Chinese Physics Letters, 2020, Vol. 37, No. 6, Article code 066401Express Letter Pressure-Induced Topological and Structural Phase Transitions in an Antiferromagnetic Topological Insulator * Cuiying Pei (裴翠颖)1†, Yunyouyou Xia (夏云悠悠)1,2,3†, Jiazhen Wu (邬家臻)4, Yi Zhao (赵毅)1, Lingling Gao (高玲玲)1, Tianping Ying (应天平)4, Bo Gao (高波)5, Nana Li (李娜娜)5, Wenge Yang (杨文革)5, Dongzhou Zhang (张东舟)6, Huiyang Gou (缑慧阳)5, Yulin Chen (陈宇林)1,7,8, Hideo Hosono (细野秀雄)4, Gang Li (李刚)1,8**, Yanpeng Qi (齐彦鹏)1** Affiliations 1School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China 2Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China 3University of Chinese Academy of Sciences, Beijing 100049, China 4Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama 226-8503, Japan 5Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, China 6Hawai'i Institute of Geophysics and Planetology, School of Ocean and Earth Science and Technology, University of Hawai'i at Manoa, Honolulu, Hawaii 96822, USA 7Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK 8ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China Received 17 April 2020, online 09 May 2020 *Supported by the National Key Research and Development Program of China under Grant Nos. 2018YFA0704300 and 2017YFE0131300, the National Natural Science Foundation of China under Grant Nos. U1932217, 11974246, 11874263 and 10225417, and the Natural Science Foundation of Shanghai under Grant No. 19ZR1477300. The authors thank the support from Analytical Instrumentation Center (SPST-AIC10112914), SPST, ShanghaiTech University. This work was partially supported by Collaborative Research Project of Materials and Structures Laboratory, Tokyo Institute of Technology, Japan. Part of this research is supported by COMPRES (NSF Cooperative Agreement EAR-1661511).
These authors contributed equally to this work.
**Corresponding authors. Email: qiyp@shanghaitech.edu.cn; ligang@shanghaitech.edu.cn
Citation Text: Pei C Y, , Wu J Z, Zhao Y and Gao L L et al 2020 Chin. Phys. Lett. 37 066401    Abstract Recently, natural van der Waals heterostructures of (MnBi$_{2}$Te$_{4}$)$_{m}$(Bi$_{2}$Te$_{3}$)$_{n}$ have been theoretically predicted and experimentally shown to host tunable magnetic properties and topologically nontrivial surface states. We systematically investigate both the structural and electronic responses of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ to external pressure. In addition to the suppression of antiferromagnetic order, MnBi$_{2}$Te$_{4}$ is found to undergo a metal–semiconductor–metal transition upon compression. The resistivity of MnBi$_{4}$Te$_{7}$ changes dramatically under high pressure and a non-monotonic evolution of $\rho (T)$ is observed. The nontrivial topology is proved to persist before the structural phase transition observed in the high-pressure regime. We find that the bulk and surface states respond differently to pressure, which is consistent with the non-monotonic change of the resistivity. Interestingly, a pressure-induced amorphous state is observed in MnBi$_{2}$Te$_{4}$, while two high-pressure phase transitions are revealed in MnBi$_{4}$Te$_{7}$. Our combined theoretical and experimental research establishes MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ as highly tunable magnetic topological insulators, in which phase transitions and new ground states emerge upon compression. DOI:10.1088/0256-307X/37/6/066401 PACS:64.70.Tg, 03.65.Vf, 07.35.+k © 2020 Chinese Physics Society Article Text Magnetic topological insulators (MTIs), possessing both magnetic and topological properties, provide a promising material platform for the realization of exotic topological quantum phenomena, such as the quantum anomalous Hall (QAH) effect, axion insulator states, the proximity effect and Majorana modes.[1–6] Thereinto the QAH effect has been observed experimentally in magnetically doped topological insulator (TI) thin films,[7] while the fabrication of homogeneous thin films has long been limited by deposition techniques, hindering extensive studies of the unique material systems. Hence, intrinsic MTIs with homogeneous magnetic and electronic properties are desired and can provide new opportunities to study novel topological quantum phenomena. Recently, intrinsic MTIs of (MnBi$_{2}$Te$_{4}$)$_{m}$(Bi$_{2}$Te$_{3}$)$_{n}$ has been theoretically predicted and experimentally synthesized to have tunable magnetic properties and topologically nontrivial surface states.[11–23] As shown in Fig. 1, (MnBi$_{2}$Te$_{4}$)$_{m}$(Bi$_{2}$Te$_{3}$)$_{n}$ crystallizes in a van der Waals layered structure, sharing a similar crystal structure with Bi$_{2}$Te$_{3}$,[8] a typical TI under ambient conditions. Crystallizing in a rhombohedral structure with space group $R\bar{3}m$, MnBi$_{2}$Te$_{4 } (m = 1$, $n = 0$) consists of Te-Bi-Te-Mn-Te-Bi-Te septuple layers (SLs) as the building block, each of which can be viewed as a Bi$_{2}$Te$_{3}$ quintuple layer (QL) intercalated by a MnTe bilayer. MnBi$_{4}$Te$_{7}$ ($m = 1$, $n = 1$) adopts space group $P\bar{3}m1$ with a hexagonal superlattice crystal structure with alternate stacking of one MnBi$_{2}$Te$_{4}$ SL and one Bi$_{2}$Te$_{3}$ QL. MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ are both identified to be natural van der Waals heterostructures as evidenced by high-angle annular dark field (HAADF)-STEM measurements.[12] Pressure as a conventional thermodynamic parameter is a clean and useful means to tune the interatomic distance and consequently, can be used to engineer the electronic and, subsequently, the macroscopic physical properties of the system. In addition, it is possible to trigger novel structural and/or electronic transitions. Indeed, we recently observed pressure-induced topological phase transitions and even superconductivity in topological materials.[24–27] In this work, we study the effect of pressure on the electrical transport properties and crystal structures of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ in a diamond anvil cell (DAC) apparatus. The antiferromagnetic (AFM) metallic ground state of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ single crystal is gradually suppressed by pressure, and the conductance as well as the crystal structure change dramatically upon further compression. Through ab initio band structure calculations, we find that the application of pressure does not qualitatively change the electronic and topological nature of the two systems until the structural phase transition is observed in the high-pressure regime. Based on synchrotron XRD and Raman spectroscopy measurements, detailed high-pressure crystal structure and phase transitions are discussed.
Fig. 1. Crystal structure of Bi$_{2}$Te$_{3}$ ($R\bar{3}m$, No. 166),[8] MnTe ($P6_{3}/mmc$, No. 194),[9] MnBi$_{2}$Te$_{4}$ ((MnBi$_{2}$Te$_{4})_{1}$(Bi$_{2}$Te$_{3})_{0}$, $R\bar{3}m$, No. 166)[10] and MnBi$_{4}$Te$_{7}$ ((MnBi$_{2}$Te$_{4})_{1}$(Bi$_{2}$Te$_{3})_{1}$, $P\bar{3}m1$, No. 164),[11] respectively. The MnBi$_{2}$Te$_{4}$ unit cell consists of three septuplet monoatomic layers with a stacking sequence of Te(1)-Bi(1)-Te(2)-Mn(1)-Te(2)-Bi(1)-Te(1) along the $c$-axis, and the seven monoatomic layers are centro-symmetrical with respect to Mn. In detail, Mn crystallographic sites are of octahedral coordination and are surrounded by six Te(2) atoms at the same distance as under ambient conditions. Bi is at the center of a distorted octahedron and is surrounded by three Te(2) atoms and three Te(1) atoms as the nearest neighbors. Triple slabs of MnTe$_{6}$ and BiTe$_{6}$ are octahedral edge-linked with each other, and similarly for the SL of MnBi$_{4}$Te$_{7}$. Alternation of QL (Te(2)-Bi(1)-Te(1)-Bi(1)-Te(2)) and SL (Te(3)-Bi(2)-Te(4)-Mn(1)-Te(4)-Bi(2)-Te(3)) blocks stack along the $c$-axis and MnBi$_{4}$Te$_{7}$ is in the trigonal space group $P\bar{3}m1$.
The MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ single crystals in this work were grown using a flux-assisted method.[12] High-pressure resistivity measurements were performed in a nonmagnetic DAC. A cubic BN/epoxy mixture layer was inserted between BeCu gaskets and electrical leads. Four Pt foils were arranged in a van der Pauw four-probe configuration to contact the sample in the chamber for resistivity measurements. NaCl was used as the pressure transmitting medium (PTM) and pressure was determined by the ruby luminescence method.[28] An in situ high-pressure Raman spectroscopy investigation of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ was performed using a Raman spectrometer (Renishaw inVia, UK) with a laser excitation wavelength of 532 nm and low-wavenumber filter. A symmetric DAC with anvil culet sizes of 400 µm was used, with silicon oil as the PTM. The in situ high-pressure XRD measurements were performed at beamline 13-BM-C of the Advanced Photon Source (APS) (x-ray wavelength $\lambda = 0.4340$ Å) and beamline BL15U of Shanghai Synchrotron Radiation Facility (x-ray wavelength $\lambda = 0.6199$ Å). Symmetric DACs with anvil culet sizes of 400 µm and 300 µm and T301 gaskets were used. Neon was used as the PTM and pressure was determined by the ruby luminescence method.[28] The two-dimensional diffraction images were integrated into angle-resolved diffraction intensity profiles using the software DIOPTAS.[29] Rietveld refinements on crystal structures under high pressure were performed using the General Structure Analysis System (GSAS) and the graphical user interface EXPGUI.[30] The ab initio calculations were performed within the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP),[31] with the exchange-correlation functional considered in the generalized gradient approximation potential.[32] A k-mesh of $9\times 9\times1$ for MnBi$_{2}$Te$_{4}$ and $9\times 9\times 3$ for MnBi$_{4}$Te$_{7}$ was applied. The experimental lattice constants were adopted under different pressures with atomic positions optimized for a total energy tolerance of 10$^{-5}$ eV. To account for the correlation effect of the transition metal element Mn in both MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$, the GGA+$U$ functional with $U = 3$ eV for the $d$-orbitals of Mn is adopted. The spin–orbital coupling was considered self-consistently in this work. The topological surface states were calculated by applying the iterative Green's function approach[33] as implemented in WannierTools[34] based on the maximally localized Wannier functions[35] as obtained through the VASP2WANNIER90[36] interfaces in a non-self-consistent calculation. As a typical layered material, the electrical transport and magnetic properties of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ are expected to be sensitive to the competition between interlayer and intralayer interactions, which can be effectively tuned by applying external pressure. We performed resistivity measurements on several single crystals at various pressures. Figures 2(a), 2(b), and 2(c) show the typical $\rho (T)$ curves of MnBi$_{2}$Te$_{4}$ for pressures up to 34.0 GPa. As shown in Fig. 2(a), the resistivity–temperature slope $d\rho/dT$ of MnBi$_{2}$Te$_{4}$ clearly shows a positive value, indicating metal-like conduction in the low-pressure range. With an increase of pressure, $\rho (T)$ curves show an upturn behavior at low temperatures. Upon further compression, a metal–semiconductor transition is observed and $\rho (T)$ displays a semiconductor-like behavior for $P > 12$ GPa. Interestingly, the resistivity ultimately undergoes a metallization at a pressure above 16.3 GPa and does not change significantly in response to further increases in the pressure. No superconductivity was observed down to 1.8 K in this pressure range.
Fig. 2. Electrical resistivity of MnBi$_{2}$Te$_{4}$ as a function of temperature for pressures up to 10.3 GPa (a), 15.5 GPa (b) and 34.0 GPa (c); (d) detail of the normalized resistivity of MnBi$_{2}$Te$_{4}$ as a function of temperature at various pressures to monitor the shift of the AFM transition kink. The inset shows the enlarged resistivity–temperature curve at 4.1 GPa and fitting of the AFM transition temperature as a function of pressure.
Fig. 3. Electronic phase diagrams of MnBi$_{2}$Te$_{4}$ (a) and MnBi$_{4}$Te$_{7}$ (b). The black, blue and red solid circles represent different runs of electrical resistivity measurements at 1.8 K. The black open circles indicate AFM transition temperatures due to the transport measurements.
It should be noted that $\rho (T)$ of MnBi$_{2}$Te$_{4}$ displays a kink at the AFM transition $T_{\rm N} = 24.5$ K at 0.4 GPa (Fig. 2(d)), which is consistent with the magnetic measurements shown in Fig. S1 (see the Supplemental Material) and those in other reports.[20] The rapid drop of resistivity below $T_{\rm N}$ is attributed to the reduction of spin scattering after the formation of long-range AFM order.[37] As indicated by the arrow in Fig. 2(d), $T_{\rm N}$ determined from the resistivity kink shifts to lower temperatures with increasing pressure. Over 4.9 GPa, the upturn resistivity trend at lower temperature becomes much stronger and the kink merges into the $\rho (T)$ curve. The fitting results demonstrate that $T_{\rm N}$ approaches zero at approximately 9.3 GPa. Since the interlayer distance deceases under high pressure, it is speculated that the pressure-induced enhancement of antiferromagnetic/ferromagnetic competition and the partial delocalization of Mn-3$d$ electrons not only destroys long-range AFM order, but also promotes charge-carrier localization through enhanced spin fluctuations and/or the formation of a hybridization gap at high pressure. The high-pressure experiments have been repeated on different samples with good reproducibility of the observed transition temperatures. Based on the above resistivity measurements, we summarize a $T$–$P$ phase diagram for MnBi$_{2}$Te$_{4}$ single crystals in Fig. 3(a). The resistivity of MnBi$_{2}$Te$_{4}$ shows non-monotonic evolution with increasing pressure. Over the entire temperature range, the resistivity is first suppressed with applied pressure and reaches a minimum value at about 2 GPa. As the pressure further increases, the resistivity increases with a maximum occurring at 11.0 GPa and the AFM order shifted to a lower temperature. Accompanying the suppression of the AFM transition, the electrical transport properties also change qualitatively from metal-like $d\rho/dT > 0$ to semimetal- or semiconducting-like behavior $d\rho/dT < 0$. For $P > 12$ GPa, the resistivity abruptly decreases and a transition from semiconducting to metallic behavior takes place at further increased pressure. Similarly, pressure-induced non-monotonic evolution was also observed in MnBi$_{4}$Te$_{7}$, as shown in Fig. 3(b). Although resistivity changes significantly under high pressure, $\rho (T)$ exhibits a metallic behavior over the whole temperature range (Fig. S2). No transition from metallic to semiconducting behavior was observed within the studied pressure range. The AFM order of MnBi$_{4}$Te$_{7}$ shifted to a lower temperature with increasing pressure, which is similar to that of MnBi$_{2}$Te$_{4}$ (Fig. S3). The angular dispersive XRD patterns of MnBi$_{2}$Te$_{4}$ at various pressures are shown in Fig. 4(a). Under ambient conditions and in the low-pressure range ($P\le 14.6$ GPa), all the diffraction peaks of MnBi$_{2}$Te$_{4}$ could be indexed to the rhombohedral $R\bar{3}m$ (No. 166) structure by Rietveld refinement (Fig. 4(b)). High-pressure XRD experiments in pressure steps of 1–2 GPa were performed on MnBi$_{2}$Te$_{4}$ via a DAC. At pressures exceeding 14.6 GPa, structural disorder becomes apparent. Above 17.4 GPa, diffraction peaks from crystalline phase disappear, and a new broad peak appears at approximately 2.65 Å in $d$-spacing. This indicates that the sample has completely transformed into an amorphous state.
Fig. 4. XRD patterns collected at various pressures for MnBi$_{2}$Te$_{4}$ with an x-ray wavelength of $\lambda = 0.4340$ Å (a) and MnBi$_{4}$Te$_{7}$ with an x-ray wavelength of $\lambda = 0.6199$ Å (c); the black open circles are from PTM neon; typical Rietveld refinement of phase I of MnBi$_{2}$Te$_{4}$ (b) and MnBi$_{4}$Te$_{7}$ (d), respectively. The experimental and simulated data are indicated by black stars and red lines, respectively. The solid lines shown at the bottom of the figures are the residual intensities. The vertical bars indicate peak positions.
In contrast, a different structure evolution for MnBi$_{4}$Te$_{7}$ is observed under high pressure (Fig. 4(c)). In the low-pressure range, phase I of MnBi$_{4}$Te$_{7}$ crystallizes in a trigonal space group $P\bar{3}m1$ (No. 164), as shown in Fig. 4(d). At 14.4 GPa, a high-pressure phase, phase II, was observed. This phase is only stable in a narrow pressure range and coexists with the phase I or the phase III upon compression. Above 18.6 GPa, only phase III exists and no further transitions are observed up to 50.6 GPa. Upon decompression, phase III persists to 24.0 GPa. When the pressure is decreased to 2.5 GPa, phase II and phase I recover and coexist. After a full pressure release, MnBi$_{4}$Te$_{7}$ recovers the ambient-pressure structure. To verify our speculation on the crystallographic structural phase transition sequence under high pressure, Raman scattering spectroscopy was employed to characterize the pressure-induced phase transition (Fig. 5(a)). According to group theory analysis and the results in the literature,[38] there are four Raman-active modes (2$E_{\rm g} + 2A_{\rm 1g}$) for MnBi$_{2}$Te$_{4}$. The $E_{\rm g}$ and $A_{\rm 1g}$ modes are related to the in-plane $A$(VI)–$B$(V) and out-of-plane lattice vibrations, respectively (Fig. 5(b)). At 0.3 GPa, four peaks are assigned as follows: 47.4 cm$^{-1}$($E_{\rm g}$), 67.4 cm$^{-1}$($A_{\rm 1g}$), 104.2 cm$^{-1}$($E_{\rm g}$), and 139.8 cm$^{-1}$($A_{\rm 1g}$).[38] As the pressure increases, all four modes exhibit blue shift due to the increase in the strength of the Bi–Te covalent interaction (Fig. 5(c)). Upon further compression exceeding a pressure of 17.8 GPa, all the peaks disappear. The pressure-induced amorphization occurs at 17.8 GPa, which coincides with the XRD result at 17.4 GPa. In addition, a reversible phase transition associated with a compressed lattice (where the lattice constants are decreased) is verified by the Raman spectrum of the sample after recovery to 1 atm. The Raman spectra of MnBi$_{4}$Te$_{7}$ were also measured using a DAC and a similar phenomenon was observed under high pressure (Fig. S4). It should be noted that no new Raman modes were observed under higher pressure, although a structural phase transition is observed by synchrotron XRD measurements. One can expect that pressure-induced metallization or vibration modes become weaker under high pressure, which may account for the absence of Raman modes.
Fig. 5. (a) Raman spectra at various pressures for MnBi$_{2}$Te$_{4}$; (b) phonon mode symmetry and direction of vibration for MnBi$_{2}$Te$_{4}$; (c) Raman mode frequencies for MnBi$_{2}$Te$_{4}$ in compression (solid circle) and decompression (open circle); (d) pressure dependence of $I_{E_{\rm g}}/I_{A_{\rm 1g}}$ intensity ratio for MnBi$_{2}$Te$_{4}$. For accurate peak intensity comparison, the strong $E_{\rm g}$ and $A_{\rm 1g}$ modes with respective Raman shifts of 104.2 cm$^{-1}$ and 139.8 cm$^{-1}$ at 1 atm are chosen. Peak intensity and peak position are obtained by Gaussian and Lorentzian mixed line shape fitting. Open circles represent data recovered for 1 atm.
To understand the non-monotonic change of the measured resistivity under different pressures, we performed detailed ab initio calculations and examined both the bulk and surface electronic structures of MnBi$_{2}$Te$_{4}$ (Figs. 6 and S5). Electron transportation is mainly determined by the states around the Fermi level which can be effectively tuned by external pressure. Concerning a topological system, these states contain both the bulk and the topological surface/edge contributions. It is widely known that the topology of a topological system is fully determined by the symmetry and the associated Berry curvature of the bulk bands. As long as they are qualitatively unchanged, the topology persists (Fig. S5). However, external perturbations, such as the pressure, can modify the dispersions of both the bulk and surface bands, resulting in different transport responses. In Fig. 6(a) the electronic structures of MnBi$_{2}$Te$_{4}$ are displayed for different pressures. MnBi$_{2}$Te$_{4}$ is a semiconductor with a gap of 243.4 meV at atmospheric pressure. Once external pressure is applied, the conduction band bottom changes from $Z$ to $\varGamma$ and the gap size gradually decreases with increasing pressure. At the highest pressure applied which maintains the crystal symmetry of MnBi$_{2}$Te$_{4}$, a global gap remains but it is significantly reduced to 16.3 meV. Due to the topological nature of this system, the total conductance/resistance experimentally measured is subjected to contributions from both the bulk and surface electrons. We, thus, further determined the surface electronic structure of the experimentally cleaved (001) surface (Fig. 6(b)). In sharp contrast to the bulk electronic structure, an overall reentrant behavior of the gapped surface states is observed upon the increase of pressure. Below 4.9 GPa, the magnetic surface states move from below to above the Fermi level, leading to a metal–semiconductor transition solely caused by the surface electrons. The surface states, with a clear separation from the bulk bands at pressures below 4.9 GPa, completely merge into the bulk bands at pressures above 10.5 GPa. Above this pressure, the contribution to the resistivity is mainly determined by the bulk gap and electrons. Thus, the decrease in the bulk gap results in a decrease of the resistivity as shown in Fig. 3(a) above 10.5 GPa. However, below 10.5 GPa, the bulk and surface electrons behave differently, i.e., the surface electrons are gradually localized, and the bulk electrons become more mobile with increasing pressure. Thus, the competition between the two types of electrons results in the decrease–increase behavior of the resistivity observed in Fig. 3(a). More precisely, we suspect that the decrease in the resistivity below 3.1 GPa is mainly induced by the delocalization of the bulk electrons as the surface electrons remain metallic; while the increase in the resistivity is mainly a consequence of the localization of the surface electrons, as the surface states are no longer metallic and have not yet merged into the bulk states.
Fig. 6. Bulk and surface electronic structures of MnBi$_{2}$Te$_{4}$ at different pressures. (a) The bulk electronic structure remains gapped under all applied pressures with roughly monotonic decrease of gap size. (b) The topological surface states on (001) display a reentrant behavior upon the increase of pressure.
A similar analysis can be applied to MnBi$_{4}$Te$_{7}$ (Figs. S5 and S6). We note that the bulk gap shown in Fig. S6(a) decreases under increasing pressure with the minimum gap decreasing from 196.7 meV to 174.8 meV at $\varGamma$, which only renders more substantial contribution to its conductance at higher pressures. At low pressure, the contribution from the surface states becomes dominant. As MnBi$_{4}$Te$_{7}$ can be naturally cleaved at MnBi$_{2}$Te$_{4}$ and Bi$_{2}$Te$_{3}$ layers, the total surface conductance includes components from both terminations. The topological surface states with MnBi$_{2}$Te$_{4}$ termination intersect the Fermi level under all examined pressures (Fig. S6(b)), presenting a metallic background in the measured pressure range. Meanwhile, the surface electrons terminated at Bi$_{2}$Te$_{3}$ become more localized with increasing pressure. The surface band crosses the Fermi level at 2.5 GPa, and gradually moves to higher binding energies with further increase of pressure. The competition between the two types of electrons again results in the decrease–increase behavior of resistivity observed in Fig. 3(b). Below 2.5 GPa, the delocalization of the bulk electrons is attributed to the decrease of resistivity, while the subsequent increase of the resistivity above 2.5 GPa mainly stems from the localization of the surface electrons. At approximately 10.4 GPa, the surface bands merge into the bulk states, after which the resistivity is mainly determined by the bulk electrons, and thus shows a sharp decline as observed in the transport measurements.
Fig. 7. Schematic representation of the evolution of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ structures under high pressure.
Next, we discuss the high-pressure phase transition. To gain an insight into the structural evolution, pressure-induced bond length and angle variations in MnTe$_{6}$ and BiTe$_{6}$ octahedra are derived from the Rietveld refinements (Fig. S7). The Mn–Te bond length decreases with an increase of pressure and the bond angle of Te(2)–Mn(1)–Te(2) changes only slightly (Figs. S7(a) and S7(b)). Below 3.1 GPa, the pressure coefficients of Bi(1)–Te(1) and Bi(1)–Te(2) bond lengths show the same sign. Also, both the Te(1)–Bi(1)–Te(1) bond angle and the distance between the two Te(1)'s of the near neighbor septuple blocks decrease with increasing pressure (Figs. S7c and S7d). However, Bi(1)–Te(2) and Bi(1)–Te(1) bond lengths show opposite responses to pressure near 4 GPa, and Te(1)–Bi(1)–Te(1) bond angle also behaves differently from Te(1)–Bi(1)–Te(2) and Te(2)–Bi(1)–Te(2) bond angles (Figs. S7(c) and S7(d)). These results indicate that the distorted octahedral BiTe$_{6}$ deforms more significantly above 3.1 GPa and bends towards Mn atoms (Fig. S7(e)). This releases stress along the $c$-axis and weakens the interaction between the nearest neighbor SL. Upon further compression, interlayer interaction enhancement dominates and ultimately the interlayer Te(1)–Te(1) bond is formed. The pressure dependence of the $c/a$ ratio for the $R\bar{3}m$ phase of MnBi$_{2}$Te$_{4}$ (plotted in Fig. S8(a)) shows a minimum at approximately 3.1 GPa. This is consistent with the Raman spectroscopy observations. The in-plane Bi–Te vibration was enhanced significantly with pressure. With further compression, the ratio of out-of-plane Bi–Te vibrations is enhanced when the pressure exceeds 3.8 GPa as shown in the evolution of the intensity ratio ($I_{E_{\rm g}}$/$I_{A_{\rm 1g}}$) in Fig. 5(d). A similar phenomenon was observed in the MnBi$_{4}$Te$_{7}$ phase (Fig. S4(d)). It is clear that the structural change induced by external pressure will significantly modify the corresponding electronic structure. The reduced interlayer distance will enhance the three-dimensional dispersion of the system. As a result, the electronic states around the Fermi level will be considerably modified, which, ultimately, influences the macroscopic resistivity. Thus, such layered MTIs with large inter-layer distances are ideal for pressure engineered materials. In compression, there is a quite distinct compression behavior between MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$. Figure 7 shows the pressure-induced structural evolution of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$, respectively. The former transforms to an amorphous phase at approximately 17.4 GPa, while the latter transforms from a rhombohedral to a mixed high-pressure phase at 14.4 GPa, and finally phase III obtained at 18.6–50.6 GPa. For phase II of MnBi$_{4}$Te$_{7}$, Le Bail refinement yielded a monoclinic structure with $a = 14.4192(3)$ Å, $b = 3.9415(9)$ Å, $c = 17.1202(7)$ Å, and $\beta = 148.62(7)^{\circ}$. The XRD pattern of phase III is simple and can be indexed to an $Im\bar{3}m$ (No. 229) structure with $a = 3.6796(0)$ Å (Fig. S9, Table S1). The different compression behavior is related to the distortion of MnTe$_{6}$ and BiTe$_{6}$, which is induced by competition under high pressure. In MnBi$_{2}$Te$_{4}$, the Te(2)–Te(2) bond forms besides Te(1)–Te(1) linked in the low-pressure range accompanied by MnTe$_{6}$ octahedron flattening. In contrast, the distances of Bi(1)–Te(1) (5.002 Å) and Bi(1)–Te(2) (4.900 Å) are shorter than Bi(2)–Te(4) (5.043 Å) in MnBi$_{4}$Te$_{7}$ and Bi(1)–Te(2) (5.206 Å) in MnBi$_{2}$Te$_{4}$. As a result, the pressure-induced distorted Bi(1)Te$_{6}$ octahedron in the Bi$_{2}$Te$_{3}$ quintuple block tends to form a heptahedrally coordinated BiTe$_{7}$ unit and further Bi(Te)$_{n}$ ($n > 7$). At 18.6 GPa, the Te–Te and Bi–Te distances in MnBi$_{4}$Te$_{7}$ are close to each other because of the flatter MnTe$_{6}$ octahedron as well as the improved interaction between QL and SL (Fig. S10). An alternating Bi, Te structure with Mn intercalation exists during the formation of an isotropic phase along the layers and perpendicular to the layers. The structural evolution of MnBi$_{4}$Te$_{7}$ under high pressure resembles the situation in the case of Bi$_{2}$Te$_{3}$.[8,39,40] Recent sister compounds MnBi$_{6}$Te$_{10}$ ($m = 1$, $n = 2$) and MnBi$_{8}$Te$_{13}$ ($m = 1$, $n = 3$) have been grown successfully.[41–44] It will be interesting to characterize the structural evolution of this series (MnBi$_{2}$Te$_{4}$)$_{m}$(Bi$_{2}$Te$_{3}$)$_{n}$ of compounds and summarize pressure-induced phase transition in these layered compounds. In conclusion, we have performed a comprehensive high-pressure study on the electrical transport properties and crystal structures of the MTIs MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ in DACs. The AFM metallic ground state of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$ single crystals are gradually suppressed by pressure. The pressure-dependent resistivity over a wide temperature range passes through a minimum at around 3 GPa. Upon further increasing the pressure, resistivity starts to increase rapidly, reaching a maximum at a pressure above 10 GPa. Through ab initio calculations, we find that the application of pressure does not destroy the nontrivial topology of the system before structural phase transition. However, the bulk and surface states respond differently to external pressure, resulting in competing contributions to the macroscopic resistivity. Based on synchrotron XRD and Raman spectroscopy measurements, we find that MnBi$_{2}$Te$_{4}$ transforms to an amorphous phase at around 17.4 GPa, while MnBi$_{4}$Te$_{7}$ transforms to two new high-pressure phases. Application of pressure effectively tuned the electronic properties and crystal structure of MnBi$_{2}$Te$_{4}$ and MnBi$_{4}$Te$_{7}$. Considering both intriguing magnetism and topology in this layered material, our results call for further experimental and theoretical studies on (MnBi$_{2}$Te$_{4}$)$_{m}$(Bi$_{2}$Te$_{3}$)$_{n}$ and related materials for a better understanding of the interplay between magnetic and topological nature, and its potential application in realizing topological superconductivity. We thank Dr. Zhenhai Yu for valuable discussions. We thank the staffs from BL15U1 at Shanghai Synchrotron Radiation Facility for assistance during data collection. Portions of this work were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation-Earth Sciences (EAR-1634415) and Department of Energy-GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract Nos. DE-AC02-06CH11357.
References Antiferromagnetic topological insulatorsMagnetic topological insulatorsTailoring exchange couplings in magnetic topological-insulator/antiferromagnet heterostructuresA topological insulator surface under strong Coulomb, magnetic and disorder perturbationsTopological antiferromagnetic spintronicsA magnetic heterostructure of topological insulators as a candidate for an axion insulatorExperimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological InsulatorSubstitutional Alloy of Bi and Te at High PressureThe MnTeGeTe phase diagramCrystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi2MnTe4Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: Synthesis and crystal structureNatural van der Waals heterostructural single crystals with both magnetic and topological propertiesExperimental Realization of an Intrinsic Magnetic Topological Insulator *Topological Axion States in the Magnetic Insulator $MnBi 2 Te 4$ with the Quantized Magnetoelectric EffectIntrinsic magnetic topological insulators in van der Waals layered MnBi 2 Te 4 -family materialsA van der Waals antiferromagnetic topological insulator with weak interlayer magnetic couplingTopological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator $MnBi 2 Te 4$Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator $MnBi 2 Te 4$Dirac Surface States in Intrinsic Magnetic Topological Insulators $EuSn 2 As 2$ and $MnBi 2 n Te 3 n + 1$Prediction and observation of an antiferromagnetic topological insulatorQuantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi 2 Te 4Experimental Observation of the Gate-Controlled Reversal of the Anomalous Hall Effect in the Intrinsic Magnetic Topological Insulator MnBi 2 Te 4 DeviceRobust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulatorSuperconductivity in Weyl semimetal candidate MoTe2Pressure-driven superconductivity in the transition-metal pentatelluride $\mathrm{HfT}{{e}}_{5}$Topological Quantum Phase Transition and Superconductivity Induced by Pressure in the Bismuth Tellurohalide BiTeIPressure-induced superconductivity and topological quantum phase transitions in a quasi-one-dimensional topological insulator: Bi4I4Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditionsDIOPTAS : a program for reduction of two-dimensional X-ray diffraction data and data explorationEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleHighly convergent schemes for the calculation of bulk and surface Green functionsWannierTools: An open-source software package for novel topological materialsMaximally localized generalized Wannier functions for composite energy bandswannier90: A tool for obtaining maximally-localised Wannier functionsSuppression of the antiferromagnetic metallic state in the pressurized $\mathrm{MnB}{{i}}_{2}{T}{{e}}_{4}$ single crystalVibrational spectra of Pb 2 Bi 2 Te 3 , PbBi 2 Te 4 , and PbBi 4 Te 7 topological insulators: temperature-dependent Raman and theoretical insights from DFT simulationsPressure-induced phase transition of Bi $2$ Te $3$ to a bcc structureLocal structural changes during the disordered substitutional alloy transition in Bi 2 Te 3 by high-pressure XAFSLayered manganese bismuth tellurides with GeBi 4 Te 7 - and GeBi 6 Te 10 -type structures: towards multifunctional materialsMagnetic and transport properties in the magnetic topological insulators $\mathrm{MnB}{{i}}_{2}{T}{{e}}_{4}{\left({B}{{i}}_{2}{T}{{e}}_{3}\right)}_{n}$ ( $n=1,2$ )A-type Antiferromagnetic order in MnBi4Te7 and MnBi6Te10 single crystalsRealization of an intrinsic, ferromagnetic axion insulator in MnBi8Te13
 [1] Mong R S K, Essin A M and Moore J E 2010 Phys. Rev. B 81 245209 [2] Tokura Y, Yasuda K and Tsukazaki A 2019 Nat. Rev. Phys. 1 126 [3] He Q L, Kou X, Grutter A J, Yin G, Pan L, Che X, Liu Y, Nie T, Zhang B, Disseler S M, Kirby B J, Ratcliff I I W, Shao Q, Murata K, Zhu X, Yu G, Fan Y, Montazeri M, Han X, Borchers J A and Wang K L 2017 Nat. Mater. 16 94 [4] Wray L A, Xu S Y, Xia Y, Hsieh D, Fedorov A V, Hor Y S, Cava R J, Bansil A, Lin H and Hasan M Z 2011 Nat. Phys. 7 32 [5] Šmejkal L, Mokrousov Y, Yan B and MacDonald A H 2018 Nat. Phys. 14 242 [6] Mogi M, Kawamura M, Yoshimi R, Tsukazaki A, Kozuka Y, Shirakawa N, Takahashi K S, Kawasaki M and Tokura Y 2017 Nat. Mater. 16 516 [7] Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C and Xue Q K 2013 Science 340 167 [8] Zhu L, Wang H, Wang Y, Lv J, Ma Y, Cui Q, Ma Y and Zou G 2011 Phys. Rev. Lett. 106 145501 [9] Johnston W D and Sestrich D E 1961 J. Inorg. Nucl. Chem. 19 229 [10] Lee D S, Kim T H, Park C H, Chung C Y, Lim Y S, Seo W S and Park H H 2013 CrystEngComm 15 5532 [11] Aliev Z S, Amiraslanov I R, Nasonova D I, Shevelkov A V, Abdullayev N A, Jahangirli Z A, Orujlu E N, Otrokov M M, Mamedov N T, Babanly M B and Chulkov E V 2019 J. Alloys Compd. 789 443 [12] Wu J, Liu F, Sasase M, Ienaga K, Obata Y, Yukawa R, Horiba K, Kumigashira H, Okuma S, Inoshita T and Hosono H 2019 Sci. Adv. 5 eaax9989 [13] Gong Y, Guo J, Li J, Zhu K, Liao M, Liu X, Zhang Q, Gu L, Tang L, Feng X, Zhang D, Li W, Song C, Wang L, Yu P, Chen X, Wang Y, Yao H, Duan W, Xu Y, Zhang S C, Ma X, Xue Q K and He K 2019 Chin. Phys. Lett. 36 076801 [14] Zhang D, Shi M, Zhu T, Xing D, Zhang H and Wang J 2019 Phys. Rev. Lett. 122 206401 [15] Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W and Xu Y 2019 Sci. Adv. 5 eaaw5685 [16] Hu C, Gordon K N, Liu P, Liu J, Zhou X, Hao P, Narayan D, Emmanouilidou E, Sun H, Liu Y, Brawer H, Ramirez A P, Ding L, Cao H, Liu Q, Dessau D and Ni N 2020 Nat. Commun. 11 97 [17] Chen Y, Xu L, Li J, Li Y, Wang H, Zhang C, Li H, Wu Y, Liang A, Chen C, Jung S W, Cacho C, Mao Y, Liu S, Wang M, Guo Y, Xu Y, Liu Z, Yang L and Chen Y 2019 Phys. Rev. X 9 041040 [18] Hao Y J, Liu P, Feng Y, Ma X M, Schwier E F, Arita M, Kumar S, Hu C, Lu R E, Zeng M, Wang Y, Hao Z, Sun H Y, Zhang K, Mei J, Ni N, Wu L, Shimada K, Chen C, Liu Q and Liu C 2019 Phys. Rev. X 9 041038 [19] Li H, Gao S, Duan S, Xu Y, Zhu K, Tian S, Gao J, Fan W, Rao Z, Huang J, Li J, Yan D, Liu Z, Liu W, Huang Y, Li Y, Liu Y, Zhang G, Zhang P, Kondo T, Shin S, Lei H, Shi Y, Zhang W, Weng H, Qian T and Ding H 2019 Phys. Rev. X 9 041039 [20] Otrokov M M, Klimovskikh I I, Bentmann H, Estyunin D, Zeugner A, Aliev Z S, Gass S, Wolter A U B, Koroleva A V, Shikin A M, Blanco-Rey M, Hoffmann M, Rusinov I P, Vyazovskaya A Y, Eremeev S V, Koroteev Y M, Kuznetsov V M, Freyse F, Sanchez-Barriga J, Amiraslanov I R, Babanly M B, Mamedov N T, Abdullayev N A, Zverev V N, Alfonsov A, Kataev V, Buchner B, Schwier E F, Kumar S, Kimura A, Petaccia L, Di Santo G, Vidal R C, Schatz S, Kissner K, Unzelmann M, Min C H, Moser S, Peixoto T R F, Reinert F, Ernst A, Echenique P M, Isaeva A and Chulkov E V 2019 Nature 576 416 [21] Deng Y, Yu Y, Shi M, Xu Z, Wang J, Chen X and Zhang Y 2020 Science 367 895 [22] Zhang S, Wang R, Wang X, Wei B, Chen B, Wang H, Shi G, Wang F, Jia B, Ouyang Y, Xie F, Fei F, Zhang M, Wang X, Wu D, Wan X, Song F, Zhang H and Wang B 2020 Nano Lett. 20 709 [23] Liu C, Wang Y, Li H, Wu Y, Li Y, Li J, He K, Xu Y, Zhang J and Wang Y 2020 Nat. Mater. 19 522 [24] Qi Y, Naumov P G, Ali M N, Rajamathi C R, Schnelle W, Barkalov O, Hanfland M, Wu S C, Shekhar C, Sun Y, Sü V, Schmidt M, Schwarz U, Pippel E, Werner P, Hillebrand R, Forster T, Kampert E, Parkin S, Cava R J, Felser C, Yan B and Medvedev S A 2016 Nat. Commun. 7 11038 [25] Qi Y, Shi W, Naumov P G, Kumar N, Schnelle W, Barkalov O, Shekhar C, Borrmann H, Felser C, Yan B and Medvedev S A 2016 Phys. Rev. B 94 054517 [26] Qi Y, Shi W, Naumov P G, Kumar N, Sankar R, Schnelle W, Shekhar C, Chou F C, Felser C, Yan B and Medvedev S A 2017 Adv. Mater. 29 1605965 [27] Qi Y, Shi W, Werner P, Naumov P G, Schnelle W, Wang L, Rana K G, Parkin S, Medvedev S A, Yan B and Felser C 2018 npj Quantum Mater. 3 4 [28] Mao H K, Xu J and Bell P M 1986 J. Geophys. Res. 91 4673 [29] Prescher C and Prakapenka V B 2015 High Press. Res. 35 223 [30] Larson A C and Dreele R B V 2004 Los Alamos Natl. Laboratory Report LAUR pp 86–748 [31] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169 [32] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [33] Sancho M P L, Sancho J M L and Rubio J 1985 J. Phys. F 15 851 [34] Wu Q, Zhang S, Song H F, Troyer M and Soluyanov A A 2018 Comput. Phys. Commun. 224 405 [35] Marzari N and Vanderbilt D 1997 Phys. Rev. B 56 12847 [36] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D and Marzari N 2008 Comput. Phys. Commun. 178 685 [37] Chen K, Wang B, Yan J Q, Parker D S, Zhou J S, Uwatoko Y and Cheng J G 2019 Phys. Rev. Mater. 3 094201 [38] Mal P, Bera G, Turpu G R, Srivastava S K, Gangan A, Chakraborty B, Das B and Das P 2019 Phys. Chem. Chem. Phys. 21 15030 [39] Einaga M, Ohmura A, Nakayama A, Ishikawa F, Yamada Y and Nakano S 2011 Phys. Rev. B 83 092102 [40] Guo Z, Zhu H, Dong J, Jia Q, Gong Y, Wang Y, Li H, An P, Yang D, Zhao Y, Xing H, Li X and Chen D 2018 J. Appl. Phys. 124 065901 [41] Souchay D, Nentwig M, Günther D, Keilholz S, de Boor J, Zeugner A, Isaeva A, Ruck M, Wolter A U B, Büchner B and Oeckler O 2019 J. Mater. Chem. C 7 9939 [42] Shi M Z, Lei B, Zhu C S, Ma D H, Cui J H, Sun Z L, Ying J J and Chen X H 2019 Phys. Rev. B 100 155144 [43] Yan J Q, Liu Y H, Parker D, McGuire M A and Sales B C 2019 arXiv:1910.06273 [cond-mat.mtrl-sci] [44] Hu C, Ding L, Gordon K N, Ghosh B, Li H, Lian S W, Linn A G, Tien H J, Huang C Y, Reddy P V S, Singh B, Agarwal A, Bansil A, Xu S Y, Lin H, Cao H, Chang T R, Dessau D and Ni N 2019 arXiv:1910.12847 [cond-mat.str-el]