Non-trivial topological spin-polarized surface states induced nonreciprocal transport in the hourglass semimetal

Abstract

Quantum materials such as topological semimetals have gained consummate interest due to their exotic band crossings and protected surface states. In particular, Ta₃GeTe₆ has emerged as a prototypical hourglass Dirac semimetal, as confirmed by both experimental and theoretical analysis. The ARPES confirm the topological hourglass-type band dispersions and Rashba-like surface band, while Hall measurements reveal a high hole carrier concentration and nonreciprocal transport behavior. These findings are further supported by a phenomenological toy model, which predicts a nonreciprocal resistance, consistent with the observed direction-dependent magnetoresistance. Furthermore, the Raman spectroscopy uncovers two-fold and four-fold phonon symmetries drag of highly anisotropic phonons, which establishes symmetry-dependent resistance. DFT calculations reveal Dirac-like and hourglass Dirac band crossings near the Fermi level for the bulk, with Rashba-type spin splitting induced by the surface inversion-symmetry breaking, leading to spin-polarized surface states. The combined experimental and theoretical results demonstrate that Ta₃GeTe₆ hosts a non-trivial electronic topology, with the inversion-symmetry breaking at the surface as the driver of this nonreciprocal transport behavior.

Graphical abstract

Keywords

Dirac semimetal / ARPES / nonreciprocal transport / Rashba effect / DFT

1 Introduction

Two-dimensional materials have been under investigation, especially after the realization of a single-layer graphene [1]. The advent of topology in condensed matter opened many new avenues to explore the thrilling physical properties of quantum systems [2, 3]. In this regard, topological semimetals (TSMs) have emerged as an exciting class of quantum materials possessing exotic symmetry-protected Fermions, unmatched and superior electronic properties, unique transport properties, and exceptional carrier mobilities [4−7]. Different classes of TSMs, e.g., Dirac semimetals, nodal-line semimetals, nodal surface semimetals, and Weyl semimetals are gaining popularity since the classification of materials based on symmetry and topology to insulators, metals, or semimetals [8, 9]. Exotic band crossings are a prime feature of topological semimetals, which are ostensibly protected by specific crystalline symmetries, e.g., time reversal symmetry, particle-hole symmetry, etc. Some work has been done to establish a relationship between massless Dirac surface states and their topological protection due to these symmetries. Some of these findings have revealed that in such materials, some anomalous, albeit versatile Fermion states corresponding to crystal lattice symmetries exist [10, 11]. These crystal symmetries may result in Dirac Fermion state crossings, hence originating a Dirac point or generating a manifold Dirac nodal point, a Dirac nodal curve or a Dirac nodal loop in k-space. With Dirac Fermions, these materials show exceptional carrier mobility, unique transport behaviour and electrical properties [12−14], making them highly promising candidates for future device applications in areas such as spintronics, high-frequency quantum rectifiers, and directional thermal management.

Recently, the investigations of materials possessing topology-protected electronic properties have become a vital topic of research. Though many TSMs have been proposed theoretically to date, their experimental realization especially for 2D TSMs, is still unusual. In this regard, Nb₃XTe₆ (X = Si, Ge) single crystals got enormous attention due to their non-trivial topological properties and hourglass semi-metallic nature of manifold symmetry [15]. They are van der Waals (vdW) materials, which can be exfoliated to achieve a few layers using the mechanical exfoliation technique [16]. The protected symmetry with linear band crossing and Dirac-like dispersions was observed in M₃XTe₆ (M = Nb, Ta; X = Si, Ge) compounds [15, 17−19] belonging to centrosymmetric space group No.62 (Pnma). These vdW materials showed the unique topological phase of hosting the weak TI and hourglass TSM characteristics. For this space group, multiple Dirac-like dispersions at the Brillouin zone boundary are robust against SOC, resulting from the interplay of structural anisotropy and nonsymmorphic symmetry [20, 21]. Nb₃GeTe₆ is perceived to be a topological semimetal possessing fourfold degenerate nodal-line crossing without spin-orbit coupling (SOC), while an hourglass Dirac loop with the inclusion of SOC [15] in addition to the Dirac-like points. Tuning the SOC interactions in these kinds of compounds can realize various effects. Surface states in topological materials exhibit various SOC physics. The bilinear magnetoelectric resistance of spin-momentum locking and nonreciprocal charge transport is observed in topological materials and other heterostructures attributed to the SOC effect [22−25]. The effect can be observed by applying current and magnetic fields. It shows the resistance can be linearly varied with the applied magnetic field and with the direction of the electric current related to the crystallographic axes of the material. Such a unidirectional magnetoresistance (UMR) was studied in various kinds of non-magnetic and magnetic TIs [22−27]. While recent studies have successfully mapped the bulk electronic structure and nonsymmorphic symmetry-protected bulk nodal lines of Ta₃GeTe₆ [28], these investigations typically assume a centrosymmetric bulk framework. However, the critical consequence of surface inversion symmetry breaking, and its associated spin-momentum locking, remains entirely unexplored in this material family. Consequently, the correlation between its topological surface states and nonreciprocal electrical transport has not yet been demonstrated. Owing to the technological importance of TSMs, it is imperative to experimentally understand and systematically explore interesting physical phenomena in such materials.

In this work, we present comprehensive experimental and theoretical investigations of the hourglass Dirac semimetal Ta₃GeTe₆, shifting the focus from purely bulk properties to surface-driven quantum transport_. High-quality single crystals were synthesized via the chemical vapor transport method and characterized using angle-resolved photoemission spectroscopy (ARPES), Hall transport measurements, and polarized Raman spectroscopy. While our ARPES and Raman data confirm the characteristic hourglass-type band dispersions and structural anisotropy of the material, magnetotransport measurements reveal a distinct nonreciprocal transport mechanism. To understand this, a toy model based on Onsager’s relation was developed, predicting a nonreciprocal resistance term consistent with the experimentally observed direction-dependent magnetoresistance. Crucially, our first-principles DFT calculations reveal that while Ta₃GeTe₆ is a bulk semimetal, spin-polarized Rashba-like surface states with spin–momentum locking emerge natively at the surface due to broken inversion symmetry. Together, these features account for the nonreciprocal transport observed experimentally. Collectively, these results establish Ta₃GeTe₆ as a premier platform for exploring surface-mediated nonreciprocal quantum transport, making it a highly potential candidate for future spintronic devices.

2 Results and discussion

High-quality single crystals were synthesized via the chemical vapor transport method (for details, see the method part in supplementary information). The crystal structure was confirmed by using the single-crystal X-ray diffraction method [see Fig. S1(b), supplementary information]. Whereas the core-level spectroscopy was used to identify the elemental composition of the cleaved Ta₃GeTe₆ single crystal surface, with reference to the binding energies [see Fig. S1(c), supplementary information]. The integrated intensity of each element in the sample can be clearly observed at the corresponding binding position of the present elements. Furthermore, the stoichiometric ratio was measured and confirmed by X-ray spectroscopy (EDS) and the corresponding elemental mapping [Figs. S1(d)−(h), supplementary information]. In addition, the crystal structure was measured using scanning transmission electron microscopy (STEM) [see Fig. S2(a)], which forms a zigzag-like structure due to the different oxidation states of Ta atoms with Ge and Te atoms. This structure shows the schematic 1D zigzag structure of the Ta₃GeTe₆, having a distorted edge-sharing TaTe₆ trigonal prisms interlinked by Ge atoms. The chain propagation vector is a = 6.44758 Å, with out-of-plane vdW stacking axis is b = 13.93736 Å, and inter-chain spacing is c = 11.52903 Å. When projected into quasi-2D TMD-like layers, phase slips (a/2 translational domain boundaries) or grain boundaries between 90°/120°-rotated domain variants interrupt the continuous 1D Ta-Ta motifs, forming localized domain walls [see Fig. S2(b)].

We further conducted ARPES measurements on Ta₃GeTe₆ single crystals to explore the electronic properties and band characteristics. Figure 1(a) reveals that the crystal structure of Ta₃GeTe₆ belongs to a vdW material family, with Ta and Ge sandwiched between two Te layers. Figure 1(b) represents the 3D first bulk Brillouin zone (BZ) with highlighted high-symmetry points used in the ARPES measurements. In Fig. 1(c), the constant energy contour (CEC) at zero binding energy reveals the Fermi surface (FS) with high symmetry directions marked as directed in the BZ. The FS displays a dumbbell-like shape centred at the zone center and expanding to the Y direction, while the open hourglass-like arches (necks at both sides from the zone center from ~ k_x = −0.2 Å⁻¹) away from the zone center to the R point of the zone boundary in the first BZ. These features are associated with nodal line bands in these two directions. The FS was further scrutinized at different binding energies, which shows the asymmetric dispersion around the zone center at R and R′ in moment space, revealing the anisotropic feature of the FS (see Fig. S3, supplementary information). The CEC plots [Fig. S3(a), supplementary information] and the change in position of k_x and k_y in moment space at different binding energies along R and R′ points [see Fig. S3(b), supplementary information] from the zone boundaries. The results indicate that the k_x and k_y are asymmetric with the anisotropic nature [see Fig. S3(c)]. These observed momentum-dependent spectral features directly demonstrate electronic anisotropy, consistent with the anisotropic Fermi surface of Ta₃GeTe₆.

Figure 1(d) reveals the band dispersion along the R−Γ−R′, which illustrates a clear band crossing at the R point making a line crossing band visible at the R point, while the cut is subsequently extended to the R point with a clear X-type band crossing [see Fig. 1(e)] at around 100 meV below the Fermi level (FL). Figure 1(e) clearly indicates the sharp nodal lines (seen at ~0.1–0.15 Å⁻¹, see Fig. S4) band crossing in those specific directions with an intersection at the R and R′ point, revealing the nodal lines features of this sample. Figure S4 indicates a band that disperses downward from FL, with the intensity increases in the deeper binding energy, suggesting the band crosses FL somewhere between k = 0.0 and k = 0.2 Å⁻¹, indicating the nodal line band crossing. Figure 1(f) shows the same cut, which was measured at 24 eV, to show both R and R′ points for a more visible band crossing. At the same time, the cut along the high symmetry Y′−Γ−Y direction was measured, which shows the different band features [see Fig. 1(g)]. In Fig. 1(g), the γ band reveals the Dirac-type band at the FL along Y and Y′ points, which can also be seen in the calculated band structure. The two parabolic bands illustrate the two spited bands of Rashbha types represented as α and β. The dispersion of these two bands demonstrates that the bands along the Y−Γ−Y′ point possess the dispersive electron-like bands crossing the Fermi level, while at lower binding energy, a hole-like parabolic band touches the β band at ~−200 meV. The corresponding second derivative [see Fig. 1(h)] clearly shows such band features. On the other hand, along X and X′ it shows the linear band dispersion, which can cross the FL, revealing [see Fig. 1(h)] a clear nodal-line feature similar to Ta₃SiTe₆ [19]. These results reveal the linear band crossing along the specified symmetry direction, which is an indication of not only the topological semimetal features but also reveals, these Rashba-like bands, which are spin-polarized, confirmed by the spin-polarized surface calculations as well [see Fig. 4(g)]. Furthermore, the band dispersion was measured at different photon energies, with varying intensities, affirming the 3D dispersion of the bulk states with k_z dependency in Ta₃GeTe₆, as confirmed by the constant energy contour (CEC) map of k_z vs k_x plots (see Fig. S5). At different binding energies, the varying intensities of the CEC map along the k_z direction confirm the topological feature of this sample. Whereas the nodal line and Dirac-like bands also show the distinguished band curvature, indicating the anisotropic electronic properties of this material, as elucidated from the Fermi surface plot as well.

The Hall bar device was fabricated (see methods part for details, in supplementary information) on the thin flake of Ta₃GeTe₆ with a thickness of around ~22 nm, as shown in Figs. 2(a) and (b). Figure 2(c) represents the resistivity plot of the Ta₃GeTe₆ device as a function of temperature measured at different magnetic fields (B) (0 T, 1 T, 3 T). It can be seen that the sample shows metallic behaviour under all tested temperatures and B, with a slight change in resistivity under the applied B. The room temperature resistivity of ρ_{300 K} was recorded to be ~1.27 mΩ, while the value of resistivity at the lowest recorded temperature, i.e., at 2 K (ρ_{2 K}) was found to be 0.45 mΩ. The residual resistivity (ρ_{300 K}/ρ_{2 K}) value is 2.903, which manifests the strong conductivity of the grown crystals. However, the resistance increases with the applied B, having no upturn can be observed in resistance, indicating the typical strong metallic nature of Ta₃GeTe₆. Figure 2(d) and Fig. S6(a) revealed that the longitudinal magnetoresistance (MR) at different temperatures was measured under a DC applied current (I_dc) and an applied B perpendicularly to the ab plane or parallel to the c plane. It can be noticed that MR is positive and increases monotonically with increasing B without any signs of saturation, showing a typical metal or semimetal nature of high carriers. On the other hand, the MR increases with decreasing temperature and reaches ~3% at 2 K without saturation. This non-saturating MR is somewhat anomalous and cannot be explained using semiclassical theory for a trivial band structure [29]. Therefore, such results are closely linked with the nontrivial or surface bands, directly related to the topological features. The transverse resistivity (ρ_xy) [see Fig. S6(b)] as a function of the magnetic field increases with increasing magnetic field with a positive slope, indicating the p-type conductivity, which can endorse the majority of the hole carrier density. Therefore, we have further estimated the carrier density and carrier mobilities as a function of temperature from the Hall resistivity data using two band model fitting [30] {\sigma }_{xy}=\left(\frac{n_{\mathrm{e}}{\mu }_{\mathrm{e}}^2}{1+{\mu }_{\mathrm{e}}^2{B}^2}+\frac{n_{\mathrm{h}}{\mu }_{\mathrm{h}}^2}{1+{\mu }_{\mathrm{h}}^2{B}^2}\right)eB [see Fig. S6(c)]. Here n_e and n_h show the carrier density of electrons and holes, while μ_e and μ_h indicate the carrier mobility of electrons and holes, respectively. The results indicated that the carrier concentration and mobility of both electrons and holes decreased with increasing temperature, having the hole concentration larger than the electron concentration at all tested temperatures, which reveals a typical strong metallic nature with the majority of the hole carrier density [see Fig. S6(d)]. The ARPES measurements further depict the Fermi level lying inside the valence band (see Fig. 1). These results revealed that the carrier density of such kinds of nodal-line semimetals is comparable with Dirac/Weyl semimetals [30, 31]. Whereas, the carrier mobility of electrons and holes shows a decreasing trend with temperature for Ta₃GeTe₆ [see Fig. S6(e)].

With the existence of the anisotropic surface features, we have further measured the nonreciprocal magnetoresistance on the fabricated device [see Fig. 2(a)] using a four-probe configuration device with applied I_ac = ± 1 mA [see Fig. 2(e)]. Figure 1(e) shows the nonreciprocal MR in response to both forward and backward charge flows, I_ac = ± 1 mA, in a magnetic field sweep perpendicular to the c-axis. We can clearly see that with increasing B can detect a substantial resistance variation for the forward and reverse current flow. A higher resistance can be observed for the positive B with applied forward current flow, while the resistance becomes higher for negative B in the reverse current flow. The reverse MR effect can represent the directional charge transport in this thin flake Ta₃GeTe₆ sample. At the same time, the observed nonreciprocal MR, defined as ΔMR = MR(+I)–MR(−I), displays a linear increase under the magnitude of an applied magnetic field [see Fig. S5(f)]. The observed asymmetry of the MR is attributed to the nonreciprocal MR, which is further implicit in the current-induced effective Rashba-type charge-induced field normal to a current flow in the polar kind of system.

To interpret the experimentally observed current-direction-dependent magnetoresistance, we model the nonreciprocal transport within the framework of Onsager’s reciprocal relations (Toy model). The electrical conductivity tensor for a system with diffusive charge carriers in an external magnetic field B can be written [32] as

(1){\sigma }_{ij}\left(\mathit{B},\mathit{k}\right)={\sigma }_{ji}\left(-\mathit{B},-\mathit{k}\right),

where k is the average wave vector of the diffusing particles. Expanding Eq. (1) in terms of the symmetry-breaking polarity vector p and B, we obtain

(2){\sigma }_{ij}\left(\mathit{B},\mathit{k}\right)={\sigma }_{ij}^{(0)}+{\sigma }_{ij}^{\left(1\right)}k.\left(\mathit{p}\times \mathit{B}\right)+{\sigma }_{ij}^{(2)}{\mathit{B}}^2+\cdots ,

where {\sigma }_{ij}^{(0)}is the conductivity without p and B, while {\sigma }_{ij}^{\left(1\right)}and {\sigma }_{ij}^{(2)} are first- and second-order contributions in B, respectively. The average wave vector k is driven by the applied electrical current I. By retaining terms up to second order in B, the expression can be recast in terms of resistance as

(3)R\left(I,B,p\right)=R_0[1+\chi \mathit{p}\cdot \left(\mathit{B}\times \mathit{I}\right)+\alpha {\mathit{B}}^2],

where p=0 corresponds to inversion-symmetric systems, and p\ne 0 describes inversion symmetry breaking. Here, \chi denotes the nonreciprocal magnetoresistance coefficient, I is the current, \alpha is the symmetric magnetoresistance coefficient, and R_0 is the zero-field longitudinal resistance. Microscopically, the coefficient \chi is intrinsically tied to the surface-state parameters and scales as \chi \propto P_{\mathrm{s}}\cdot {\alpha }_{\mathrm{R}}, where P_{\mathrm{s}} is the magnitude of the surface spin polarization and {\alpha }_{\mathrm{R}} represents the surface Rashba spin−orbit coupling strength. A larger {\alpha }_{\mathrm{R}} enhances the current-induced effective magnetic field \left({\mathit{B}}_{\text{eff}}\propto \mathit{v}\times \mathit{E}\right) stemming from the surface inversion symmetry breaking (p\ne 0), while a higher P_s maximizes the asymmetry in spin-dependent scattering channels when an external magnetic field is applied. Equation (3) shows that magnetoresistance depends on the relative orientation of the applied magnetic field and injected current. For inversion-symmetric systems p=0, the MR response remains symmetric upon current reversal. In contrast, when inversion symmetry is broken (p\ne 0), the MR exhibits an asymmetric, nonreciprocal behavior. Figure 2(f) illustrates the results of this toy model, which aligns well with our experimental observations. Thus, both the DFT and phenomenological Toy model consistently validate that the unidirectional transport in Ta₃GeTe₆ originates from the synergy between strong SOC and surface inversion-symmetry breaking.

With such anisotropic charge flow in this vdW material, we further performed details magnetotransport measurements along with second harmonic experiments using DC (I_dc) and AC currents (I_ac). Figure 3(a) presents the typical schematic design of the electrodes on the sample with applied current and voltage direction for nonreciprocal charge transport measurement and simple transport experiments. The current can be applied to the x-axis, and a longitudinal voltage will be measured while applying a magnetic field. The angle-dependent magnetoresistance (ΔR_xx) of the device was measured at different temperatures using B = 9 T and I_dc = 3 mA. The ΔR_xx can be obtained from the relation [ΔR_xx = R_xx(θ) − R_xx(θ = 0)]/R_xx(θ = 0), while rotating a device in the xy plane [see Fig. 3(b)]. The results indicated that the MR shows asymmetric behavior of directional dependent transport with the two-fold anisotropy of the device. The resistivity of the sample varies sinusoidally with respect to the angle, with the highest amplitude being observed at 90° while the lowest is at 0° and 180°. The variation of resistivity with angle follows R = ΔRsinθ, where ΔR is the amplitude, and θ is the rotation angle. With increasing temperature, the amplitude of the ΔR_xx decreases; however, the trend of the anisotropy exists up to 50 K. At the same time, we have measured the ΔR_xx as a function of theta at different B values from a positive B to a negative B [see Fig. 3(c)]. Interestingly, ΔR_xx flips when the magnetic field direction is changed, which corroborates the unidirectional magnetoresistance [22, 26, 27, 33, 34]. With decreasing B, the amplitude of ΔR_xx is reduced for both positive and negative B. Additionally, we have performed the measurements at varying currents, as shown in Fig. 3(d). With increasing applied current, the ΔR_xx is monotonically increasing. These results also indicate that the asymmetric trend in response to the current with increasing differential resistance.

With these careful investigations of the unidirectional MR effect, we have further examined the device under applied AC current [I = I₀sin(ωt)], having phase detection for ΔR. We have measured the nonreciprocal resistance (R_2ω), which was directly measured from the out-of-phase component, as R_2ω = V_2ω/I₀ = 1/2 γR₀BI₀sinθ [35]. Figure 3(e) exhibits the angle-dependent R_2ω measured at B = ± 9 T and at T = 2 K for I_ac = 1 mA. It is observed that the sinusoidal resistance curves at out-of-plane rotational B = +9 T, with the maximum amplitude appearing at 90° (+y) on the positive side and 270 degrees (−y) on the negative side. However, when changing the sign of the field, i.e., B = −9 T, one can reverse the angle-dependent R_2ω curve, illustrating the nonreciprocal unidirectional behaviour of MR at the AC. At the same time, we have measured the R_2ω by changing the phase of the AC current, which can also flip the sign; nevertheless, the amplitude is quite similar with a slight decrease due to the applied field strength [see Fig. 3(f)]. The R_2ω exhibits the angular dependence of the direction of the current with respect to the crystallographic axes of the sample. These results follow the relation of R_2ω(I, B) = −R_2ω(−I, B) = −R_2ω(I, −B) = R_2ω(−I, −B), which can demonstrate the unidirectional magnetoresistance in thin Ta₃GeTe₆ that is odd concerning the polarity of either I or B [22]. Our results clearly demonstrate that the magneto-transport study of Ta₃GeTe₆ shows the nonreciprocal charge transport characteristics, which are the signatures of the spin-orbit coupling and spin-polarized Rashba-type effect in such thin flake anisotropic systems. To further demonstrate the structural anisotropy, we have used the polarized Raman spectroscopy measurements (see Fig. S7). The polarized Raman spectra clearly demonstrate the two-fold and four-fold phonon symmetries, reflecting the structural anisotropy of this crystal. These specific anisotropic phonon modes responsible for this directional electron scattering link the anisotropic structure with directional transport properties.

To validate and conclude the analysis, we have used the density functional theory (DFT) calculations, which reveal that Ta₃GeTe₆ crystallizes in a layered orthorhombic structure with space group Pnma, composed of Ta–Ge–Ta zigzag chains sandwiched between the Te layers [Fig. 4(a)]. The bulk and (001) surface projected Brillouin zones are shown in Fig. 4(b). The bulk band structure illustrated in Fig. 4(c) exhibits Dirac-like dispersions near the Fermi level at the border of the Brillouin zone, confirming the semimetallic nature, revealing multiple symmetry-protected band crossings, which endorse our ARPES results. An hourglass Dirac dispersion is observed along the XS direction close to the Fermi level. Figures 4(d–f) displays the complex Fermi surfaces, further highlighting the anisotropic electronic topology, while surface-projected spectral functions shown in Fig. 4(g) demonstrate topologically nontrivial states localized at the (001) surface. The spin-resolved band structure calculations in Fig. 4(h) clearly reveal spin splitting and Rashba-type features indicating spin–momentum locking, directly resulting from inversion-symmetry breaking at the surface and strong SOC from Ta 5d orbitals. Such a Rashba-like band was also observed in the ARPES data in Fig. 1(g).

These results establish a link between the electronic structure and the transport properties: the bulk of Ta₃GeTe₆ retains inversion symmetry, but the inversion symmetry breaking at the surface induces Rashba-type spin-polarized states, a clear signature enabling a nonreciprocal transport mechanism in the structure. Microscopically, as schematically illustrated in Fig. 4(i), surface termination breaks \mathcal{P}-symmetry to produce an hourglass semimetal with spin-momentum locked helical Fermi surfaces (middle panel). When a longitudinal current I and an in-plane magnetic field B\mathrm{\perp }I are applied (right panel), the Zeeman field shifts these momentum-locked sub-bands, breaking the +k/-k carrier degeneracy \left[\epsilon \left(k,B\right)\ne \epsilon \left(-k,B\right)\right]. This momentum asymmetry induces non-equivalent carrier group velocities and scattering lifetimes, directly generating the second-harmonic nonreciprocal resistance (R^{2\omega }\propto I\cdot B). Collectively, these results establish Ta₃GeTe₆ as an hourglass semimetal with non-trivial topology and nonreciprocal transport behavior, making it a potential candidate for future quantum devices.

3 Conclusion

High-quality Ta₃GeTe₆ single crystals were successfully synthesized. After characterization, the structural and electronic anisotropic nature of these single crystals was unambiguously proved by using ARPES, magneto-transport, and Raman spectroscopy experiments. ARPES has unequivocally proved the non-trivial topological and Dirac-like hourglass semimetal ic features of these single crystals. Transport properties in combination with ARPES have shown that Ta₃GeTe₆ possesses hole-type carriers. Additionally, magneto-transport studies on Ta₃GeTe₆ show non-saturating magneto-resistance, which changes with an applied magnetic field and depicts the phenomenon of unidirectional magnetoresistance along with structural anisotropy as demonstrated by Raman spectroscopy. The experimental observations were complemented with the first-principles DFT calculations, revealing that Ta₃GeTe₆ is an hourglass semimetal with spin-polarized surface states and broken inversion symmetry on the surface, providing the microscopic origin of nonreciprocal charge transport observed experimentally. Moreover, the toy model quantitatively captures the nonreciprocal resistance term, which is in excellent agreement with the measured direction-dependent magnetoresistance. Together, these theoretical and experimental findings establish Ta₃GeTe₆ as a platform for exploring nonreciprocal transport and anisotropic quantum phenomena in topological semimetals.

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