ microflakes with AAs. The physical mechanism behind above phenomena has been ascribed to the enhanced electron scattering rate due to the electron–antidot interactions. This method by introducing AAs to suppress MR may be useful for PtSe₂-based device applications to immure magnetic field.

This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 11604310, 61301015), the National Key Scientific Instrument and Equipment Development Project of China (Grant No. 2014YQ090709), the Key Laboratory of Ultra-Precision Machining Technology Foundation of CAEP (Grant No. ZZ15003) and Hubei Key Laboratory of Pollutant Analysis and Reuse Technique (Hubei Normal University) (Grant No. PA20170204).