Absence of diode effect in chiral type-I superconductor NbGe2

Introduction

Stemming from the nonreciprocal phenomena in quantum materials^1,2,3, novel functionalities such as the superconducting diode effect (SDE) have been achieved in prototype devices through symmetry engineering⁴. Analogous to the semiconductor p-n junctions, superconducting diodes carry dissipationless supercurrent in one direction and show finite resistance in the opposite direction. An asymmetry parameter, called the diode efficiency (Qequiv frac{|{{{rm{I}}}}_{{{rm{c}}}}^{+}-{{{rm{I}}}}_{{{rm{c}}}}^{-}|}{({{{rm{I}}}}_{{{rm{c}}}}^{+}+{{{rm{I}}}}_{{{rm{c}}}}^{-})/2}), was introduced to quantify the difference between the opposite critical currents I_c⁺ and I_c⁻ in SDE⁵. The SDE is crucial in realizing energy-efficient and quantum-based superconducting circuits, attracting extensive attention from the superconducting electronics community⁶. However, intense controversy has recently emerged regarding the mechanism of SDE⁷. Specifically, mainstream theories suggest that the SDE arises from the intrinsic inequality of Cooper-depairing currents along opposite directions^8,9,10,11. In contrast, the experimentally measured I_c is considered by other groups to be the vortex-depinning current from a practical viewpoint¹² and the SDE is hence thought to originate from the asymmetric vortex pinning potential^7,13,14,15.

The central question is how to avoid or even regulate the vortex effect in the study of SDE. Vortices are inevitably generated by the negative interface energy in type-II superconductors but are absent in type-I superconductors with positive interface energy¹⁶. On the other hand, as one kind of nonreciprocal response, the superconducting diodes require intrinsic space-inversion symmetry breaking. Therefore, investigating SDE in chiral type-I superconductors is an elegant method to circumvent the complicated vortex effect. However, both type-I superconductivity and chiral structures are unusual, rendering the overlap extremely rare. The only identified candidates for chiral type-I superconductors are polycrystalline BeAu (space group P2₁3)¹⁷ and single crystalline NbGe₂ (space group P6₂22/P6₄22)¹⁸ so far. NbGe₂ belongs to the Kramers-Weyl semimetals¹⁹ with a noticeable antisymmetric spin-orbit coupling (SOC) effect²⁰. Meanwhile, the chiral symmetry facilitates the formation of a coupled electron-phonon liquid in NbGe₂ below T′ ~ 50 K²¹. The electron fluid property leads to an ultralow resistivity in NbGe₂ crystals, posing a large obstacle to comprehensively investigating the subtle nonreciprocal charge transport^22,23.

This challenge can be overcome by preparing micro-sized devices using the well-established focused ion beam (FIB) technique²⁴. FIB offers an excellent method for investigating quantum materials in the mesoscopic regime, particularly for materials like NbGe₂ that are incompatible with mechanical exfoliation. Another advantage of FIB devices is their flexibility in tailoring geometry, enabling diverse experimental configurations for transport measurements. Here, we successfully fabricated the NbGe₂ devices using FIB and systematically investigated their nonreciprocal transport. An unexpected outcome of FIB milling is the superconducting amorphous NbGe surface, which coincidentally exhibits type-II superconductivity with a superconducting critical temperature T_c higher than that of NbGe₂ bulk. This artificial structure allows for the incorporation of vortex dynamics into NbGe₂ devices by suppressing the bulk superconductivity. While most nonreciprocal transport results align well with theoretical predictions, the field dependence of diode efficiency Q is in strong contrast to anticipations. The main message of this paper is that the SDE is negligible (Q < 2%) at low field regimes but emerges (Q exceeding 50%) at high field regimes, corresponding to the strongly suppressed or activated vortex dynamics. Our study reveals that, in addition to the well-known symmetry rules, the ubiquitous vortex effect plays a nonnegligible and even critical role in realizing the SDE.

Results and discussion

Type-I superconductivity in chiral NbGe₂

NbGe₂ belongs to the hexagonal C40 structural group, with right- and left-handed helix structures along the c-axis corresponding to space groups P6₂22 (No. 180) and P6₄22 (No. 181), respectively (Fig. 1a). The left-handedness of these two enantiomers in the studied NbGe₂ crystal was confirmed using single-crystal diffraction (Supplementary Table 1). Superconductivity in NbGe₂ was first found in 1978²⁵ and has recently been revisited due to its chiral crystal structure^{18,20,21,26,27}. Figure 1b shows the temperature-dependent resistivity of a NbGe₂ crystal with a residual resistivity ratio RRR = 96. The T_c is consistent across electrical transport (T_c = 1.96 K) and magnetic susceptibility measurements (T_c = 2.01 K). It is worth noting that the magnetic susceptibility is identical in both the zero-field-cooled (ZFC) and field-cooled (FC) measurements (Fig. 1c). In type-II superconductors, the diamagnetism measured in the FC mode is smaller than that of the ZFC mode due to the trapped vortices. However, it has been confirmed that the superconductivity in NbGe₂ exhibits rare type-I behavior^18,20, which is responsible for the absence of the vortex pinning effect in our FC measurement. As the temperature decreases from 1.8 K to 400 mK (Fig. 1d), we observe a crossover in NbGe₂ from type-I superconductivity at low fields to type-II/1 superconductivity at higher fields²⁸. The so-called type-II/1 superconductivity significantly differs from the conventional type-II superconductivity, although magnetic flux will penetrate both superconductors. The interaction between flux quanta is attractive, rather than repulsive, in type-II/1 superconductors²⁹. This feature strongly suppresses the vortex dynamics in type-II/1 superconductivity, rendering it more like type-I than the conventional type-II superconductivity.

**Fig. 1: Type-I superconductor NbGe₂.**

To enhance the charge transport signals, we fabricated micro-sized NbGe₂ devices using FIB (“Methods”). As shown in Fig. 2a, we have deliberately designed the NbGe₂ device D3 to simultaneously measure the c-axis and a-axis transport properties. The a-axis resistivity is higher than the c-axis resistivity in NbGe₂, consistent with previous report²¹. As the temperature-dependent resistivity remains consistent between the NbGe₂ bulk and NbGe₂ devices in their normal states (Fig. 2b), we believe that the transport properties measured in these devices reliably reflect the bulk characteristics of NbGe₂ in the normal state. For instance, one of the chirality-induced anomalies in NbGe₂ is the coupled electron-phonon liquid²¹, leading to a kink feature in the Kohler scaling³⁰. We also measured the magnetoresistance and indeed observed similar results in NbGe₂ device D1 (Supplementary Fig. 1), demonstrating the high quality of our NbGe₂ devices. According to the crystal symmetry, the chirality-induced nonreciprocal transport response (R={R}_{0}left[1+gamma left({{boldsymbol{B}}}cdot {{boldsymbol{I}}}right)right]) appears when I and B are applied along the helix axis^1,31. And the nonreciprocal coefficient (gamma =frac{2{R}^{2{{rm{omega }}}}}{{R}^{{{rm{omega }}}}{BI}}) is obtained by the associated first-harmonic resistance R^ω and second-harmonic resistance R^2ω in lock-in measurements³². Figures 2c and d show the raw data of field dependent R^2ω/R^ω measured under red I//B//c and black I//a⊥B//c configurations, respectively. The R^2ω/R^ω data consists of extrinsic symmetric contribution and intrinsic antisymmetric signals. We then extract the intrinsic R^2ω/R^ω response from the asymmetric part. The c-axis nonreciprocal response (I//B//c) is significantly stronger than the a-axis one (I//a, B//c) as anticipated (Fig. 2e). With decreasing temperature, the chirality-induced nonreciprocal coefficient γ eventually saturates at approximately 7.0 × 10⁻²T⁻¹ A⁻¹ at low temperatures (Fig. 2f), which is of the same order as that observed in the chiral molecular conductor³³. In principle, the two-fold rotational symmetry (2₀₀₁) prohibits the generation of nonreciprocal response in any direction other than along the c-axis. The observation of a tiny R^2ω response along the a-axis (I//a⊥B//c) suggests the presence of additional symmetry breaking in the NbGe₂ device beyond its intrinsic crystal symmetry, potentially arising from the polar symmetry along the b-axis of the artificial surface, as discussed below.

**Fig. 2: Chirality induced nonreciprocal transport in the normal state of NbGe₂.**

Type-II superconductivity in artificial NbGe surface

It is well known that the FIB damages the material surface, leaving an artificial amorphous layer due to ion irradiation²⁴. The FIB-induced surface damage is gentle and confined to a typical thickness of around 10 nm, ensuring that the transport properties remain unaffected in FIB-fabricated microdevices, as confirmed by our measurement in the normal state (Fig. 2b). However, the situation became complicated when we investigated the superconducting state. As shown in Fig. 3, we found that both T_c and upper critical fields H_c2 are significantly enhanced from the NbGe₂ bulk (T_c = 2.01 K_, H_c2 = 40 mT) to NbGe₂ devices (T_c = 2.95 K_, H_c2 = 4 T in D1). The enhanced superconductivity originates from the amorphous NbGe surfaces induced by FIB irradiation, as demonstrated by the following observations. Firstly, the scanning transmission electron microscope (STEM) image provides direct evidence of an amorphous surface, with a thickness ranging from 10 to 15 nm (Fig. 3b). The six-fold symmetry is observed in the crystalline region 2 and absent in the amorphous region 1 as expected. The composition of the amorphous surface is identified as NbGe using spatial-resolved electron energy loss spectroscopy (EELS) (Supplementary Fig. 2). Secondly, the broad superconducting resistive transition is fitted well by the Halperin-Nelson formula³⁴, showing a Berezinskii-Kosterlitz-Thouless (BKT) transition with a higher T_c = 2.95 K in device D1 (Fig. 3c). The fitted BKT transition temperature T_BKT in the resistivity is 2.50 K, which is almost identical to T_BKT = 2.49 K derived from the fitted exponent V∝I ^α at α (T_BKT) = 3 (Fig. 3d). Note that the BKT transitions were reproducibly observed in another NbGe₂ device D2 with a different T_c = 2.50 K (Supplementary Figs. 3a–d). Lastly, the upper critical fields H_c2 of NbGe₂ device are two orders of magnitude higher than that of NbGe₂ bulk (Fig. 3e, f), but are consistent with the H_c2 of NbGe³⁵ (Supplementary Note 3). It is anomalous to observe such a considerable enhancement of H_c2 if the superconductivity comes from NbGe₂ bulk.

**Fig. 3: Surficial type-II superconductivity in NbGe₂ devices.**

Based on these results, the amorphous NbGe shell as depicted in Fig. 3a results in enhanced superconducting properties, such as T_c and H_c2, in transport measurements. Similar amorphous niobium surfaces were created and responsible for the induced superconductivity in non-superconducting NbAs devices via FIB milling³⁶. Since twice the superconducting coherence length 2ξ = 32 nm is larger than the thickness of NbGe surface (see Supplementary Note 4), our results strongly suggest that the NbGe surface hosts 2D superconductivity in NbGe₂ devices^37,38. Additionally, it is worth noting that the vortex dynamics is always absent (strongly suppressed) below the critical field H_c (H_c2) of NbGe₂ due to its type-I (-II/1) superconductivity and its significantly larger cross-section compared to the NbGe surface. However, as confirmed by the observations of BKT transitions, the excitations of vortices/antivortices could penetrate the devices due to the type-II nature of the amorphous NbGe surfaces at higher temperature. This result indicates that we can easily switch between type-I and type-II superconductivity in different regimes, as delineated in the H–T phase diagram of Fig. 3f.

Nonreciprocal transport near T
_c in NbGe₂ devices

The amorphous NbGe surface is distinctly separated from the crystalline NbGe₂ core, resulting in a well-defined NbGe₂/NbGe interface. This sharp boundary is attributed to the self-annealing process occurring at room temperature²⁴. Akin to other artificial interfaces, this interface will induce the Rashba-like SOC, which gives rise to polarization in the perpendicular direction. To investigate this additional space-inversion symmetry breaking, we systematically investigated the nonreciprocal electrical transport in NbGe₂ devices near T_c. The polarization-induced second harmonic resistance R^2ω is expressed as ({R}^{2omega }propto left({{boldsymbol{P}}}times {{boldsymbol{B}}}right)cdot {{boldsymbol{I}}}=-{BI}sin theta), where θ represents the angle between the current I and magnetic field B when they are perpendicular to the polarization P^22,39. We indeed observed significant R^2ω responses in NbGe₂ device D2 under the polar configuration of I⊥B⊥P (Fig. 4a) and its typical angular dependence (Fig. 4b). Figure 4c shows the temperature dependence of γ, which features a peak at T_BKT with a value of 3.2 × 10⁵T⁻¹ A⁻¹. Figure 4d illustrates that R^2ω progressively deviates from the anticipated linear behavior in the low-current regime and exhibits a decline in the high-current regime, consistent with previous observations in gated SrTiO₃⁴⁰. Figure 4e, f show the magnetic field dependence of first-harmonic resistance R^ω and R^2ω at various T down to 0.3 K respectively. It shows that the R^2ω responses are noticeable in the superconducting transition regions but undetectable in the normal state. All the current, temperature, and field dependencies of R^2ω are well reproducible in another NbGe₂ device D1 (Supplementary Fig. 4).

**Fig. 4: Nonreciprocal transport of a NbGe₂ device D2 near the superconducting transition.**

These observations confirm the presence of a polar NbGe₂/NbGe interface, which induces a significant nonreciprocal transport in NbGe₂ devices near T_c. There are two major factors that contribute to the substantial increase of γ from around 10⁻¹T⁻¹ A⁻¹ in the normal state to approximately 10⁵T⁻¹ A⁻¹ in the superconducting state. First, due to the remarkable reduction of the electronic energy scale from Fermi energy to superconducting gap, the γ value is gigantically increased when electrons condense into Cooper pairs⁴¹. The second factor is the BKT transition, which further enhances the γ value in the 2D NbGe₂/NbGe interfaces. This involves a two-step evolution of γ(T)⁴¹, characterized by ({{rm{gamma }}}left(Tright) sim ({T}_{{{rm{c}}}},-T)) and ({{{rm{gamma }}}left(Tright) sim (T-{T}_{{{rm{BKT}}}})}^{-3/2}), as the temperature decreases from T_c to T_BKT. With a further decreasing T, γ falls to zero associated with the bound vortex/antivortex pairs in the superconducting ground state. This evolution explains why we observe a peak feature in Fig. 4c. It is worth noting that our observations are highly similar to previous reports in various platforms including gated MoS₂ (γ ~ 8 × 10²T⁻¹ A⁻¹)³², gated SrTiO₃ (γ ~ 3.2 × 10⁶T⁻¹ A⁻¹)⁴⁰, Bi₂Te₃/FeTe interfaces (2D γ’ ~ 6.5 × 10⁻³T⁻¹ A⁻¹ m)⁴², NbSe₂ antennas (γ ~ 3.4 × 10⁴T⁻¹ A⁻¹)⁴³, etc. Albeit these materials possess various origins of broken space-inversion symmetry, the theoretical analysis indicated that the nonreciprocal responses are similar in these 2D superconductors due to the BKT transition⁴¹. Our results show that the motion of unpaired vortices boosts γ significantly in NbGe₂ devices, emphasizing the importance of vortex dynamics in nonreciprocal transport^41,44.

Absence of SDE in type-I NbGe₂ regime

Albeit resistance, whether nonreciprocal or not, vanishes in the superconducting ground state, the supercurrents retain the nonreciprocal characteristics, as manifested itself by the SDE³. Owing to a small penetration depth, the theoretical depairing critical current I_c of NbGe₂ is significantly larger than that of the NbGe surface (see Supplementary Note 6). This feature suggests that the superconductivity of NbGe₂ can be detected in terms of I_c (Fig. 5a), in contrast to the H–T phase diagram (Fig. 3f), where the superconductivity of NbGe₂ is obscured by the NbGe surface. Hence, the I–V characteristics can be divided into two different regimes based on the H_c2 of NbGe₂: the type-I (or type-II/1) NbGe₂ regime at low magnetic fields and the type-II NbGe regime at high magnetic fields. We characterized the I–V curves in both positive and negative directions under different magnetic fields at 0.3 K, and summarized the field dependence of I_c in Fig. 5b. The difference between I_c⁺ and I_c⁻ becomes noticeable once B exceeds 40 mT, aligning with the H_c2 of NbGe₂ at 0.3 K. The associated I–V curves exhibit clear distinctions between the pale purple NbGe₂ regime and the pale orange NbGe regime. In the NbGe₂ regime like B = 20 mT, the I_c is equal in opposite directions I_c⁺ = I_c⁻. A tiny nonreciprocity appears in the middle dissipative regime, which is difficult to define as the SDE phenomenon (Fig. 5c). In contrast, when the applied magnetic field increases to 100 mT, I_c becomes distinct along opposite directions, I_c⁺ ≠ I_c⁻, showing the emergence of SDE in the NbGe regime (Fig. 5d). One vital functionality of SDE is the perfect rectification effect without dissipation, which is also verified in Supplementary Fig. 5. We notice that its polarity is effectively switched by reversing the magnetic fields, as marked by the contrasting red and gray colors. The switchable polarity of SDE in NbGe₂ device is similar to that in polar artificial multilayers^4,45, patterned thin-films^13,15, few-layer NbSe₂⁴⁶ and others, but in contrast to the strained trigonal superconductor PbTaSe₂⁴⁷, where the polarity of SDE is fixed and the underlying diode mechanism should be distinct from others.

**Fig. 5: Anomalous field dependence of diode efficiency Q in NbGe₂ devices.**

To characterize the difference in vortex dynamics between NbGe₂ and NbGe regimes, we extract the vortex creep rate S using the relation S ~ 1/(N-1), where the flux creep exponent N is derived from I–V curves V(I) ∝ I^N in the vicinity of I_c⁴⁸. Figure 5e displays the corresponding field dependence of S, in which the slope of S abruptly increases at the same threshold of 40 mT. This result confirms that the vortex dynamics are strongly suppressed in the NbGe₂ regime but effectively activated in the NbGe regime. Additionally, the structural disorder within the amorphous NbGe layer could broaden the I–V transition in the type-II regimes (Fig. 5d) compared to the type-I regimes (Fig. 5c). Given that two sources of space-inversion symmetry breaking are observed in NbGe₂ devices, we measured I–V curves under both configurations: I⊥B⊥P (devices D1 and D2) and I//B//c (device D3). The I–V characteristics are highly consistent across different NbGe₂ devices, and the field dependence of their diode efficiency Q are shown in Fig. 5f. Distinct from the linear enhancement of Q (B) in previous reports of SDE^4,13, the Q value fluctuates within 2% below 40 mT, indicating the absence of SDE even under conditions of simultaneous space-inversion and time-reversal symmetry breaking. The similar evolution of Q(B) and S(B) suggests an underlying relationship between them, highlighting the significance of vortex dynamics in triggering SDE. We also observed small Q values ~ 0.2 when the external magnetic fields were parallel to the currents in device D3, a configuration in which the unidirectional Lorentz force should be absent, and thus the SDE is expected to be negligible. However, the applied currents inevitably generate vortex and antivortex pairs, known as the self-field effect¹². The excitation of vortex/antivortex pairs could induce giant nonreciprocality even when B = 0⁴⁴, providing a possible explanation for our observations in the B//I configuration.

Conclusions

In summary, we systematically performed nonreciprocal transport measurements on FIB fabricated NbGe₂ devices and confirmed the critical role of vortex dynamics in realizing a significant SDE. By inducing artificial NbGe surfaces through FIB irradiation, we observed enhanced superconductivity in these devices. Both types of space-inversion symmetry breaking, chirality in the NbGe₂ bulk and polarization at the NbGe₂/NbGe interface, were detected in the nonreciprocal transport measurements. Additionally, two-dimensional vortex excitations emerged on the NbGe surfaces as the type-I superconductivity of NbGe₂ bulk was suppressed, leading to the BKT transition and a dramatic increase in the nonreciprocal coefficient. The SDE was negligible in the NbGe₂ bulk at low magnetic fields but became pronounced in the NbGe surface under high magnetic fields, aligning with the abrupt increase in vortex creep rates.

Although we did not observe the SDE in chiral NbGe₂, likely due to the weak antisymmetric SOC, we cannot dismiss the possibility of exotic superconductivity induced SDE, such as the finite momentum Cooper pairing⁴⁹. Due to the inevitable excitation of vortices in type-II superconductors, it is challenging to distinguish between contributions to SDE from intrinsic crystal symmetry and those from extrinsic vortex effects. Therefore, it is crucial to exercise caution when attributing the widely observed SDE to the inherent symmetry breaking in superconductivity, rather than to the artificial asymmetry. Additional phase-sensitive experiments, such as those measuring the interference patterns⁵⁰ or Little–Parks oscillations⁵¹, are necessary and promising to support the existence of exotic superconductivity in these platforms.

From the perspective of electronic applications, we have confirmed that artificial superconducting surfaces can host the SDE. This functionality can be readily replicated in various quantum materials containing superconducting elements, such as niobium, using FIB technology. Consequently, we envision a significant expansion of the SDE application into a broader range of electronic devices, including potential integration with non-superconducting quantum materials, such as the Weyl semimetal NbAs. Our findings suggest that the unique properties of these materials could be harnessed in conjunction with SDE to develop advanced electronic components with enhanced performance and functionality.

Methods

Crystal synthesis and characterizations

NbGe₂ single crystals were synthesized by vapor transport using iodine as the transport agent. At first, the polycrystalline NbGe₂ samples, prepared via solid-state reaction at a heating temperature of 850 °C, were ground into a powder and mixed with iodine in a glove box. The reactants were then sealed under vacuum in a quartz tube and placed in a two-zone furnace, with the hot end maintained at 850 °C and the cold end at 800 °C. After two weeks, hexagonal crystals with typical sizes of 0.5 mm × 0.5 mm × 0.3 mm were obtained after ultrasonic cleaning in ethanol. Magnetization measurements were performed in a Quantum Design MPMS-XL system. The isothermal magnetization down to 400 mK was collected in an MPMS-3 system equipped with the He3 option. The NbGe₂ crystal structures are drawn by VESTA⁵².

Devices fabrication

All NbGe₂ devices were fabricated by a FEI Helios-600i FIB under an acceleration voltage of up to 30 kV with Ga ion sources. Similar to the methods developed by Moll et al.²⁴, the whole procedure of FIB device preparation can be summarized as four steps.

First step: preparing the lamella from bulk samples

The crystallographic orientation of the NbGe₂ bulk was checked by the Laue diffraction and mounted in the SEM sample holder. We then cut the lamella with a typical size of 150 × 40 × 2 μm³ from bulk like the routine sample preparation for the transmission electron microscope. A high 65 nA was used to dig the grooves, and a smaller current of 2.5 nA was then used to polish the sidewalls into a flat shape under grazing incidence.

Second step: transferring the lamella to substrate

Firstly, we place a hundred-micrometer-sized droplet of Araldite epoxy glue on the sapphire substrate with lithographically prepatterned gold contact pads. We vertically picked up the lamellas from crystals and then horizontally, flat sides down, put them onto the droplet using an ex-situ micromanipulator. The continuous and smooth contacting profile between lamella and droplet was built by the capillary forces of epoxy liquid.

Third step: evaporating gold electrical contacts

The droplet was first heated at 150 °C for one hour to release the bubble from the epoxy droplet. A brief argon etching was used to clean the surface of the lamellas before the following gold evaporation. By using a homemade shadow mask, typical Ti/Au (5/300 nm) layers were deposited on the region covering lamellas and contact pads. The deposited gold layers serve as the electrical contacts with a typical contact resistance of a few Ohms.

Final step: shaping the measured region

We put the substrate with covered lamellas back into the FIB chamber and proceeded with the final cutting. The covered gold layers were carefully removed by FIB milling at 1.6 nA, 5 kV. Then, the overall shape of the measured region and the position of the corresponding contact was cut by FIB at 0.79 nA, 30 kV. Finally, the outer gold layer is selectively cut through to ensure the applied current flows only as designed for transport measurements.

STEM on amorphous surfaces

To characterize the FIB induced amorphous damage, STEM specimens were prepared using the same FIB machine with the same milling parameters as those used for NbGe₂ devices. Atomically resolved high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and electron energy loss spectroscopy (EELS) were conducted on a JEOL ARM200F transmission electron microscopy (TEM) equipped with a probe-forming spherical-aberration corrector.

Electrical transport measurements

The temperature-dependent resistance and magnetoresistance were conducted in a Quantum Design PPMS-9 system. The dc I–V measurements were collected by two Keithley meters 6221 and 2182. The ac R^ω and R^2ω were obtained by the Stanford SR830 lock-in amplifiers with a frequency of 137.77 Hz, and a phase offset as −90° was set to collect R^2ω in the nonreciprocal transport measurements. To obtain a higher cooling power during the current-voltage measurements at 300 mK, similar transport measurements were performed in a top-loading He-3 refrigerator with a 15 T superconducting magnet.

Note added: We noticed a similar study on FIB fabricated NbGe₂ device during the peer review process⁵³.