Pressure induced superconductivity in the antiferromagnetic Dirac material BaMnBi2

The so-called Dirac materials such as graphene and topological insulators are a new class of matter different from conventional metals and (doped) semiconductors. Superconductivity induced by doing or applying pressure in these systems may be unconventional, or host mysterious Majorana fermions. Here, we report a successfully observation of pressure-induced superconductivity in an antiferromagnetic Dirac material BaMnBi2 with T c of ~4 K at 2.6 GPa. Both the higher upper critical field, μ 0 H c2(0) ~ 7 Tesla, and the measured current independent of T c precludes that superconductivity is ascribed to the Bi impurity. The similarity in ρ ab(B) linear behavior at high magnetic fields measured at 2 K both at ambient pressure (non-superconductivity) and 2.6 GPa (superconductivity, but at the normal state), as well as the smooth and similar change of resistivity with pressure measured at 7 K and 300 K in zero field, suggests that there may be no structure transition occurred below 2.6 GPa, and superconductivity observed here may emerge in the same phase with Dirac fermions. Our findings imply that BaMnBi2 may provide another platform for studying SC mechanism in the system with Dirac fermions.

Ba atoms below and above the square net result in unit cell doubling. This leads to folding of the dispersion Bi 6p bands and makes the two Bi p x,y bands cross each other. The Ba-Bi hybridization lifts the degeneracy of the folded bands except the momentum space along the Γ-M symmetry line, resulting in the formation of the Dirac cone. A small gap near the Dirac point appears due to the presence of the spin-orbital coupling (SOC). The magnetotransport properties, nonzero Berry phase, small cyclotron mass measurements 15 on BaMnBi 2 also confirm the presence of Dirac fermions in Bi square net. The quantum oscillations 15 in the Hall channel suggest the presence of both electron and hole pockets, whereas Dirac and parabolic states coexist at the E F . On the other hand, the Dirac materials AnMnBi 2 (An = Ca, Sr, Ba) are suggested to be promising parent compounds for superconductivity, due to their striking similarity to the superconducting iron pnictides. Up to now, superconductivity has not been observed in these materials, although several authors suggested that chemical doping may introduce superconductivity in these systems 16,20 . Here, we report a successfully observation of pressure-induced superconductivity in an antiferromagnetic Dirac material BaMnBi 2 with T c of ~4 K, at 2.6 GPa. Our findings imply that BaMnBi 2 may provide another platform for studying SC mechanism in the system with Dirac fermions.

Results and Discussion
We grew the BaMnBi 2 crystals using a self-flux method (see the method in details). The x-ray diffraction (XRD) pattern [see Fig. 1(b)] of BaMnBi 2 powder created by grinding pieces of crystals confirms its tetrahedral structure with space group I4/mmm, and its Rietveld refinement [see Fig. 1(b)] gives the lattice parameters of a = 4.628(1) Å and c = 24.092(4) Å, in consistent with the previous results reported by Li et al. 15 . Single crystal XRD pattern [see Fig. 1(d)] shows that the basal plane of a cleaved crystal is the crystallographic ab-plane. The energy-dispersive x-ray spectroscopy (EDX) results indicate that the crystals are rather homogenous and the determined average atomic ratios are Ba:Mn:Bi = 1.02:0.99:2.00 when fixing Bi stoichiometry to be 2, confirming the stoichiometry of BaMnBi 2 .
The physical properties of BaMnBi 2 crystal are summarized in Fig. 2. The temperature dependence of the in-plane, ρ ab , and out-plane, ρ c , resistivity at ambient pressure is shown in Fig. 2(a). Both ρ ab (T) and ρ c (T) exhibit a metallic behavior. However, ρ c is almost two orders of magnitude larger than ρ ab , i.e. at 300 K ρ c /ρ ab ≈ 41. The strong anisotropy in resistivity is consistent with its quasi-2D electronic structure in BaMnBi 2 as discussed above. Figure 2(b) shows ρ ab (T) curves at various magnetic fields. It is clear that the magnetic field induced metal-insulator transition occurs, such as, at 6 Tesla, its ρ ab increases with decreasing temperature, and reaches a constant at the low temperatures, i.e. exhibiting a semiconductor-like behavior. Even at room temperature (300 K), there is also a large different in resistance at different magnetic fields, indicating that BaMnBi 2 exhibits  Figure 2(d) displays the temperature dependence of magnetic susceptibility, χ(T). At the Néel temperature, T N = 288 K, an antiferromagnetic (AFM) transition was clearly observed. All these results are quite similar with that reported by Li et al. 15 , also suggesting the existence of the Dirac fermions in our crystals. However, compared with their results, a major difference is found in Hall resistivity, which is negative, indicating that the electrons are dominant carriers in our crystals, which may origin from the slight shift of the E F near the Dirac cone by a light electron-doping.
The key result of this work is shown in Fig. 3. The evolution of the normalized resistivity, ρ ab (T)/ρ ab (300 K), as a function of temperature at various pressures for BaMnBi 2 crystal is shown in Fig. 3(a). It can be seen that the metallic behavior in ρ ab (T) at higher temperatures, i.e., ρ ab monotonously deceases with deceasing temperature, is robust to pressure. At T N , no anomaly in ρ ab (T) due to AFM transition from the Mn 2+ moments was observed under all the applied pressures, which is in consistent with the conduction in BaMnBi 2 determined by the Bi states in the square net as discussed above, therefore makes it impossible to figure out the pressure dependence of T N by using only the resistance measurements. It is very interesting that a clear superconducting transition was observed at pressures above 2.4 GPa, even at 2.1 GPa a slight drop in ρ ab can be distinguished. The definition of superconducting transition temperatures of onset, midpoint, and zero resistance, for 2.6 GPa data are shown in Fig. 3(c), and T c onset = 4.13 K, T c mid = 3.97 K and T c zero = 3.69 K were obtained. Compared with the data of 2.4 GPa, it should be pointed out that there are other two kinks in resistance for 2.6 GPa at T = 5.86 K and 6.81 K, respectively. The origin of these two kinks is not clear yet, however, we suggest that they may be associated with other two superconducting transitions, since they are smoothed out by the applied field. This result indicates that SC with higher T c may emerges at higher pressures. At the same time, we plot the resistivity data at 2.6 GPa as a function of T 2 up to 30 K, as shown in the inset of Fig. 3(c), in which the good ρ ab (T) ~ T 2 behavior above T c indicates its fermi liquid ground state. In order to check whether the structure transition occurs by applying pressure, we plot the resistivity data at 300 K and 7 K as a function of pressure, as shown in Fig. 3(b). It can be seen that the resistivity deceases smoothly with increasing pressure. The smooth and similarity of ρ ab changing with pressure at both temperatures may preclude the possibility of structure transition occurring below 2.6 GPa. However, further work is still needed to confirm this result.
About the origin of the superconductivity, we noted that the T c for BaMnBi 2 is very close to that of Bi single crystal under high pressure 24,25 . To assure what has been observed in Fig. 3 is indeed a superconducting transition and to exclude the SC originating from Bi impurity, we further conducted the measurements at variant external magnetic field at 2.6 GPa. As shown in Fig. 4(a), with the increase of magnetic field, the superconducting transition temperature decreases, and the width of superconducting transition increases gradually from 0.4 K at zero field to 1.2 K at 1 T. The upper critical field μ 0 H c2 as a function of T c onset , T c mid , and T c zero is plotted in Fig. 4(b), respectively. It can be seen that μ 0 H c2 (T) near T c has a positive curvature, a characteristic of two band clean-limit type-II superconductors, like YNi 2 B 2 C, LuNi 2 B 2 C 26 , MgB 2 27 , or TlNi 2 Se 2 28 . According to the Ginzburg-Landau theory, the zero temperature upper critical field H c2 (0) can be estimated by using the formula H c2 (T) = H c2 (0) (1 − t 2 )/(1 + t 2 ), where t is the reduced temperature t = T/T c . Using the T c onset , T c mid , and T c zero , the fitting result yields the value of μ 0 H c2 (0) = 7.0, 4.6, and 2.4 Tesla, respectively. Compared with the critical field of Bi element under high pressure, these values are two orders of magnitude larger. Besides, we also carried out resistivity measurements with different applied currents, and no obvious difference in T c was observed. So, we conclude that the observed SC is intrinsic to BaMnBi 2 , and can't be ascribed to the Bi impurity.
In addition to the SC in BaMnBi 2 at high pressures, the large magnetoresistivity effect [see Fig. 4(a)] due to the presence of Dirac fermions is also survived. Figure 4(c) displays the ρ ab at 2 K measured at both ambient and 2.6 GPa pressure, respectively, as a function of magnetic field, B. It can be seen that the ρ ab measured at ambient pressure increases with increasing magnetic field, and exhibits a linear behavior at higher field, while ρ ab (B) measured at 2.6 GPa has a similar behavior as B > 4 Tesla (at the normal state). The similarity in ρ ab (B) behavior measured both at ambient pressure and 2.6 GPa in the high magnetic field range indicates that SC observed here emerges in the same phase with Dirac fermions. Therefore, we suspect that the Dirac fermions may preserve under high pressure and play an important role in the SC in BaMnBi 2 . Our findings imply that BaMnBi 2 may provide another platform for studying SC mechanism in the system with Dirac fermions. Finally, we should point out that BaMnBi 2 , as an AFM compound of Mn 2+ 3d 5 half-filled electrons with T N = 288 K at ambient pressure, is expected to be a promising parent for SC. As we know, in the cuprates, Fe-pnictides, and heavy-fermion compounds, doping or applying a pressure can suppress the AFM order, then unconventional SC emerges. Here, although we can't figure out the pressure dependence of T N by using only resistance measurements as discussed above, we suspect that the AFM order in BaMnBi 2 seems impossible to be suppressed by such low pressure (≤2.6 GPa), just like the robust antiferromagnetism under high pressure in (Ba 0.61 K 0.39 )Mn 2 Bi 2 29 , which contains the similar Mn 2 Bi 2 layers. Taken this assumption, then the SC observed here should originate from the electrons in Bi square net, which host both Dirac and parabolic states. Therefore, SC in the pressurized BaMnBi 2 may coexist with the AFM order. It is urgently needed to figure out the relationship among SC, AFM and Dirac fermions, as well as the symmetry of Cooper pairs in this system in the near future.
In summary, we present resistivity measurements on the antiferromagnetic (T N = 288 K) Dirac material BaMnBi 2 under various pressures up to 2.6 GPa. At T N , no anomaly in ρ ab (T) due to AFM transition was observed, which makes it impossible to figure out the pressure dependence of T N by using only the resistance measurements. ρ ab (T) shows a clear superconducting transition with T c ~ 4 K at 2.4 GPa, but does not drop to zero. Under 2.6 GPa, a sharp superconducting transition with T c onset = 4.13 K, T c mid = 3.97 K and T c zero = 3.69 K was observed. Both the higher upper critical field, μ 0 H c2 (0) ~ 7 Tesla, close to its Pauli limit H p = 1.84 T c ≈ 7.2 T, and the measured current independent of T c precludes that SC is ascribed to the Bi impurity. The similarity in ρ ab (B) linear behavior at high magnetic fields measured at 2 K both at ambient pressure and 2.6 GPa indicates that SC observed here would emerge in the same phase with Dirac fermions. Our findings imply that BaMnBi 2 may provide another platform for studying SC mechanism in the system with Dirac fermions.

Methods
High quality BaMnBi 2 single crystals were grown using self-flux method. First, Ba chunks, and Mn, Bi powders were mixed according to an appropriate stoichiometry and were put into alumina crucibles and sealed in an evacuated silica tube. The mixture was heated up to 850 °C and kept for 3 hours. Then the melting mixture was cooled down to 450 °C with a rate of 3 °C/h. Finally the furnace was cooled to room temperature after shutting down the power. The structure of single crystals was characterized by powder X-ray diffraction (XRD) measurement at ambient pressure. To avoid exposure to air, the sample was sealed using N-grease during the XRD data collecting. The elemental analysis was performed using an energy-dispersive x-ray spectroscopy (EDX) in a Zeiss Supra 55 scanning electron microscope. The measurements of resistivity under various hydrostatic pressures below 3 GPa, were carried out in the QuantumDesign Physical Properties Measurement System PPMS-9. The magnetic susceptibility χ(T) was measured using the QuantumDesign MPMS-SQUID. Pressure was generated in a Teflon cup filled with Fluorinert FC-75, which was inserted into a nonmagnetic, piston-cylinder type, Be-Cu pressure cell with a core made of NiCrAl alloy. The pressure was determined at low temperature by monitoring the shift in the T c of pure lead.