Colossal switchable photocurrents in topological Janus transition metal dichalcogenides

Nonlinear optical properties, such as bulk photovoltaic effects, possess great potential in energy harvesting, photodetection, rectification, etc. To enable efficient light-current conversion, materials with strong photo-responsivity are highly desirable. In this work, we predict that monolayer Janus transition metal dichalcogenides (JTMDs) in the 1T' phase possess colossal nonlinear photoconductivity owing to their topological band mixing, strong inversion symmetry breaking, and small electronic bandgap. 1T' JTMDs have inverted bandgaps on the order of 10 meV and are exceptionally responsive to light in the terahertz (THz) range. By first-principles calculations, we reveal that 1T' JTMDs possess shift current (SC) conductivity as large as $2300 ~\rm nm \cdot \mu A / V^2$, equivalent to a photo-responsivity of $2800 ~\rm mA/W$. The circular current (CC) conductivity of 1T' JTMDs is as large as $10^4~ \rm nm \cdot \mu A / V^2$. These remarkable photo-responsivities indicate that the 1T' JTMDs can serve as efficient photodetectors in the THz range. We also find that external stimuli such as the in-plane strain and out-of-plane electric field can induce topological phase transitions in 1T' JTMDs and that the SC can abruptly flip their directions. The abrupt change of the nonlinear photocurrent can be used to characterize the topological transition and has potential applications in 2D optomechanics and nonlinear optoelectronics.

With the development of strong light sources, nonlinear optical (NLO) materials have the potential to boost optoelectronic behaviors beyond the standard linear optical effects. In principle, any materials lacking inversion symmetry can be candidates for NLO applications. Recently, the generation of nonlinear direct photocurrent upon light illumination has evoked particular interest. This is known as bulk photovoltaic effect (BPVE). The photocurrent under linearly polarized light, or the shift current (SC), has been theoretically predicted and experimentally observed in materials such as multiferroic perovskites [1][2][3][4][5][6] and monolayer monochalcogenides [7][8][9] . The BPVE is a promising alternative source of photocurrent for energy harvesting. Compared with the conventional solar cells based on pn junctions, BPVE is not constraint by the Shockley-Queisser limit 10 and can produce open-circuit voltage above the bandgap 3 . Besides SC, the circular photogalvanic effect [11][12][13][14][15] (CPGE) that generates circular current (CC) (aka injection current) under circularly polarized light is yet another nonlinear photocurrent effect. In time-reversal invariant systems, SC is the response under linearly polarized light, while CC is the response under circularly polarized light, and the direction of CC can be effectively controlled by the handedness of circularly polarized light.
Besides energy harvesting, the nonlinear photocurrent effects can also be utilized for photodetection, especially in the mid-infrared (MIR) to terahertz (THz) regions, where efficient photodetectors are highly desirable. Compared with traditional infrared detectors such as MCT (HgCdTe) detector, photodetectors based on nonlinear photocurrent do not require biasing, hence the dark current can be minimized, which is advantageous especially at elevated temperatures.
Topological materials may be promising candidates for the NLO photodetection. For example, Weyl semimetals (WSMs) have singular Berry curvature around the Weyl nodes, leading to strong linear and nonlinear optical responses [16][17][18][19][20][21] . Recently, the unoptimized third-order photoresponsivity of WSM TaIrTe 4 is reported to be 130.2 mA/W under 4 μm illumination at room temperature 20 , comparable with that of state-of-art MCT detectors (600 mA/W) operating at low temperature 22,23 . Meanwhile, many other WSMs are predicted to have even larger second-order photo-responsivity 21 .
Compared to WSMs in 3D, which have vanishing bandgap and may lead to the overheating problem under strong light, 2D topological insulators (TIs) with finite bandgap on the order of 0.01 − 0.1 eV (within the MIR/THz range) may be a better choice, thanks to their good optical accessibility and easy band dispersion manipulation. (As a matter of nomenclature, despite small bandgap values ~ room , we still call these materials "insulators" due to the literature convention of topological insulators.) Due to the band inversion, TIs also have augmented Berry connections near the bandgap, which could enhance their optical responses 24,25 . In order better illustrate this effect, we first adopt a generic and minimal two-band model that can describe the band-inversion process 25  In Ref. 25 , it was demonstrated that band inversion ( > 0) would enhance the interband transition matrix ⟨ | | ⟩ (Figure 1 therein), where | ⟩ and | ⟩ are the wavefunction of the conduction and valence band, is the position operator. This is due to the orbital character mixture when band inversion occurs (e.g., both and orbital components are mixed in the valence and conduction bands of 1T' TMD monolayers 26 due to band inversion). Note that |⟨ | | ⟩| determines the response strength of the shift and circular currents, thus it should be expected that the band inversion would boost the nonlinear photocurrent responses.
Then we can calculate the shift current response function for the model Hamiltonian above. We first set = 2, = 1, = 0.1, and vary . The results are shown in Figure 1(a). One can see that when is positive (with band inversion, blue curve), | | is ~3 times larger than that when is negative (no band inversion, red curves) with the same absolute value | |. This clearly shows that band inversion can boost the nonlinear photocurrent responses for low frequencies near the bandgap. Besides, one can see that for positive and negative , has different signs, indicating that the photocurrents flow in opposite directions 24 . Another remarkable feature is that, when | | becomes smaller, the magnitude of the photoconductivity would increase, and there is a rough scaling relation | |~1/| |. Note that in the current model, | | measures the bandgap ( ∼ 2| |). Hence, we suggest that small bandgaps would also boost the nonlinear photoconductivity. We would like to note again that it is the band inversion, rather than the topological nature, that boosts the nonlinear photocurrent. Materials with band inversion can be topologically trivial. Furthermore, the magnitude of the photocurrent response is also dependent on the strength of inversion asymmetry. To elucidate this effect, we fix = 2, = 1, =1 and vary . The results are shown in Figure 1(b). One can see that scales approximately linearly with .
The model above suggests that materials with 1) band inversion, 2) strong inversion asymmetry, and 3) small bandgaps may well have large nonlinear photoconductivity. Guided by these principles, we predict that monolayers of Janus transition metal dichalcogenides (JTMDs, denoted as MXY, M = Mo, W , X, Y = S, Se, Te ) in their 1T′ phase possess colossal nonlinear photocurrent conductivity with first-principles calculations. Being TIs 26 , 1T′ JTMDs enjoy enhanced optical responses due to the band inversion, and the maximum SC conductivity is found to be around 2300 nm ⋅ μA/V 2 in THz range. Such colossal SC conductivity is also about tenfolds larger than that of many WSMs reported by far 21 and other non-centrosymmetric 2D materials, such as 2H TMDs 27 and monochalcogenides [7][8][9] . The CC conductivity of 1T′ JTMDs is also extremely large. The peak value of the CC conductivity is around 8.5 × 10 3 nm ⋅ μA/V 2 with a carrier lifetime of 0.2 ps. Owing to the small bandgap (∼ 10 meV), the SC conductivity peaks lie within the THz region, and quickly decay with increasing light frequency. The inert responsivity to light with higher frequencies renders 1T′ JTMDs selective photodetectors in the THz range. Furthermore, we find that the band topology and Rashba splitting of valence and conduction bands of 1T′ JTMDs can be effectively switched/tuned by small external stimuli such indicate trivial and nontrivial band topology, respectively). This is because the large Rashba splitting from the inversion symmetry-breaking could change the band topology by remixing the wavefunctions around the ±Λ point. As we will show later, both in-plane strain and out-of-plane electric field can induce a topological phase transition by closing and reopening the fundamental bandgap [35][36][37][38] . Regardless of the band topology ( 2 number), the band inversion around Γ point gives rise to a strong wavefunction mixing between valence bands (VB) and conduction bands (CB) 25 , which could significantly boost the linear and nonlinear responses.
In materials without inversion symmetry , NLO direct currents (dc) can be generated upon photo-illumination. This current can be divided into two parts, the shift current SC and the circular current CC where , , are Cartesian indices and ( ) is the Fourier component of the optical electric field at angular frequency . Eq. (1) indicates that when the optical electric field has both and components ( and can be the same), there will be a direct current along the -th direction when / is non-zero. In materials with time-reversal symmetry , the response functions within the independent particle approximation in clean, cold semiconductors are 39 Here all dependencies on are omitted. is the carrier lifetime. , are band indices, while Where is the frequency of the light. Here ≡ ⟨ |̂| ⟩ is the velocity matrix element. Eq. (2) uses the length gauge, while Eq. μA/V 2 respectively, more than ten-fold larger than those of other non-centrosymmetric 2D materials, such as hexagonal BN (hBN), 2H MoS 2 , GeS, and SnSe, which are on the order of 10 ∼ 100 nm ⋅ μA/V 2 (inset of Figure 4e). When light with intensity 10 mW/cm 2 is shining on single layer MoSTe with 1 cm × 1 cm dimension, the photocurrent generated is on the order of 1 nA.
Note that the nonlinear photocurrent can be boosted by 1) focusing the light beam. For example, when the light with the same total power is focused onto a 0.01 cm 2 spot size, the electric field is enhanced 10 1 ×, the photocurrent density would be 10 2 × and the total photocurrent would be 100 nA ; 2) stacking single layer detectors to increase the cross-section. Notably, the SC conductivities quickly decay for ≳ 0.1 eV, indicating that 1T′ MoSTe is relatively insensitive to For insulating materials at zero temperatures, the intraband part should be zero. But since 1T' JTMDs have small bandgaps comparable with room temperature ( room ∼ 26 meV), we have also calculated the intraband contribution due to anomalous velocity at finite temperatures. The results are shown in the SM, and one can find that the intraband contributions can be on the same order as the interband contributions. As discussed above, around the ±Λ points, the Rashba splitting breaks the degeneracy and could close and reopen the bandgap, leading to topological phase transitions. The magnitude of the Rashba splitting could be engineered with external stimuli, such as in-plane strain, external electric field, etc. For example, with a tensile strain, the vertical chalcogen distance of 1T′ JTMD shrinks (inset of Figure 5a). The bandgap of MoSSe as a function of biaxial in-plane strain is plotted in Figure 5a  around Λ upon the topological transition 24 . As discussed above, the major contributions to the total SC conductivity come from -points around Λ point (Figure 3b). When the bandgap is closed and reopened, the wavefunctions of the lowest CB and highest VB around Λ point undergo a substantial remixing. In ideal cases such as a two band model 24 , ; = ; + ; would flip sign since and is interchanged and ; is purely imaginary. This is consistent with the results with the model Hamiltonain before. When more band contributions are incorporated, ; does not always flip its sign, but would still experience a drastic change. The arguments above are verified by the -specific contribution to and as shown in Figure 5(cf), where we can see ( ) are significantly different on two sides of the topological transition.
In addition to in-plane strain, an out-of-plane electric field, which also modifies the magnitude of the Rashba splitting, can trigger the topological transition and alter the SC conductivities as well (see SM). Thus, we propose that the abrupt jump of nonlinear photocurrent is a universal signature of the topological phase transition in non-centrosymmetric materials, and can be used as an online diagnostic tool. The mechanical, electrical and even optomechanical 47,48 approaches to switching the NLO responses would pave the way for efficient and ultrafast nonlinear optoelectronics.
It is also intriguing to investigate how the nonlinear photocurrents vary when the Fermi level is buried in the CB or VB by carrier doping. The SC and CC conductivities of MoSTe as the function of the Fermi level F are shown in Figure 6a. We can see that for F within ±50 meV ( F is set as 0 when the Fermi level is on the top of the VB), the SC and CC conductivities remain extremely large in their magnitudes. While for F far away from the fundamental bandgap (heavily carrier doped), both SC and CC conductivities decay to zero. Here, the pure intraband nonlinear anomalous Hall current discussed by Wang et al. 49 is not considered. A noteworthy feature is that, when F is slightly above (below) the bandgap, would jump to an enormously positive (negative) value, about ten times larger in amplitude than that when F is inside the bandgap. This effect can be understood by looking at the band structure ( Figure 3a) and the k-specific contribution ( ) (Figure 4c). As discussed above, the major contribution to the total SC conductivity comes from k-points close to the fundamental bandgap Λ. When the VB and CB are occupied and empty respectively, (Λ + ) and (Λ − ) ( is a small positive parameter) have opposite values and tend to cancel each other. On the other hand, with a positive F , those CB below the Fermi level would be occupied as well, and the CB-VB transition cannot contribute to ( ) anymore (Figure 6b). However, a lager region on the Λ − side would have occupied CB than on the Λ + side. This is because the CB cone is tilted and the band velocity is smaller on the Λ − side, leading to a larger partial density of states in this region. As a result, the positive ( ) on the Λ + side would be cancelled less by the negative ( ) on the Λ − side, leading to a larger total SC conductivity. A similar analysis could show that when F is within the VB, the total SC would have a significant negative value. These observations indicate that the photocurrent conductivity could be further enhanced by Fermi-level tuning in materials with tilted CB and/or VB, such as type-II WSM 50 . From Figure 6a, one can see that a ~ 1 meV shift in can dramatically enhance . In practice, can be tuned by e.g., gate voltage.
Assuming a gate coupling efficiency of 0.1, then a ~10 mV gate volgate would be able to achieve the enhancement. Before concluding, we would like to note that, in addition to nonlinear photocurrents, other NLO effects such as the second-harmonic generation are also colossal in 1T′ JTMDs (see SM).
Besides, the inversion symmetry of 1T′ PTMDs can be broken externally by e.g., an out-of-plane electric field, resulting in nonlinear photocurrents, which can be regarded as a third-order nonlinear effect. The SC conductivity can be giant as well and can flip direction under a vertical electric field ( Figure 7). Also, the SC conductivity depends approximately linearly on the electric field, which characterizes the strength of inversion asymmetry. This is consistent with results with the model Hamiltonian before, when plays a similar role as the electric field.
In conclusion, we reveal the colossal nonlinear photocurrent effects in 1T′ JTMDs. The photo-responsivity peaks within the THz range. As a result, the 1T′ JTMDs can be efficient and selective photodetectors in the THz range. We also investigate the topological order of 1T′ JTMDs and find that it can be conveniently switched by a small external stimulus such as in-plane strain and out-of-plane electric field. Upon the topological transitions, the photocurrents undergo an Nonlinear photoconductivity. After all the ingredients, , and ; , are obtained from the Wannier interpolations, the nonlinear photoconductivity is calculated based on Eq. (2) in the main text. The BZ integration is sampled with a 1601 × 3201 -mesh in the first BZ. The -mesh convergence is tested with a denser 2251 × 4501 -mesh, and the difference is found to be negligible (SM).
Code Availability. The data that support the findings within this paper and the MATLAB code for calculating the shift and circular current conductivity are available from the corresponding authors upon reasonable request.