Introduction

The investigation of topological materials, including topological insulators (TIs), topological semimetals, and topological superconductors, has attracted tremendous interest over the past few decades1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. These topological materials possess exotic fermions (such as Dirac fermions, Weyl fermions, and Majorana fermions) and fascinating physical properties. Therefore, they have potential applications in both spintronics and quantum computation. TIs have a bulk band gap similar to ordinary insulators but exhibit gapless boundary states protected by time-reversal symmetry. In the last decade, the topological configuration of the electronic states of the system has become increasingly rich by the consideration of additional symmetries20,21,22. Among them, crystal symmetries have played an important role in topological classification, such as crystal point group symmetries, leading to the concept of topological crystalline insulators (TCIs)23,24,25. Recently, by studying spatial symmetries that translated the origin by a fraction of the lattice period, Wang et al. predicted that nonsymmorphic symmetries could protect a novel surface fermion with dispersion shapes similar to an hourglass, and they also proposed KHgX (X = As, Sb, Bi) as a material class to achieve this new hourglass-shaped dispersion26. Different from the previously discovered TIs protected by either time-reversal or mirror crystal symmorphic symmetry, the band topology of KHgX relied on nonsymmorphic symmetries. Subsequently, angle-resolved photoemission spectroscopy measurements provided experimental evidence of hourglass fermions on the (010) surface of crystalline KHgSb27,28.

Usually, topological materials show superconductivity under pressure or by carrier doping29,30,31,32,33,34,35,36, which is considered a possible way to achieve topological superconductivity. However, identifying their topological superconductivity is still a difficult task and under debate35. In most cases, the transition from TIs to superconductors is accompanied by the crystal and/or electronic structural transition30,33. It remains unclear whether this transition is indeed necessary to induce superconductivity in TIs. Therefore, searching for superconductivity in new TIs and identifying the possibility of topological superconductors is still an open question.

In this work, we grew single crystals and conducted a comprehensive study on the electrical transport properties and structural phase transition under high pressure for the nonsymmorphic topological insulator KHgAs. We observed transformations from a semiconductor to a metallic state then to a superconducting state as the pressure increased. High-pressure X-ray diffraction measurements combined with crystal structure prediction indicated that the structure changed from the P63/mmc structure at ambient pressure into Pnma, then to P63mc, and finally changed to a new P63/mmc structure at pressures of 2.1 GPa, 21.5 GPa, and 26.7 GPa, respectively.

Results and discussion

Physical characterization under ambient pressure

The crystal structure of KHgAs is shown in Fig. 1a. It belongs to the hexagonal crystal structure with the space group of P63/mmc(194)37. The Hg-As planar honeycomb layers and K ion layers stack alternately along the c axis, and the K ion is located at an inversion center between the two adjacent Hg-As layers. The obtained crystals were flake-like, and the crystal size could reach 1 mm × 0.8 mm × 0.1 mm (see inset of Fig. 1b). Figure 1b shows the X-ray diffraction pattern of the as-grown KHgAs crystals. Only (00 l) reflections were observed, indicating that the crystals were well oriented along the c axis. A Le Bail fit to the diffraction data yielded a c value of 9.9855 Å, which coincided with a previous result37. The chemical composition of the as-grown single crystals was measured by energy-dispersive X-ray spectroscopy (EDX), as shown in Fig. 1c. The atomic ratio of K:Hg:As was determined to be 1.03(99):1.00:0.94(18), which is close to the ideal stoichiometric formula of KHgAs. The scanning electron microscope image of a KHgAs single crystal is shown in the inset of Fig. 1c. Figure 1d shows the temperature-dependent electrical resistivity of the KHgAs single crystal under ambient pressure. The overall behavior of resistivity displayed a typical semiconducting-like feature, except for a slight resistivity anomaly at approximately 125 K. A similar anomaly was also observed in the three-dimensional topological material ZrTe538 and Rashba semiconductor BiTeCl39, which was attributed to the possible Lifshitz transition or charge density wave behavior, though its origin still remains controversial38,39,40. According to the thermal activation model, the resistivity ρ is proportional to \(\exp ({\Delta }_{\rm{g}}/2{k}_{\rm{B}}T)\), where \({\Delta }_{\rm{g}}\) is the semiconducting band gap and \({k}_{\rm{B}}\) is Boltzmann’s constant. Hence, the curve of ln(ρ) versus 1/T is plotted in the inset of Fig. 1d. The curve could be effectively fitted, and the band gap \({\Delta }_{\rm{g}}\) of KHgAs was evaluated to be ~143 meV.

Fig. 1: Crystal structure and characterization of KHgAs under ambient pressure.
figure 1

a Crystal structures of KHgAs from the side view and top view. b X-ray diffraction pattern of a KHgAs single crystal along the c-axis. The inset shows a photograph of the KHgAs single crystals. c Energy-dispersive X-ray (EDX) spectroscopy collected on a KHgAs single crystal. The inset shows the scanning electron microscope image of the KHgAs single crystal. d Temperature dependence of resistivity for the KHgAs single crystal at ambient pressure. The inset shows the curve of ln(ρ) versus 1/T and its linear fitting.

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High-pressure transport properties

Figure 2 shows the high-pressure electrical transport measurements for the KHgAs single crystal. Below 10.3 GPa, the sample maintains semiconductor activity, and the resistances gradually increase with pressure (see Fig. 2a). The anomalous behavior of resistance is gradually suppressed, and the anomalous temperature is reduced to approximately 74 K at 10.3 GPa. From 10.3 GPa to 12.2 GPa, there is a greater increase in resistance at low temperature, which indicates that the sample becomes more insulating. The anomalous behavior of the resistance basically disappears at 12.2 GPa. However, a large resistance anomaly at approximately 90 K reappears at 14.2 GPa, as shown in Fig. 2b. With further increasing pressure, the anomaly peak shifts toward higher temperatures, accompanied by the appearance of metallic transport behavior at low temperature. The phenomenon of anomalies being initially suppressed and then enhanced at low pressure has also been observed in the topological material HfTe541. At 20 GPa, the anomaly peak disappears, and the R-T curve shows metallic behavior over the whole temperature range.

Fig. 2: High-pressure electrical transport measurement of a KHgAs single crystal.
figure 2

a, b Temperature dependence of ab plane resistances below 20 GPa. c Temperature dependence of ab plane resistances at various pressures ranging from 21 GPa to 55 GPa. The pressure-induced superconducting transition is observed within this pressure range. d, e Electrical resistance drop and zero-resistance behavior at low temperatures. A superconducting transition with \({T}_{c}^{{onset}}\) of approximately 3.5 K is observed at 21 GPa. The inset of d shows the definition of \({T}_{c}^{{onset}}\) based on the differential of resistance over temperature (dR/dT) at 21 GPa. f Temperature dependence of resistance under various external magnetic fields aligned along the c axis of the KHgAs single crystal at 27.8 GPa. The inset shows the change in \({T}_{c}^{{onset}}\) as a function of magnetic field H.

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Additionally, a pressure-induced superconducting transition is observed, as shown in Fig. 2c. The transition temperature of onset (\({T}_{c}^{{onset}}\)) is approximately 3.5 K at 21 GPa, which is defined based on the differential of resistance over temperature (dR/dT)31; see the inset of Fig. 2d. Under further compression, \({T}_{c}^{{onset}}\) rapidly grows, and a zero-resistance state is observed at 28.7 GPa. Subsequently, \({T}_{c}^{{onset}}\) reaches a maximum of approximately 6.6 K at 31.8 GPa, followed by a slow decline with a further increase in pressure.

Figure 2f shows the temperature dependence of resistance under various external magnetic fields along the c-axis of the KHgAs single crystal at 27.8 GPa. The transition temperature \({T}_{c}^{{onset}}\) is gradually suppressed as the magnetic field increases, which provides strong evidence that the transition is superconducting in nature. According to the Werthamer-Helfand-Hohenberg (WHH) formula42, \({H}_{c2}\left(0\right)=\,-0.691{\left[{{dH}}_{c2}\left(T\right)/{dT}\right]}_{{T=T}_{c}}* {T}_{c}\), the upper critical field Hc2(0) is determined to be 5.0 T. The Pauli-limiting upper critical field estimated via HP(0) = 1.84Tc is approximately 9.6 T, far exceeding the measured Hc2(0), indicating that the spin paramagnetic effect can be neglected.

High-pressure synchrotron X-ray diffraction

Next, we focus on the crystal structure evolution under pressure. X-ray diffraction patterns of KHgAs polycrystalline powder at various pressures are shown in Fig. 3. Below 2.1 GPa, all peaks are effectively indexed as a P63/mmc phase (phase I). Then, a set of new diffraction peaks appear at 2.1 GPa, 3.1 GPa, and 4.8 GPa, which are marked with inverted triangles, rhombi, and asterisks, respectively (see Fig. 3a). By carefully analyzing the diffraction data, we preliminarily conclude that these new peaks all belong to the first high-pressure phase (phase II). Phase I coexists with phase II in the pressure range of 2.1–4.8 GPa, and then the diffraction peaks of phase I almost disappear. When the pressure further increases to 21.5 GPa, two new diffraction peaks marked with arrows appear (see Fig. 3b), which indicates the appearance of another new high-pressure phase (phase III). Upon further increasing the pressure to 26.7 GPa, the third high-pressure phase (phase IV) appears and gradually becomes the main phase up to 55.1 GPa (see Fig. 3b). Moreover, phase II and phase III still exist until 55.1 GPa.

Fig. 3: Synchrotron X-ray diffraction patterns of polycrystalline KHgAs at different pressures up to 55.1 GPa (λ = 0.6199 Å).
figure 3

a XRD patterns at various pressures ranging from 0.9 GPa to 13 GPa. b XRD patterns at various pressures ranging from 16.3 GPa to 55.1 GPa. The peaks marked with inverted triangles, rhombi, asterisks, arrows, and solid circles denote the emerging new diffraction peaks.

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High-pressure structure prediction

Structure prediction based on the CALYPSO methodology was performed to obtain a deep understanding of the crystal structure evolution of KHgAs under pressure. Figure 4a shows the calculated enthalpy curves of low-energy structures. Below 3.0 GPa, the most stable phase possesses P63/mmc symmetry (Fig. 4b). Then, it undergoes a series of structural evolutions from P63/mmc to Pnma (Fig. 4c), C2/m (Fig. 4d), P63mc (Fig. 4e), and finally to a new P63/mmc phase (named P63/mmc-II, Fig. 4f). Upon a thorough examination of the high-pressure XRD pattern, the sample possesses a hexagonal structure as the ambient phase below 2.1 GPa (see Supplementary Fig. S1a in the Supplementary Information). The first high-pressure phase (phase II, appears at 2.1 GPa) is indexed as a Pnma phase. Almost all peaks of the predicted Pnma phase can be effectively fitted with the experimental pattern at 10.5 GPa except for an unknown peak at approximately 13 degrees (see Supplementary Fig. S1b in the Supplementary Information). The origin of this peak is discussed in the following section. The XRD patterns between 21.5 GPa and 26.7 GPa can be effectively fitted using the combination of structures of Pnma and P63mc (except for an additional peak similar to the case at 10.5 GPa, see Supplementary Fig. S1c in the Supplementary Information), rather than the predicted C2/m phase. Notably, there are Hg-Hg and As-As bonds in the HgAs layers in the C2/m structure (see the right panel of Fig. 4d). These layers are distinctly different from the HgAs layers in the other stable structures, where Hg and As are arranged alternatively. Therefore, a large energy barrier may need to be overcome in the structural transition from Pnma to the C2/m phase. This is the potential reason that there is no appearance of the C2/m phase. Finally, the XRD patterns of KHgAs above 26.7 GPa are fitted with the phases Pnma + P63mc + P63/mmc-II (see Supplementary Fig. S1d in the Supplementary Information). The evolutions of unit cell volumes vs. pressure for different phases are illustrated in Supplementary Fig. S2 in the Supplementary Information. The unit cell volumes of all phases monotonically decrease with increasing pressure.

Fig. 4: High-pressure crystal structure prediction of KHgAs.
figure 4

a Calculated enthalpy curves of predicted stable structures in the pressure range from 0 to 50 GPa. The P63/mmc phase stabilized under ambient pressure is used as the reference structure. Predicted stable structures of P63/mmc (b), Pnma (c), C2/m viewed along two directions (d), P63mc (e), and P63/mmc-II (f). The solid line indicates the unit cell. The gray, green and purple spheres represent the Hg, As and K atoms, respectively.

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To explore the unknown peak of the XRD pattern at 10.5 GPa that cannot be indexed using the predicted Pnma structure under hydrostatic pressure conditions, we then investigated the evolution of the structural parameter and XRD pattern with changing external nonhydrostatic stress along typical high symmetric crystal directions. This kind of stress usually exists in ultrahigh-pressure experiments induced by nonideal transmitting media and can effectively modulate the interatomic distances and bonding patterns. Here, we investigated the evolution of XRD patterns for the Pnma structure at 10.5 GPa with changing external stress along the typical [001], [110], and [111] crystal directions. The applied strain effectively modulated the interatomic distances and bonding patterns, e.g., peak shifting, splitting, and broadening. When the tensile strain increased from 0% to 5%, the simulated theoretical XRD data along the [001] tensile strain showed excellent agreement with the experimental patterns, especially for the unknown peak position near 13 degrees, as shown in Supplementary Fig. S3a in the Supplementary Information. Similarly, the XRD pattern at 23.3 GPa could also be excellently fitted by the introduction of 5% tensile strain along the [001] deformation direction (Supplementary Fig. S3b).

Temperature‒pressure phase diagram

Based on the results of electrical transport measurements, structure prediction, and structure refinement at high pressures, the phase diagram of KHgAs as a function of pressure is obtained, as shown in Fig. 5. Below 12.2 GPa, KHgAs shows semiconductor activity. The anomalous temperature is reduced from ~125 K at ambient pressure to ~74 K at 10.3 GPa and basically disappears at 12.2 GPa. Then, a large resistance anomaly at approximately 90 K reappears at 14.2 GPa, and the temperature of the anomaly peak increases to 200 K with increasing pressure, accompanied by the appearance of metallic transport behavior at low temperature. At 20 GPa, the anomaly peak disappears, and the R-T curve shows metallic behavior over the whole temperature range. Then, a clear superconducting transition with \({T}_{c}^{{onset}}\) of ~3.5 K appears at 21 GPa. The \({T}_{c}^{{onset}}\) is enhanced to a maximum value of ∼6.6 K at 31.8 GPa and then is slowly suppressed under further compression. Finally, a dome-shaped pressure dependence of \({T}_{c}^{{onset}}\) is obtained.

Fig. 5: The phase diagram of KHgAs as a function of pressure up to 55 GPa.
figure 5

The triangle symbols denote T*, the peak temperature of the resistance anomaly. The circles represent the onset temperature of the resistance drop (\({T}_{c}^{{onset}}\)) extracted from the electrical resistance measurements. The structure changes from the P63/mmc structure at ambient pressure into Pnma, P63mc, and finally to the P63/mmc-II structure.

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For the structural change under pressure, KHgAs maintains the ambient structure below 2.1 GPa with P63/mmc and then shifts to a new orthorhombic structure with space group Pnma under pressure. This phase exists over almost the entire pressure range. A new phase with space Group P63mc appears at approximately 21.5 GPa. Notably, the superconducting transition also appears at approximately 21 GPa, this result indicates that there may be some intrinsic connection between superconductivity and the P63mc phase, which warrants in-depth study. Both the Pnma and P63mc phases exist under heavy compression but with the appearance of a new P63/mmc-II phase at approximately 26.7 GPa.

Conclusion

In summary, we successfully grew high-quality single crystals of the newly developed nonsymmorphic topological insulator KHgAs and examined the pressure effect below 55 GPa. Our electrical transport measurement showed a semiconductor-metal transition between ∼16 and 20 GPa, and finally, pressure-induced superconductivity with a \({T}_{c}^{{onset}}\) of ~3.5 K was successfully observed at 21 GPa. \({T}_{c}^{{onset}}\) was enhanced to a maximum value of ∼6.6 K as the pressure increased to 31.8 GPa and then was slowly suppressed under further compression. High-pressure X-ray diffraction combined with crystal structure prediction indicated that the structure changed from the P63/mmc structure at ambient pressure into a new orthorhombic structure with space group Pnma at 2.1 GPa, then changed to the P63mc structure at 21.5 GPa, and finally changed to the P63/mmc-II structure at approximately 26.7 GPa. Moreover, nonhydrostatic stress played an important role in the high-pressure behavior of KHgAs. Our results showed the possible coexistence of superconductivity and a topologically nontrivial feature protected by nonsymmorphic symmetries and could potentially provide a new platform to investigate the interplay between topological properties and superconductivity. However, detailed band structure calculations for the high-pressure phase of KHgAs are needed to provide definitive evidence.

Materials and methods

Sample preparation and characterization

Single crystals of KHgAs were grown using the melting method. To grow single crystals, we first prepared polycrystalline samples of KHgAs. High-purity K (99.95%) and As (99.999%) were mixed at a molar ratio of 1:1, sealed into a titanium tube filled with high-purity Ar gas, and heated to 500 °C to prepare the precursor KAs. Then, the mixtures of KAs and Hg in a molar ratio of 1:1 were placed into an Al2O3 capsule and sealed into a titanium tube filled with high-purity Ar gas. The mixture was heated to 500 °C and held for 20 h before cooling to room temperature. Finally, the obtained polycrystalline samples were sealed into a niobium tube and then an evacuated quartz tube. The quartz tube was heated to 900 °C at a rate of 4 °C/min and maintained at this temperature for 10 h. Then, the sample was slowly cooled to 500 °C at a rate of 3 °C/h. To protect the samples from reacting with air or water, all the synthesis processes were carried out in a high-purity Ar atmosphere. X-ray diffraction (XRD) at ambient pressure was performed on a Rigaku Ultima VI (3KW) diffractometer using Cu Kα radiation generated at 40 kV and 40 mA. The chemical composition of the as-grown single crystals was measured by energy-dispersive X-ray spectroscopy (EDX) using a spectrometer (Model EDAX GENESIS XM2 SYSTEM 60x) equipped with a field-emission scanning electron microscope (Hitachi S-4800). The electrical resistivity under ambient pressure was measured on a Quantum Design physical property measurement system (PPMS) using the four-probe method.

High-pressure electric transport measurement

The electronic transport properties of KHgAs single crystals under high pressure and low temperatures were investigated via the four-probe electrical conductivity method in a diamond anvil cell (DAC) made of CuBe alloy as described in refs. 31,43. The pressure was generated by a pair of diamonds with a 100 μm diameter culet. A gasket made of T301 stainless steel was pressed from a thickness of 250 μm to 10 μm, and a center hole with a diameter of 120 μm was drilled. Fine cubic boron nitride (c-BN) powder was used to cover the gasket to protect the electrode leads insulated from the metallic gasket. The electrodes were slim Au wires with a diameter of 18 μm. A 50-μm-diameter center hole in the insulating layer served as the sample chamber. The dimensions of the sample were approximately 35 μm × 35 μm × 5 μm, and NaCl powder was used as the pressure transmitting medium. The pressure was measured via the ruby fluorescence method at room temperature before and after each cooling44. A diamond anvil cell was placed inside a MagLab system to perform the experiments. The temperature was automatically controlled by a program of the MagLab system. A thermometer was mounted near the diamond in the diamond anvil cell to monitor the exact sample temperature.

High-pressure ADXRD experiments

In situ high-pressure angle-dispersive X-ray diffraction (ADXRD) experiments were performed using a symmetric Mao Bell DAC at the Beijing Synchrotron Radiation Facility. The X-ray wavelength was 0.6199 Å. The sample in the DAC was a finely grounded polycrystalline powder, and ruby balls were placed near the sample as pressure markers. The two-dimensional image plate patterns were converted to one-dimensional 2θ versus intensity data using the Fit2d software package45. The high-pressure synchrotron X-ray diffraction patterns were refined by the Rietveld method46 through the GSAS program.

Crystal structure prediction

The structure prediction was performed using the swarm-intelligence-based CALYPSO method47,48, which is a leading structure prediction method and can be used to search multidimensional PESs in an unbiased manner. The structural searches were carried out with simulation cell sizes of 2, 4, 6, and 8 formula units at 5, 22, 30, and 50 GPa. The density functional theory framework as implemented in the Vienna Ab Initio simulation package (VASP)49 was used for the structure optimization and total energy evaluation. The projector-augmented wave method50 is adopted, and 3p64s1, 5d106s2, and 4s24p3 are used as the valence electrons for K, Hg, and As, respectively. The generalized gradient approximation of Perdew, Burke, and Ernzernhof51 was selected for the exchange-correlation functional. The plane-wave kinetic energy cutoff of 500 eV and a Monkhorst−Pack K-spacing of 2π × 0.025 Å−1 in reciprocal space were chosen to ensure that the total energy converged to less than 1 meV/atom.