Abstract
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 twodimensional or threedimensional materials and is far from being thoroughly investigated. In this work, we boost the electronic properties of the quasionedimensional topological insulator bismuth iodide βBi_{4}I_{4} by applying high pressure. Superconductivity is observed in βBi_{4}I_{4} for pressures, where the temperature dependence of the resistivity changes from a semiconductinglike behavior to that of a normal metal. The superconducting transition temperature T_{c} 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 pressureinduced topological quantum phase transitions as well as a structural–electronic instability.
Introduction
Dirac materials such as topological insulators (TI),^{1,2,3} Dirac semimetals (DSM),^{4,5,6,7,8,9,10,11,12} and Weyl semimetals (WSM)^{13,14,15,16,17,18,19,20,21} have topologically nontrivial band structures and therefore exhibit unique quantum phenomena. Achieving a superconducting state, which is the state of quantum condensation of paired electrons, in topological materials has already led to some unprecedented discoveries. Indeed, the realization of superconductivity in topological compounds has been regarded as an important step toward topological superconductors.
Superconductivity has been induced by using doping or pressure in TIs (Bi_{2}Se_{3},^{22,23,24,25} Bi_{2}Te_{3},^{26,27,28} Sb_{2}Te_{3}^{29}), DSMs (Cd_{3}As_{2},^{30,31,32} ZrTe_{5},^{33} and HfTe_{5}^{34}), and WSMs (TaAs,^{35} TaP,^{36} WTe_{2},^{37, 38} and MoTe_{2}^{39}). However, from a structural perspective, most topological materials are limited to twodimensional or threedimensional structures. Superconductivity has not been thoroughly explored in lowdimensional topological materials. Recently βBi_{4}I_{4} has been theoretically predicted and experimentally confirmed as a new Z_{2} TI.^{40} Importantly, βBi_{4}I_{4} crystallizes in a quasionedimensional (quasi1D) structure and thus hosts highly anisotropic surfacestate Dirac fermions.
In this work, we systematically investigate the highpressure behavior of the novel quasi1D TI βBi_{4}I_{4}. 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 pressuredependent resistivity data. Superconductivity is observed in βBi_{4}I_{4} when the temperature dependence of ρ(T) changes from a semiconductinglike behavior to that of a normal metal. The superconducting transition temperature T_{c} increases with applied pressure and reaches a maximum value of 6 K at 23 GPa for βBi_{4}I_{4}, followed by a slow decrease.
Results
Structure and transport properties under ambient pressure
Prior physical property measurements, βBi_{4}I_{4} crystals used for the study were structurally characterized using singlecrystal Xray diffraction (SXRD) and highangle annular darkfield scanning transmission electron microscopy (HAADFSTEM). Energydispersive Xray spectroscopy 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} βBi_{4}I_{4} crystallizes in a monoclinic structure (space group C12/m1, No. 12), as shown in Fig. 1a, b. The 1D building blocks of βBi_{4}I_{4}, aligned along the baxis, can be viewed as narrow nanoribbons of a bismuth bilayer (four Bi atoms in width) terminated by iodine atoms. The atomic arrangement of βBi_{4}I_{4} was determined using HAADFSTEM images and diffraction patterns (Fig. 1c). One primitive cell consists of four I atoms and four Bi atoms, which can be divided into two nonequivalent 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 Fig. 2 the temperature dependence of the resistivity ρ(T) of βBi_{4}I_{4} for various pressures is shown. For P = 0.5 GPa, ρ(T) displays a semiconductinglike behavior similar to that observed at ambient pressure^{40, 41}; however, our crystals do not show an upturn below ≈100 K.^{40} In a lowpressure region, increasing the pressure initially induces a weak but continuous suppression of the overall magnitude of ρ with a minimum occurring at P_{min} = 3 GPa. Upon further 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 semiconductorlike behavior for βBi_{4}I_{4} (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 T_{min} = 1.9 K). Zero resistivity is achieved for P ≥ 17.6 GPa, indicating the emergence of superconductivity. The critical temperature of superconductivity, T_{c}, gradually increases with pressure, and the maximum T_{c} of 6 K is attained at P = 23 GPa, as shown in Fig. 2c. Beyond this pressure, T_{c} decreases slowly, showing a domelike behavior (Fig. 2d).
The appearance of bulk superconductivity in βBi_{4}I_{4} is further supported by the evolution of the resistivitytemperature 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 μ_{0}H = 2.5 T removes all signs of superconductivity above 1.9 K. The upper critical field μ_{0}H_{c2} is determined using the 90% points on the transition curves, and plots of H_{c2}(T) are shown in Fig. 2f. A simple estimate using the conventional oneband Werthamer–Helfand–Hohenberg approximation, neglecting the Pauli spinparamagnetism effect and spin–orbit interaction,^{42} i.e., μ_{0}H_{c2}(0) = −0.693 × μ_{0}(dH_{ c2 }/dT) × T_{c}, yields a value of 2.5 T for βBi_{4}I_{4}. We also used the Ginzburg–Landau formula to fit the data:
where t = T/T_{c}, yielding a critical field μ_{0}H_{c2} = 2.7 T for βBi_{4}I_{4}. Both values are comparable with those determined for superconducting Bi_{2}Se_{3} and BiTeI under pressure.^{24,25, 43} According to the relationship μ_{0}H_{c2} = Φ_{0}/(2πξ^{2}), where Φ_{0} = 2.07 × 10^{−15} Wb is the flux quantum, the coherence length ξ_{GL}(0) is 11.5 nm for βBi_{4}I_{4}. Note that the extrapolated values of H_{c2}(0) are well below the Pauli–Clogston limit.
About the origin of the superconductivity, we noted that the T_{c} for βBi_{4}I_{4} is very close to that of elemental bismuth under pressure (6 vs. 8 K).^{44} The possible scenarios of decomposition into elemental bismuth and BiI_{3} should be taken into account.^{45} Recently, Pisoni et al. carried out chemical characterization of the pressuretreated samples and ruled out decomposition into Bi and BiI_{3} at room temperature condition.^{46} So we conclude that the observed superconductivity is intrinsic to βBi_{4}I_{4}, and cannot be ascribed to the Bi impurity.
Discussion
The pressure dependence of the resistivity at room temperature and the critical temperature of superconductivity for βBi_{4}I_{4} are summarized in Fig. 3. The resistivity of βBi_{4}I_{4} exhibits a nonmonotonic 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 semiconductinglike behavior to that of a metal. The superconducting T_{c} increases with applied pressure, and a typical domelike evolution is obtained.
The presented results demonstrate that high pressure dramatically alters the electronic properties in βBi_{4}I_{4}. To obtain a comprehensive understanding of the physical properties of βBi_{4}I_{4}, we performed density functional theory (DFT) calculations for the electronic band structures. Because of the underestimated band gap within the local density approximation or generalized gradient approximation (GGA), we employed the hybrid functional method (HSE) to calculate the electronic properties. The calculated band structures and density of states (DOS) are displayed in Fig. 4 and Supplementary Figs. 1 and 2. At zero pressure, the HSE calculations predict a narrow indirect band gap of 40.9 meV, with a valence band maximum (VBM) at the M point and a conduction band minimum (CBM) at the Y point. The component of VBM is mainly the p orbital of Bi1 with odd parity, while the CBM is mainly the p orbital of Bi2 with even parity. The band dispersion is relatively weak along the AГYM path, which is perpendicular to the quasi1D 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 quasi1D character of βBi_{4}I_{4}.
From the band structure at zero pressure βBi_{4}I_{4} 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.^{47} 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 pressureinduced multiple topological quantum phase transitions in βBi_{4}I_{4} are unusual, and in addition βBi_{4}I_{4} 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 quasi1D 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 by the phonon spectrum (Supplementary Fig. 4). Near 11.5 GPa, an imaginary phonon mode appears, which corresponds to vibrations along the quasi1D 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. 4e) 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 βBi_{4}I_{4} when the temperature dependence of ρ(T) changes from a semiconductinglike behavior to that of a metal.
Recently Pisoni et al. performed in situ highpressure synchrotron Xray diffraction measurements and showed amorphization of βBi_{4}I_{4} under high pressure.^{46} It is very interesting that an amorphous phase of Bi_{4}I_{4} could support superconductivity. This will stimulate further studies from both experimental and theoretical perspectives.
As a novel TI, βBi_{4}I_{4} offers a new platform for exploring exotic physics with simple chemistry. We find multiple topological quantum phase transitions under high pressure and βBi_{4}I_{4} shows electronic instabilities. Superconductivity is induced after the nonmetaltometal transition in βBi_{4}I_{4}, which may be attributed to electronic and structure instabilities.
After we submitted this paper, we learned that similar work was carried out independently by another group.^{46}
Methods
Singlecrystal growth and characterization
Single crystals of βBi_{4}I_{4} were obtained from gasphase reactions using methods similar to those described in refs. ^{40,41, 48} Thoroughly ground mixtures of bismuth metal and HgI_{2} were used as starting materials. The Bi to HgI_{2} 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 210–250 °C with the educts in the hot zone. The ampoule was tilted by 20–30°, the cold end pointing upward. After 2 weeks, needlelike crystals of size 5 × 1 × 0.5 mm had grown in the cold zone. The structures of the βBi_{4}I_{4} crystals were investigated using SXRD with Mo K_{a} radiation. To analyze the atomic structure of the material, transmission electron microscopy was performed.
Experimental details of highpressure measurements
Resistivity measurements were performed under high pressure in a nonmagnetic diamond anvil cell. A mixture of epoxy and fine cubic boron nitride powder was used for the insulating gaskets, and platinum foil with a thickness of 5 μm was used for electrodes. The diameters of the flat working surface of the diamond anvil and the hole in the gasket were 500 and 200 μm, respectively. The sample chamber thickness was ≈40 μm. Resistivity was measured using an inverting dc current with the van der Pauw technique implemented in a typical cryogenic setup at zero magnetic field, and the magnetic field measurements were performed on a magnetcryostat (PPMS9, Quantum Design, T_{min} = 1.8 K). Pressure was measured using the ruby scale for small chips of ruby placed in contact with the sample.^{49}
DFT calculations
DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP)^{50} with a planewave basis. The interactions between the valence electrons and ion cores were described using the projectoraugmented wave method.^{51, 52} The exchange and correlation energy was formulated using the GGA with the Perdew–Burke–Ernzerhof scheme.^{53} Van der Waals corrections were also included via a pairwise force field of the Grimme method.^{54, 55} Because GGA usually underestimates the band gap, we used Heyd–Scuseria–Ernzerhof (HSE) screened Coulomb hybrid density functionals to calculate the electronic band structures and Z_{2} topological invariant.^{56, 57} The HSE band structure was obtained by the interpolated Wannier function supplied by the Wannier90 code.^{58} The Z_{2} topological invariant was calculated by the products of parity eigenvalues of all the occupied bands at the timereversalinvariant momentum (TRIM) points.^{59} The planewave basis cutoff energy was set to 176 eV by default. The Γcentered k points with 0.03 Å^{−1} spacing were used for the first Brillouinzone sampling. The structures were optimized until the forces on the atoms were less than 5 meV Å^{−1}. The pressure was derived by fitting the total energy dependence on the volume using the Murnaghan equation.^{60} Note that spinorbit coupling was included in the static calculation. The phonon dispersion was performed using the finite displacement method with VASP and PHOHOPY code,^{61} and a supercell with all lattice constants larger than 10.0 Å was employed to calculate the phonon spectra.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
 1.
Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
 2.
Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
 3.
Qi, X.L. & Zhang, S.C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
 4.
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
 5.
Wang, Z. et al. Dirac semimetal and topological phase transitions in A_{3}Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).
 6.
Wang, Z., Weng, H., Wu, Q., Dai, X. & Fang, Z. Threedimensional Dirac semimetal and quantum transport in Cd_{3}As_{2}. Phys. Rev. B 88, 125427 (2013).
 7.
Liu, Z. K. et al. Discovery of a threedimensional topological Dirac semimetal, Na_{3}Bi. Science 343, 864–867 (2014).
 8.
Liu, Z. K. et al. A stable threedimensional topological Dirac semimetal Cd_{3}As_{2}. Nat. Mater. 13, 677–681 (2014).
 9.
Borisenko, S. et al. Experimental realization of a threedimensional Dirac semimetal. Phys. Rev. Lett. 113, 027603 (2014).
 10.
He, L. P. et al. Quantum transport evidence for the threedimensional Dirac semimetal phase in Cd_{3}As_{2}. Phys. Rev. Lett. 113, 246402 (2014).
 11.
Xu, S.Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2015).
 12.
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd_{3}As_{2}. Nat. Mater. 14, 280–284 (2015).
 13.
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermiarc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).
 14.
Wan, X., Vishwanath, A. & Savrasov, S. Y. Computational design of axion insulators based on 5d spinel compounds. Phys. Rev. Lett. 108, 146601 (2012).
 15.
Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).
 16.
Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the quantized anomalous hall effect in HgCr_{2}Se_{4}. Phys. Rev. Lett. 107, 186806 (2011).
 17.
Bulmash, D., Liu, C.X. & Qi, X.L. Prediction of a Weyl semimetal in Hg_{1xy}Cd_{x}Mn_{y}Te. Phys. Rev. B 89, 081106 (2014).
 18.
Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transitionmetal monophosphides. Phys. Rev. X 5, 011029 (2015).
 19.
Huang, S.M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).
 20.
Soluyanov, A. A. et al. TypeII Weyl semimetals. Nature 527, 495–498 (2015).
 21.
Sun, Y., Wu, S.C., Ali, M. N., Felser, C. & Yan, B. Prediction of Weyl semimetal in orthorhombic MoTe_{2}. Phys. Rev. B 92, 161107 (2015).
 22.
Hor, Y. S. et al. Superconductivity in Cu_{x}Bi_{2}Se_{3} and its implications for pairing in the undoped topological insulator. Phys. Rev. Lett. 104, 057001 (2010).
 23.
Kriener, M., Segawa, K., Ren, Z., Sasaki, S. & Ando, Y. Bulk superconducting phase with a full energy gap in the doped topological insulator Cu_{x}Bi_{2}Se_{3}. Phys. Rev. Lett. 106, 127004 (2011).
 24.
Kirshenbaum, K. et al. Pressureinduced unconventional superconducting phase in the topological insulator Bi_{2}Se_{3}. Phys. Rev. Lett. 111, 087001 (2013).
 25.
Kong, P. P. et al. Superconductivity of the topological insulator Bi_{2}Se_{3} at high pressure. J. Phys. Condens. Matter 25, 362204 (2013).
 26.
Zhang, J. L. et al. Pressureinduced superconductivity in topological parent compound Bi_{2}Te_{3}. Proc. Natl. Acad. Sci. USA 108, 24–28 (2011).
 27.
Zhang, C. et al. Phase diagram of a pressureinduced superconducting state and its relation to the Hall coefficient of Bi_{2}Te_{3} single crystals. Phys. Rev. B 83, 140504 (2011).
 28.
Matsubayashi, K., Terai, T., Zhou, J. S. & Uwatoko, Y. Superconductivity in the topological insulator Bi_{2}Te_{3} under hydrostatic pressure. Phys. Rev. B 90, 125126 (2014).
 29.
Zhu, J. et al. Superconductivity in topological insulator Sb_{2}Te_{3} induced by pressure. Sci. Rep. 3, 2016 (2013).
 30.
Aggarwal, L. et al. Unconventional superconductivity at mesoscopic point contacts on the 3D Dirac semimetal Cd_{3}As_{2}. Nat. Mater. 15, 32–37 (2016).
 31.
Wang, H. et al. Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd_{3}As_{2} crystals. Nat. Mater. 15, 38–42 (2016).
 32.
He, L. et al. Pressureinduced superconductivity in the threedimensional topological Dirac semimetal Cd_{3}As_{2}. npj Quantum Mater. 1, 16014 (2016).
 33.
Zhou, Y. H. et al. Pressureinduced semimetal to superconductor transition in a threedimensional topological material ZrTe_{5}. Proc. Natl. Acad. Sci. USA 113, 2904–2909 (2015).
 34.
Qi, Y. et al. Pressuredriven superconductivity in the transitionmetal pentatelluride HfTe_{5}. Phys. Rev. B 94, 054517 (2016).
 35.
Wang, H. et al. Discovery of tip induced unconventional superconductivity on Weyl semimetal. Sci. Bull. 62, 425–430 (2017).
 36.
Li, Y. et al. Superconductivity induced by high pressure in Weyl semimetal TaP. Preprint at http://arxiv.org/abs/1611.02548 (2016).
 37.
Kang, D. et al. Superconductivity emerging from a suppressed large magnetoresistant state in tungsten ditelluride. Nat. Commun. 6, 7804 (2015).
 38.
Pan, X.C. et al. Pressuredriven domeshaped superconductivity and electronic structural evolution in tungsten ditelluride. Nat. Commun. 6, 7805 (2015).
 39.
Qi, Y. et al. Superconductivity in Weyl semimetal candidate MoTe_{2}. Nat. Commun. 7, 11038 (2016).
 40.
Autes, G. et al. A novel quasionedimensional topological insulator in bismuth iodide [beta]Bi_{4}I_{4}. Nat. Mater. 15, 154–158 (2016).
 41.
Filatova, T. G. Electronic structure, galvanomagnetic and magnetic properties of the bismuth subhalides Bi_{4}I_{4} and Bi_{4}Br_{4}. J. Solid State Chem. 180, 1103–1109 (2007).
 42.
Werthamer, N. R., Helfand, E. & Hohenberg, P. C. Temperature and purity dependence of the superconducting critical field, H_{c2}. III. Electron spin and spinorbit effects. Phys. Rev. 147, 295–302 (1966).
 43.
Qi, Y. et al. Topological quantum phase transition and superconductivity induced by pressure in the bismuth tellurohalide BiTeI. Adv. Mater. 29, 1605965 (2017).
 44.
Li, Y., Wang, E., Zhu, X. & Wen, H.H. Pressureinduced superconductivity in Bi single crystals. Phys. Rev. B 95, 024510 (2017).
 45.
Chen, H. et al. Pressure induced superconductivity in the antiferromagnetic Dirac material BaMnBi2. Sci. Rep. 7, 1634 (2017).
 46.
Pisoni, A. et al. Pressure effect and superconductivity in the βBi_{4}I_{4} topological insulator. Phys. Rev. B 95, 235149 (2017).
 47.
Liu, C.C., Zhou, J.J., Yao, Y. & Zhang, F. Weak topological insulators and composite weyl semimetals: βBi4X4 (X = Br, I). Phys. Rev. Lett. 116, 066801 (2016).
 48.
von Schnering, H. G., von Benda, H. & Kalveram, C. Wismutmonojodid BiJ, eine Verbindung mit Bi(0) und Bi(II). Z. Anorg. Allg. Chem. 438, 37–52 (1978).
 49.
Mao, H. K., Xu, J. & Bell, P. M. Calibration of the ruby pressure gauge to 800 kbar under quasihydrostatic conditions. J. Geophys. Res. Solid Earth 91, 4673–4676 (1986).
 50.
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186 (1996).
 51.
Blöchl, P. E. Projector augmentedwave method. Phys. Rev. B 50, 17953–17979 (1994).
 52.
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
 53.
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
 54.
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFTD) for the 94 elements HPu. J. Chem. Phys. 132, 154104 (2010).
 55.
Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).
 56.
Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).
 57.
Heyd, J. & Scuseria, G. E. Assessment and validation of a screened Coulomb hybrid density functional. J. Chem. Phys. 120, 7274–7280 (2004).
 58.
Mostofi, A. A. Wannier90: a tool for obtaining maximallylocalised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).
 59.
Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
 60.
Murnaghan, F. D. The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci. USA 30, 244–247 (1944).
 61.
Togo, A., Oba, F. & Tanaka, I. Firstprinciples calculations of the ferroelastic transition between rutiletype and CaCl_{2}type SiO_{2} at high pressures. Phys. Rev. B 78, 134106 (2008).
Acknowledgements
Y.Q. acknowledges financial support from the Alexander von Humboldt Foundation. The authors thank Horst Blumtritt for the FIB sample preparation and Dr. Yurii Prots for singlecrystal Xray diffraction studies. This work was financially supported by Deutsche Forschungsgemeinschaft (DFG; Project EB 518/1–1 of DFGSPP 1666 “Topological Insulators”) and by the European Research Council (ERC Advanced Grant No. 291472 “Idea Heusler”).
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Y.Q. and L.W. prepared the samples, P.W., K.G.R., and S.P. performed TEM studies, Y.Q., P.N., W.S., and S.M. performed highpressure electrical resistivity, W.J.S. and B.Y. carried out the theoretical calculations. All authors discussed the results of the studies. Y.Q., B.Y., W.S., and W.J.S. cowrote the paper. All authors commented on the manuscript.
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Correspondence to Binghai Yan or Claudia Felser.
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Qi, Y., Shi, W., Werner, P. et al. Pressureinduced superconductivity and topological quantum phase transitions in a quasionedimensional topological insulator: Bi_{4}I_{4}. npj Quant Mater 3, 4 (2018). https://doi.org/10.1038/s4153501800783
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