Pressure-induced superconductivity and topological quantum phase transitions in a quasi-one-dimensional topological insulator: Bi4I4

Superconductivity and topological quantum states are two frontier fields of research in modern condensed matter physics. The realization of superconductivity in topological materials is highly desired, however, superconductivity in such materials is typically limited to two- or three-dimensional materials and is far from being thoroughly investigated. In this work, we boost the electronic properties of the quasi-one-dimensional topological insulator bismuth iodide \b{eta}-Bi4I4 by applying high pressure. Superconductivity is observed in \b{eta}-Bi4I4 for pressures where the temperature dependence of the resistivity changes from a semiconducting-like behavior to that of a normal metal. The superconducting transition temperature Tc increases with applied pressure and reaches a maximum value of 6 K at 23 GPa, followed by a slow decrease. Our theoretical calculations suggest the presence of multiple pressure-induced topological quantum phase transitions as well as a structural-electronic instability.

In this work, we systematically investigate the high-pressure behavior of the novel quasi-1D TI β-Bi4I4. Through ab-initio band structure calculations, we find that the application of pressure alters the electronic properties and leads to multiple topological quantum phase transitions: from strong TI (STI) to weak TI (WTI) and back to STI. Corresponding anomalies are visible in pressure-dependent resistivity data.
Superconductivity is observed in β-Bi4I4 when the temperature dependence of ρ(T) changes from a semiconducting-like behavior to that of a normal metal. The 4 superconducting transition temperature Tc increases with applied pressure and reaches a maximum value of 6 K at 23 GPa for β-Bi4I4, followed by a slow decrease.

Results
Structure and transport properties under ambient pressure. Prior physical property measurements, β-Bi4I4 crystals used for the study were structurally characterized using single-crystal x-ray diffraction (SXRD) and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). Energy-dispersive x-ray spectroscopy (EDXS) analysis confirms that the single crystals are homogeneous and that the atomic ratio of elements is Bi:I = 53.8(2):46.2(4), in agreement with previously reported data 40 . β-Bi4I4 crystallizes in a monoclinic structure (space group C12/m1, No. 12), as shown in Fig. 1a, b. The 1D building blocks of β-Bi4I4, aligned along the b axis, can be viewed as narrow nanoribbons of a bismuth bilayer (four Bi atoms in width) terminated by iodine atoms. The atomic arrangement of β-Bi4I4 was determined using HAADF-STEM images and diffraction patterns (Fig. 1c). One primitive cell consists of four I atoms and four Bi atoms which can be divided into two non-equivalent types of atoms: inner Bi1 atoms that bind to three bismuth atoms and peripheral Bi2 atoms that are saturated by covalent bonds to four iodine atoms.
Electrical resistivity at high pressure. In Figure 2 the temperature dependence of the resistivity ρ(T) of β-Bi4I4 for various pressures is shown. For P = 0.5 GPa, ρ(T) displays a semiconducting-like behavior similar to that observed at ambient pressure 40,41 , however our crystals do not show an upturn below  100 K. 40 In a low-pressure region, increasing the pressure initially induces a weak but continuous suppression of the overall magnitude of ρ with a minimum occurring at Pmin = 3 GPa. Upon further 5 increasing the pressure, the resistivity starts to increase gradually, reaching a maximum at a pressure above 8 GPa.
As the pressure is further increased above 8.8 GPa, ρ rapidly decreases, exhibiting semiconductor-like behavior for β-Bi4I4 (Fig. 2b). As pressure increases up to 13.5 GPa, the normal state behaves as a metal, and a small drop of ρ is observed at the lowest temperatures (experimental Tmin = 1.9 K). Zero resistivity is achieved for P  17.6 GPa, indicating the emergence of superconductivity. The critical temperature of superconductivity, Tc, gradually increases with pressure, and the maximum Tc of 6 K is attained at P = 23 GPa, as shown in Fig. 2c. Beyond this pressure, Tc decreases slowly, showing a dome-like behavior (Fig. 2d).
The appearance of bulk superconductivity in β-Bi4I4 is further supported by the evolution of the resistivity-temperature curve with an applied magnetic field. The superconducting transition gradually shifts toward lower T with the increase of the magnetic field (Fig. 2e). A magnetic field 0H = 2.5 T removes all signs of superconductivity above 1.9 K. The upper critical field 0Hc2 is determined using the 90% points on the transition curves, and plots of Hc2(T) are shown in Fig. 2f. A simple estimate using the conventional one-band Werthamer-Helfand-Hohenberg (WHH) approximation, neglecting the Pauli spin-paramagnetism effect and spin-orbit interaction 42 , i.e., 0Hc2(0) = -0.693 × 0(dHc2/dT) × Tc, yields a value of 2.5 T for β-Bi4I4. We also used the Ginzburg-Landau formula to fit the data: (1) where t = T/Tc, yielding a critical field 0Hc2 = 2.7 T for β-Bi4I4. Both values are comparable with those determined for superconducting Bi2Se3 and BiTeI under 6 pressure 24,25,43 . According to the relationship 0Hc2 = Φ0/(2πξ 2 ), where Φ0 = 2.07×10 −15 Wb is the flux quantum, the coherence length ξGL(0) is 11.5 nm for β-Bi4I4. Note that the extrapolated values of Hc2(0) are well below the Pauli-Clogston limit.

Discussion
The pressure dependence of the resistivity at room temperature and the critical temperature of superconductivity for β-Bi4I4 are summarized in Fig. 3. The resistivity of β-Bi4I4 exhibits a non-monotonic evolution with increasing pressure. Over the whole temperature range, the resistivity is first suppressed with applied pressure and reaches a minimum value at about 3 GPa. As the pressure further increases, the resistivity increases with a maximum occurring at 8 GPa. Then, the resistivity abruptly decreases.
Superconductivity is observed after the temperature dependence of ρ(T) changes from a semiconducting-like behavior to that of a metal. The superconducting Tc increases with applied pressure, and a typical domelike evolution is obtained. with even parity. The band dispersion is relatively weak along the AГYM path, which is perpendicular to the quasi-1D chain, indicating weak interaction between the chains. In contrast, the strong dispersion along the BГ direction indicates strong interaction within the chain. Thus, the dispersion clearly reflects the quasi-1D character of β-Bi4I4.
From the band structure at zero pressure β-Bi4I4 is in a STI phase with a band inversion at the Y point. As pressure increases, the CBM and the VBM meet at the M point. Band inversion occurs and the structure is driven into a WTI phase 44 . For the process of band inversion, the band gap decreases to zero and then reopens. Therefore, the resistivity decreases before the band gap closes and then increases after the band gap reopens. This trend is roughly consistent with the experimental resistivity values (see Fig. 3). When pressure continues increasing, the band at the Y point is inverted back, and the structure returns to the STI phase. This phase evolution is also shown in Fig. 3b.
When the pressure increases, the DOS near the Fermi level increases (see Fig. 4f). We also note that the increase of the DOS is mainly due to the flat bands near the Fermi level in the band structure. These heavy bands may exhibit low mobility, which may be the reason for the additional increase in resistivity in our experiments.
The pressure-induced multiple topological quantum phase transitions in β-Bi4I4 are unusual, and in addition β-Bi4I4 shows an electronic instability. DFT calculations indicate that the crystal structure abruptly changes at a critical pressure of 11.5 GPa. We can see that the lattice parameter along the quasi-1D chain direction decreases, while the parameters in the other two directions suddenly increase ( Supplementary Fig. 3a,b). We also calculated the bond length within the Bi plane. Bond 2 (bond 1) suddenly increases (decrease) at the critical pressure ( Supplementary Fig. 3c), which is further confirmed 8 by the phonon spectrum ( Supplementary Fig. 4). Near 11.5 GPa, an imaginary phonon mode appears, which corresponds to vibrations along the quasi-1D chain and leads to the collapse of the lattice along the chain direction. From the electronic band structure calculations we can see that, after the lattice constant changes, the structure is driven from an STI to a metal. The Fermi level crosses the band (see Fig. 4 e) and the DOS increases near the Fermi level (see Fig. 4f). Indeed, the resistivity abruptly decreases above the critical pressure and superconductivity is observed in β-Bi4I4 when the temperature dependence of ρ(T) changes from a semiconducting-like behavior to that of a metal.
As a novel topological insulator, β-Bi4I4 offers a new platform for exploring exotic physics with simple chemistry. We find multiple topological quantum phase transitions under high pressure and β-Bi4I4 shows electronic instabilities.
Superconductivity is induced after the nonmetal-to-metal transition in β-Bi4I4, which may be attributed to electronic and structure instabilities.

Methods
Single-crystal growth and characterization. Single crystals of β-Bi4I4 were obtained from gas phase reactions using methods similar to those described in Refs 40,41,45 .
Thoroughly ground mixtures of bismuth metal and HgI2 were used as starting materials.
The Bi to HgI2 molar ratio was 1:2 with a total mass of  3 g. After evacuation and sealing, the ampoule was inserted into a furnace with a temperature gradient of 210 to 250°C with the educts in the hot zone.