A new protocol for the preparation of superconducting KBi2

A superconducting KBi2 sample was successfully prepared using a liquid ammonia (NH3) technique. The temperature dependence of the magnetic susceptibility (M/H) showed a superconducting transition temperature (Tc) as high as 3.6 K. In addition, the shielding fraction at 2.0 K was evaluated to be 87%, i.e., a bulk superconductor was realized using the above method. The Tc value was the same as that reported for the KBi2 sample prepared using a high-temperature annealing method. An X-ray diffraction pattern measured based on the synchrotron X-ray radiation was analyzed using the Rietveld method, with a lattice constant, a, of 9.5010(1) Å under the space group of Fd3̄m (face-centered cubic, no. 227). The lattice constant and space group found for the KBi2 sample using a liquid NH3 technique were the same as those reported for KBi2 through a high-temperature annealing method. Thus, the superconducting behavior and crystal structure of the KBi2 sample obtained in this study are almost the same as those for the KBi2 sample reported previously. Strictly speaking, the magnetic behavior of the superconductivity was different from that of a KBi2 sample reported previously, i.e., the KBi2 sample prepared using a liquid NH3 technique was a type-II like superconductor, contrary to that prepared using a high-temperature annealing method, the reason for which is fully discussed. These results indicate that the liquid NH3 technique is effective and simple for the preparation of a superconducting KBi2. In addition, the topological nature of the superconductivity for KBi2 was not confirmed.


Introduction
Topological materials such as a topological insulators, Dirac and Weyl semimetals, and axion insulators have attracted signicant attention from physicists and chemists owing to their exciting and fascinating physical properties.  Gapless surface states (Dirac-like linear dispersions) in a topological insulator are protected through a time reversal symmetry, which show a spin polarization to lock the spin along a direction perpendicular to the momentum (spin-momentum locking). [1][2][3][4][5] Here, it is noted that the bulk of a topological insulator possesses a band gap, as in a traditional insulator. The representative topological insulators are Bi 1Àx Sb x , Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 , 6-10 with Bi 2 Se 3 being the most popular threedimensional (3D) topological insulator, having a single Dirac cone inside a band gap at the center of the Brillouin Zone (BZ). 7,8 Moreover, Dirac and Weyl semimetals have also elicited attention from physicists and chemists owing to their unique electronic structures, in which linear band crossings are in fourfold/twofold degenerated points. [11][12][13][14][15] A Dirac semimetal appears when both time-reversal symmetry and special inversion symmetry are maintained, whereas a Weyl semimetal appears when either the time-reversal symmetry or special inversion symmetry is broken. Namely, by breaking either the time-reversal symmetry or the special inversion symmetry, one Dirac fermion will transform into two Weyl fermions with opposite chirality in the BZ. The above semimetals are categorized as type-I or type-II depending on whether the Lorentz invariance is preserved. With type-I Dirac/Weyl semimetals, massless Dirac fermions (or Weyl fermions) should emerge at the Dirac and Weyl points, [15][16][17][18][19] whereas in type-II Dirac/Weyl semimetals, they emerge at the topologically protected crossing points of the electron and hole pockets. 17,[20][21][22] Currently, many researchers are working on the condensed matter physics of Dirac/Weyl semimetals, owing to not only the above unique electronic properties, but also interesting physical properties such as a negative magnetoresistance, 23,24 chiral magnetic effects, 25 and quantum anomalous Hall (QAH) effect. 26 Furthermore, recent interest in the complex interplay between topology and magnetism has led to a topological quantum state, which is indicated as an axion insulator. 27,28 The attempt to realize an axion insulator began in the heterostructures of QAH effect lms, 27 and is currently realized in a stoichiometric material. 28 Alkali-Bi based compounds (ABi 3 (A ¼ Na, K, or Rb)) have recently attracted signicant attention because crystalline ABi 3 has been proposed as a Dirac semimetal in which bulk 3D Dirac points are protected by a crystal symmetry. 15,29 Moreover, these materials were predicted to possess a nontrivial Fermi arc on the surface. In addition, various novel physical properties (giant diamagnetism, linear quantum magnetoresistance, and the QAH effect) were expected for ABi 3 . 29 Since the above reports, the physical properties of a family of materials (alkaline and alkaline-earth metal-Bi compounds) have been investigated owing to an interest in the coupling of a Dirac semimetal and the superconductivity, i.e., under the topological nature of the superconductivity, the particular superconducting properties of BaBi 3 were fully investigated. 30 In 2016, the superconductivity of the KBi 2 sample, which was a traditional superconductor, 31 was fully studied. 32 The detailed data of the superconductivity in KBi 2 were collected in this study. The motivation of this study is the interplay of the topological nature and the superconductivity. In addition, the strong spin orbit coupling (SOC) may affect the superconductivity in a metal-Bi compound because Bi is a heavy atom (atomic no. 83). All metal-Bi compounds were prepared using a high-temperature annealing method, [30][31][32][33][34][35] for instance, a stoichiometric amount of Bi and K were mixed and sealed in a quartz tube. The tube was heated at more than 500 C for several hours and slowly cooled. Finally, the crystals of KBi 2 were isolated using a centrifuge. Thus, the heating of metal and Bi is indispensable for the preparation of metal-Bi compounds, and isolation using a centrifuge is frequently required.
In this study, we report a new protocol for the preparation of KBi 2 in which a sample heating is not employed, i.e., the liquid ammonia (NH 3 ) technique was applied to the sample preparation of a superconducting KBi 2 . The KBi 2 sample obtained using liquid NH 3 showed a bulk superconductivity, and a clear crystalline powder was prepared. To characterize its superconductivity and crystal structure, the magnetic susceptibility (M/H) and X-ray diffraction (XRD) pattern of the obtained sample were measured; M and H refer to the magnetization and applied magnetic eld, respectively. The superconducting transition temperature, T c , and crystal structure of the KBi 2 sample prepared using liquid NH 3 were consistent with those of the sample prepared through a high-temperature annealing method. However, the magnetic behavior of the superconductivity was signicantly different from that of the KBi 2 sample reported previously, 32 which is fully discussed herein.

Experimental
Stoichiometric amounts of K and Bi were inserted into a glass tube in an Ar-lled glove box, and the space inside the glass tube was pumped to 10 À2 torr. NH 3 gas was then collected in a glass tube and frozen. The K was dissolved in liquid NH 3 at less than À50 C, and K atoms were introduced into the Bi crystallites, forming KBi 2 . Finally, NH 3 was removed through vacuum distillation, and the removal of NH 3 was then carried out through pumping under 10 À2 torr at room temperature. Because the KBi 2 sample is quite sensitive to air, the handling of the sample was achieved without air exposure. Details of the reaction process are described later.
The temperature dependence of M/H of the obtained KBi 2 sample was measured using a SQUID magnetometer (Quantum Design, MPMS2 or MPMS-SQUID-VSM). The powder XRD pattern of the sample was measured at room temperature, using synchrotron radiation at BL12B2 of SPring-8, and the wavelength l of the X-ray beam was 0.6859610Å. The XRD pattern was analyzed using a Rietveld renement. Fig. 1 shows the process of the sample preparation of KBi 2 . A photograph of the initial stage of the reaction between K and Bi is shown in Fig. 1(a), and K is dissolved in liquid NH 3 . The color of the K-dissolved NH 3 solution is dark blue. Aer 3 days, the solution became transparent and black precipitate was obtained, as shown in Fig. 1(b). Aer removal of NH 3 , a black powder sample was obtained, as shown in Fig. 1(c). The sample was then introduced into a quartz cell and glass capillary for M/ H -T and XRD measurements, respectively, in an Ar-lled glove box. Here, it should be stressed that the most important point in the sample preparation of KBi 2 is to handle the sample without exposure to air to avoid a degradation of the sample. were the same as those of the KBi 2 sample prepared using a high-temperature heating method. 32 The shielding fraction at 2.0 K determined from the M/H -T plot in ZFC mode was evaluated to be 87%, indicating a bulk superconductivity.

Results and discussion
The M/H -T plots at H ¼ 10-250 Oe in ZFC mode are shown in Fig. 2(b), exhibiting a clear suppression of the superconducting transition by applying H. The T onset c value against each H is employed for depicting the H -T phase diagram (Fig. 3(c)), as described later. Fig. 2(c) shows the M -H loop of a KBi 2 sample prepared using a liquid NH 3 technique, recorded at 2.0 K, showing a clear hysteresis loop. This behavior indicates a type-II superconductor, which is different from that (type-I superconductor) reported previously for a KBi 2 crystal, 32 which was prepared using a high-temperature annealing method. However, the M -H loop of the KBi 2 sample prepared using a liquid NH 3 technique (Fig. 2(c)) is similar to that of a a-PdBi 2 compound (type-II superconductor). 36 As described later, the values of the lower critical eld, H c1 , and the upper critical eld, H c2 , were too low, similar to those of KBi 2 . 32 Fig. 2(d) shows 4pM -H plots of a KBi 2 sample prepared using a liquid NH 3 technique, and recorded at 2.0-3.6 K. As shown in the inset of Fig. 2(d), the lower critical eld, H c1 , was evaluated to be 24 Oe at 2.0 K, whereas the H c2 value was determined to be >500 Oe at 2.0 K; the value of H c1 was determined from the deviation from the linear line with a slope of À1.0 (as shown in the inset of Fig. 2(d)). A previous report concluded that the KBi 2 prepared using an annealing method was presumably a type-I superconductor. 32 Actually, the M -H loop with a small hysteresis for the KBi 2 sample 32 was similar to other type-I superconductors such as YbSb 2 and LaRhSi 3 . [37][38][39] However, the M -H loop of KBi 2 prepared in this study (Fig. 2(c)) seems to be different from those of YbSb 2 and LaRhSi 3 .
Herein, we should discuss why a type-II like superconducting behavior can be seen in the KBi 2 sample prepared using a liquid NH 3 technique. The rst scenario is based on a type of impurity effect, and the second is based on KBi 2 prepared using liquid NH 3 , creating an intrinsically bulk type-II superconductor. In a type-II superconductor, k ¼ l x GL is larger than 1.0 x 0 ð1 À tÞ 0:5 for a clean limit, and x GL ðTÞ ¼ 0:855 ðx 0 lÞ 0:5 ð1 À tÞ 0:5 for a dirty limit, at near T c ; in addition, t ¼ T/T c . Here, x GL , l, x 0 , and l refer to the Ginzburg-Landau coherence length, magnetic penetration depth, Pippard coherence length, and mean-free path of a conduction electron, respectively. 40 Moreover, the magnetic penetration depth under a dirty limit, l eff (or l), is expressed as l eff ðtÞ ¼ l L ðtÞ x 0 1:33l 0:5 ; in addition, l L (t) is London's penetration depth. Therefore, under a dirty limit, a smaller l must lead to a smaller x GL and greater l, yielding a greater k, i.e., a type-II superconductor. Actually, l is governed by the impurity, as indicated by the fact that the conversion of a type-I superconductor into a type-II superconductor is found in the In doping of Pb. 41 To summarize, the polycrystalline powder sample of KBi 2 obtained using a liquid NH 3 technique may result in a small l because of the impurity effect. In addition, more detailed experiments such as specic heat measurements at H ¼ 0 and H s 0 will be signicant for determining either a type-I or type-II superconductor, as was achieved for a single crystal of KBi 2 . 32 In addition, the experiment results will simultaneously indicate whether the KBi 2 prepared using liquid NH 3 is a true bulk type-II superconductor, or the result of an impurity effect. Fig. 3(a) shows the value of upper critical led, H c2 , versus T plot in which H c2 value at each temperature was dened as H value providing 5% of the absolute value of minimum M, as indicated in inset of Fig. 3(a). In addition, the experimental M -H plots for the KBi 2 sample prepared in this study using high-temperature annealing substantially followed a linear line, 32 and the value of H c ($160 Oe) 32 for the KBi 2 sample at 2.0 K is close to the critical eld, H 0 c ð¼ 210 OeÞ, for KBi 2 at 2.0 K (see the inset of Fig. 3(a)). Fig. 3(b) shows the normalized temperature (t ¼ T/T c ) dependence of the reduced critical eld, h*, where h*(T) at any temperature (T) is given by the equation, : The value of H c2 (T) corresponds to that shown in Fig. 3(a), and the value of 1040 Oe was utilized for H L c2 (0); here, H L c2 (0) corresponds to T c Â À dHc2ðTÞ dT T¼Tc : It should be noted that the dirty limit superconductivity of an s-wave corresponds to the Werthamer-Helfand-Hohenberg (WHH) model (h*(0) ¼ 0.69). 42,43 In addition, the h*(0) value should reach 0.80-0.85 in the case of p-wave pairing. [44][45][46][47][48][49] As shown in Fig. 3(b), it is difficult to uniquely conclude which model follows the h*t plot between the s-wave and p-wave. The H c2 data at a temperature of lower than 2.0 K are required to achieve a unique conclusion. However, the p-wave Cooper pair coupling of KBi 2 seems to lack a positive support. Thus, the superconductivity of KBi 2 may not comprise a topologically non-trivial nature because the Cooper pair symmetry will be a p-wave (with an odd parity) in the case of a topologically non-trivial superconductor. 46-49 A more detailed study, including a theoretical approach, may be indispensable for pursuing its topological nature. In this study, we further discuss the H c2 value of the KBi 2 sample within the framework of an p-wave dirty limit model. 42,43 The H c2 value was determined to be 720 Oe based on the WHH model, using an H L c2 (0) value of 1040 Oe (Fig. 3(a)). Moreover, although we tried to determine the value of H c2 at each temperature, H c2 (T), from T onset c at each H (see Fig. 2(b)), and to depict an h*t plot, it was difficult to evaluate T onset c at high H. Therefore, an h*t plot was not created. Based on the WHH , the H c2 (0) value was determined to be 620 Oe from a linear tting at near T c for the H c2 -T plot (H L c2 (0) ¼ 900 Oe in Fig. 3(c)). An H c2 (0) value of 620 Oe may be reasonable owing to an agreement with 720 Oe, as evaluated from the H c2 -T plot shown in Fig. 3(a). As shown in Fig. 3(d), the lower critical eld (H c1 (0)) was 37 Oe, as determined from the tting of the conventional formula, , in which g is $1.0. This empirical formula was employed for an evaluation of H c1 of various   (0) to be 620 Oe, where F 0 is 2.0678 Â 10 À7 G cm 2 . By contrast, the l value was evaluated as 220 nm using the for- 40 and a H c1 (0) value of 37.0 Oe.
The value of k ¼ l x GL was $3, which is much larger than 1 ffiffiffi 2 p , indicating a type-II superconductor, as described above. Fig. 4 shows an XRD pattern of the KBi 2 sample prepared using a liquid NH 3 technique, along with the XRD pattern reproduced through a Rietveld renement with a space group of Fd 3m (face-centered cubic, no. 227). The lattice constant, a, was determined to be 9.5010(1)Å, which is consistent with that (9.5017(1)Å) from a Le Bail analysis (not shown) and a ¼ 9.5233(2)Å of KBi 2 prepared using a high-temperature annealing method. 32 This phase can be assigned to KBi 2 . Table 1 lists the atomic coordinates of KBi 2 as determined through a Rietveld renement. The actual stoichiometry of KBi 2 determined by a Rietveld renement was K 0.97(3) Bi 2 , which was evaluated from the occupancy of K and Bi atoms (see Table 1). The actual stoichiometry is the same as the nominal stoichiometry. In a Rietveld renement, an additional minor phase that can be assigned to Bi (R 3m (rhombohedral, no. 166) and a ¼ 4.53440(8) A and c ¼ 11.8310(5)Å in a hexagonal structure) was included.
The lattice constants obtained are the same as those of the Bi metal. 53 In the Rietveld renement, the experimental and calculated XRD patterns (Fig. 4) showed a good t. The values of R p and wR p were 1.55% and 2.87%, respectively.
Herein, we discuss whether NH 3 is included in the KBi 2 sample prepared using a liquid NH 3 technique. The a value of KBi 2 prepared in this study is consistent with that of the KBi 2 sample (a ¼ 9.5233(2)Å) prepared using a high-temperature annealing method. 32 For instance, the c value of ammoniated K-doped FeSe ((NH 3 ) y K x FeSe) was 14.84-16.2Å, 54,55 which is larger than that of K x FeSe, i.e., 14.0367(7)Å, prepared using a high-temperature annealing method. 56 As a consequence, the KBi 2 sample prepared using the liquid NH 3 technique is exactly KBi 2 without NH 3 . It can be concluded that the liquid NH 3 technique can exactly yield a KBi 2 sample in the same manner as a high-temperature annealing method.
A schematic representation of the crystal structure of KBi 2 depicted with the atomic coordinates determined from the Rietveld renement for an XRD pattern (Fig. 4) is shown in Fig. 5. As shown in the projection from the [111] direction, the Bi atoms form a Kagomé net, which is the same as a previously reported crystal structure. 32 The atoms of K are linked to the Bi atoms in a 3D network, as shown in Fig. 5. The crystal structure obtained is the same as that reported previously. 32 As a consequence, throughout this study, it was demonstrated that the liquid NH 3 technique can easily produce a crystalline powder sample of KBi 2 in the same manner as used in a hightemperature annealing method. The value of T c and the crystal structure are consistent with those previously reported. 32

Conclusions
A new protocol for the preparation of superconducting KBi 2 was completely veried through this study, i.e., a liquid NH 3 technique is available for the preparation of a crystalline powder of superconducting KBi 2 . The T c value of KBi 2 prepared in this study was consistent with that reported previously. 32 The crystal structure was also the same as that described elsewhere. 32 Regardless of the preparation when using liquid NH 3 , the inclusion of NH 3 or amide was not conrmed in the KBi 2 sample. Actually, the magnetic properties of a polycrystalline KBi 2 sample prepared using a liquid NH 3 technique were different from those of the single-crystal KBi 2 prepared through Fig. 5 Schematic representation of crystal structure of KBi 2 , which was determined using a Rietveld refinement (Fig. 4(b)). a high-temperature annealing method. 32 The reason why the former is a type-II superconductor and the latter is type-I remains questionable, although pursuing it may be extremely signicant from the chemistry viewpoint of material synthesis as well as the physics perspective of a superconductor. Because the liquid NH 3 technique is extremely effective and simple in terms of the preparation of KBi 2 , various metal-Bi compounds may easily be fabricated using the technique, leading to an elucidation of their superconducting behavior and quantum/topological properties. Admittedly, this type of material is interesting owing to the suggested topological nature such as a Dirac semimetal. 29,30 At the present stage, the topological nature of the superconducting KBi 2 sample was denitely not demonstrated. The pursuit of a topological nature in metal-Bi compounds must be continued; our approach regarding the preparation of a Bi-rich compound using a liquid NH 3 technique is currently being used to produce various alkali-Bi compounds such as LiBi, NaBi, RbBi 2 , and CsBi 2 as superconductors. 57 To summarize, the development of an effective, simple, and exact preparation of metal-Bi compounds as described in this paper is signicant for a detailed study on the superconducting behaviors of their compounds. The next target is to synthesize new superconducting metal-Bi compounds that have yet to be prepared using a high-temperature annealing method.

Author contributions
Huan Li, Yanan Wang, and Yutaro Aoki prepared the KBi 2 sample using a liquid NH 3 technique. In addition, Huan Li, Yanan Wang, and Yutaro Aoki carefully measured the magnetic behavior of the KBi 2 sample, under cooperation with Takashi Kambe. Huan Li, Yanan Wang, Xiaofan Yang, Tomoya Taguchi, Akari Miura, Ai Suzuki, Lei Zhi, and R. Eguchi measured the Xray diffraction patterns (XRDs) of the KBi 2 sample and analyzed the data using Le Bail and Rietveld analysis methods. The XRD measurement system using synchrotron radiation was designed by Yen-Fa Liao and Hirofumi Ishii, which allowed the suitable results of this study to be achieved. Yoshihiro Kubozono supervised all of the measurements and data analyses conducted in this study and prepared the manuscript under discussions with Hidenori Goto and Huan Li. Saki Nishiyama suggested the idea of this study, and the preliminary experiment was conducted by Yoshihiro Kubozono. All coauthors nally reviewed the manuscript.

Conflicts of interest
The authors declare no competing nancial interests.