SnTe高压结构相变与物性研究
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摘要
碲化锡（SnTe）是一种典型的窄带隙四六族半导体材料，最近理论和实验研究发现它还是一种新型拓扑绝缘体。然而，SnTe高压结构的不确定性严重阻碍了人们对其电子性质的进一步探索。本文我们利用高压同步辐射实验结合第一性原理理论计算方法研究了SnTe的高压结构、相变机制和电子性质随压力的变化行为，得到以下创新性成果：
1.通过对高压X-ray衍射实验数据、理论计算的热力学稳定性（晶体结构预测）、能垒以及声子模式的系统分析，得出碲化锡在中间相的压力区间是三个正交相Pnma、Cmcm和GeS结构的动态共存，分别建立了低压相，中间相和高压相的相边界，并进一步阐明了相应的相变机制。
2.通过电子性质的系统研究，发现面心立方相SnTe的带隙随着压强的升高而增大；动量空间的等能面形状发生变化，说明压强还导致了电子拓扑结构相变的产生，这将直接影响SnTe的光学性质和电子输运行为；发现碲化锡的拓扑绝缘态在高压下得以加强；发现压强可以改变SnTe的电子带隙和费米面拓扑行为，进而可以调控一系列物理性质。
3.高压相（体心立方结构）的电子能带中既存在比较平的能带（提供高局域的电子），又存在陡峭的电子能带（提供快速移动的电子），它们可以促使费米面处电子对的形成和超导转变温度的提高。在相变的边界18GPa，体心立方结构的超导转变温度的计算值为7.16K,与实验上观察到最大值7.5K非常接近。电子能带的计算发现，Pnma和Cmcm结构在存在的压强区间都发生了电子拓扑形貌转变，它们都是弱的金属，在费米面上仅有很小的电子态密度，并且都是超导体，超导转变温度分别是0.010.03K和0.700.37K。
Tin telluride (SnTe) is an exemplary case among IV-VI narrow-gapsemiconductors that exhibit unusual thermodynamic, vibrational, and electronicproperties which find applications in phase-change memory devices, solar cells,thermoelectric generators and infrared detectors. Recent discoveries of novelstructural and electronic states and the latest realization of a new type of topologicalorder in SnTe have reinvigorated strong interest in this fascinating material. It haslong been known that SnTe undergoes pressure-driven phase transitions from theambient-pressure Fm-3m (B1) structure through an intermediate phase to the Pm-3m(B2) structure. However, structural determination of the intermediate phase hasremained an intriguing and longstanding mystery since x-ray diffraction (XRD) isoften insufficient by itself to resolve complex phases, especially those with lowsymmetries. Previous work proposed conflicting structures such as an orthorhombicGeS structure or a pseudo-tetragonal structure. Similar uncertainties exist for otherIV-VI compounds such as SnS, which was proposed to change under pressure fromGeS to monoclinic structure, which is in contradiction to another prediction oftransition to orthorhombic Cmcm structure. Meanwhile, several orthorhombic phaseshave been proposed for the intermediate phases of PbX (X=Te, Se, S) without aconsensus view. These structural uncertainties greatly impede further exploration ofthis important class of materials. Here we unravel the convoluted high-pressure phasetransitions of SnTe using angle-dispersive synchrotron x-ray diffraction combinedwith first-principles structural search. We identify three coexisting intermediate phases of Pnma, Cmcm, and GeS type structure and establish the corresponding phaseboundaries. We further unveil the intricate pressure-driven evolution of the energetics,kinetics and lattice dynamics to elucidate its distinct phase-transition mechanisms.These findings resolve structures of SnTe, which have broad implications for otherIV-VI semiconductors that likely harbor similar novel high-pressure phases.
Topological insulators are intriguing states of quantum matter characterized byan insulating gap in the bulk and conducting gapless edges or surface states in theboundaries. Their discovery has generated great interest because of the scientificimportance of the observed phenomena and promising potential of these materials forhigh-temperature spintronics applications. Search for additional members of this classof materials has been continuing. Recent theoretical work identified tin telluride(SnTe) as a distinct type of topological crystalline insulator, in which the metallicsurface states are protected by the mirror symmetry of the crystal, in contrast to thetime-reversal symmetry protection in the earlier identified Z2topological insulators.Subsequently, angle-resolved photoemission spectra (ARPES) detected surfaceelectronic states consisting of four Dirac cones (even number of so-calledband-inversion points) in the first surface Brillouin zone, providing experimentalevidence for the topological crystalline insulator phase in SnTe. Most recently, thetopological crystalline insulator phase and topological phase transition have also beenobserved in Pb1-xSnxTe by ARPES measurements. Following these excitingdiscoveries, a pressing task is to explore the behavior the recently identifiedtopological insulating state and characterize its response to external physicalconditions that may alter the underlying fundamental physics. Of particular interestare the possible changes in the stability of its cubic crystalline phase and the natureand size of its electronic band gap, which are essential ingredients for maintaining thetopological insulating state in SnTe. Tin telluride is a direct narrow band gapsemiconductor with a gap of0.18eV (0.30eV) at room (4.2K) temperature. It has been extensively studied over the past several decades, and it has remained a topic ofgreat interest because of its fundamental physics and potential applications inelectronic devices. An unusual feature of the electronic structure of SnTe is that theordering of its conduction and valence band near the Fermi energy is inverted relativeto a normal semiconductor like PbTe whose electronic band structure connects to theatomic limit smoothly. The so-called “negative band gap”(or band inversion) in SnTeoccurs between a valence band maximum near the L points in the Brillouin zone withL6-symmetry and the conduction band minimum with L6+symmetry, which areopposite to those in PbTe. A transition from the normal band structure in PbTe to thatof SnTe with the non-trivial inverted band gap has been illustrated by examining theband gap evolution in Pb1-xSnxTe as a function of alloy composition, which shows thatthe band gap of the alloy initially decreases with increasing value of x, leading to itsfull closure, and then reopens and increases in the inverted direction with furtherrising x. Moreover, ARPES and ab initio calculations revealed complex Fermi surfacestructure near the L points, showing topological changes in the constant-energysurface from disconnected pockets, to open tubes, and then to cuboids as the bindingenergy (or hole-doping) increases. The narrow band gap of SnTe is very sensitive tochanges of external conditions such as pressure, doping, or temperature. Given theessential role of the inverted band gap in the topological insulating state of SnTe, it iscrucial that we establish an understanding of its behavior under changing externalconditions. While the response of the electronic properties of SnTe to changingtemperature and hole-doping has been extensively studied, the effect of pressure onthe structural stability of the cubic phase of SnTe and its electronic properties remainslargely unexplored. In this paper, we present a systematic first-principles study of theinfluence of applied pressure on the structural and electronic properties of thetopological insulating state that exists in the cubic phase of SnTe. We have calculatedthe phonon dispersion curve to examine the dynamic stability of the cubic SnTestructure under pressure, and our results indicate that pressure suppresses a soft optical phonon associated with a structural instability, thus strengthening the cubicphase. Our electronic band structure calculations reveal significant pressure effect onthe topological structure of the Fermi surface and its impact on the chargeredistribution which, in turn, strengthens the bonding and structural stability of thecubic phase. The band structure calculations also show that the electronic band gap ofSnTe increases in size considerably with applied pressure, making the topologicalinsulating state more robust under pressure. These results show that pressure stabilizesand enhances the topological crystalline insulator state of SnTe and effectively tunesits electronic structure and Fermi surface, which are expected to have significantimpact on the transport and optical properties crucial for its applications.
The fundamental physics and potential application as thermoelectric energyconverters and electronic devices have made SnTe a subject of intense investigation.At ambient conditions, SnTe crystallizes in the face-centered cubic (B1, Fm-3m)structure, and it undergoes a rich variety of structural, electronic, and topologicalphase transitions under changing temperature and pressure conditions. At atmosphericpressure, a phase transition in the temperature range of30-100K is accompanied by acrystal symmetry change from cubic (B1, Fm-3m) to rhombohedral (R3m) driven by asmall dimerization in the unit cell, causing changes in the temperature dependence ofvarious physical properties, e.g., M ssbauer spectroscopy, Raman scattering, electricresistivity, and thermal expansion coefficient. At high pressure, SnTe transforms to abody-centered cubic (B2, Pm-3m) structure that is superconducting with a criticaltemperature (TC) that peaks at~7.5K and then decreases with further increase ofpressure. This result raises several fundamental questions concerning the underlyingmechanism, especially the relation between the pressure induced structural phasetransition and the evolution of the electronic structure and electron-phonon couplingthat is responsible for the observed superconductivity. The electronic band structure ofSnTe exhibits a peculiar behavior in that the ordering of its conduction and valence band near the Fermi energy is inverted relative to those in a normal semiconductor(e.g., PbTe). Recent theoretical predication and experimental angle-resolvedphotoemission spectra demonstrate that the narrow band gap semiconductor SnTe is atopological crystalline insulator, in which the topological nature of the electronicstructures arises from the crystal symmetry rather than the time reversal symmetry.Subsequent calculations show that high pressure can make the topological insulatingstate in SnTe more stable and robust, as evidenced by the hardening of all the phononbranches and the increase of the inverted (negative) band gap under pressure.Furthermore, pressure and doping induced electronic topological changes in theconstant-energy surface in the face-centered cubic structure of SnTe have beenuncovered by ARPES and first-principles calculations. These studies show thatpressure has a strong influence in tuning the electronic properties of SnTe. Thepressure induced B1-B2phase transition of SnTe goes through an intermediatepressure range where some lower-symmetry structures appear. However, an accuratedetermination of the intermediate phase(s) and the phase boundaries has been plaguedby uncertainties in structural identification and refinement. Recently, the highlyconvoluted structural transitions in SnTe at high pressure have been unraveled by anintegrated approach of synchrotron X-ray diffraction measurement combined with thelatest first-principles structural search technique. Among the structures identified inthe intermediate pressure range, two phases with Pnma and Cmcm symmetry aredynamically stable and exhibit interesting and different electronic properties,especially in terms of their band gap and Fermi surface topology. In this paper, wepresent a systematic study of the pressure effect on the electronic properties andelectron-phonon coupling (EPC) in SnTe using first-principles calculations. Our studyreveals a series of pressure-induced transitions of the electronic states in SnTe in thepressure range of0-60GPa between semiconducting, metallic, superconducting andtopological insulating states. In particular, our results show that SnTe becomessuperconducting in the intermediate pressure range well before the transition to the B2 phase occurs. Once the B2phase is established, the strong EPC produces asuperconducting state with a maximum critical temperature of7.16K which is inexcellent agreement with the experimental value of about7.5K. With increasingpressure, our calculations predict a steady decline of TC, which again is in agreementwith experimental observation. These results suggest that our calculations havecaptured the main physics concerning the EPC responsible for superconductivity inSnTe, which gives confidence in our prediction of additional superconducting states inthe intermediate phases, and it may stimulate further experimental investigation insearch of such states.
1.通过对高压X-ray衍射实验数据、理论计算的热力学稳定性（晶体结构预测）、能垒以及声子模式的系统分析，得出碲化锡在中间相的压力区间是三个正交相Pnma、Cmcm和GeS结构的动态共存，分别建立了低压相，中间相和高压相的相边界，并进一步阐明了相应的相变机制。
2.通过电子性质的系统研究，发现面心立方相SnTe的带隙随着压强的升高而增大；动量空间的等能面形状发生变化，说明压强还导致了电子拓扑结构相变的产生，这将直接影响SnTe的光学性质和电子输运行为；发现碲化锡的拓扑绝缘态在高压下得以加强；发现压强可以改变SnTe的电子带隙和费米面拓扑行为，进而可以调控一系列物理性质。
3.高压相（体心立方结构）的电子能带中既存在比较平的能带（提供高局域的电子），又存在陡峭的电子能带（提供快速移动的电子），它们可以促使费米面处电子对的形成和超导转变温度的提高。在相变的边界18GPa，体心立方结构的超导转变温度的计算值为7.16K,与实验上观察到最大值7.5K非常接近。电子能带的计算发现，Pnma和Cmcm结构在存在的压强区间都发生了电子拓扑形貌转变，它们都是弱的金属，在费米面上仅有很小的电子态密度，并且都是超导体，超导转变温度分别是0.010.03K和0.700.37K。
Tin telluride (SnTe) is an exemplary case among IV-VI narrow-gapsemiconductors that exhibit unusual thermodynamic, vibrational, and electronicproperties which find applications in phase-change memory devices, solar cells,thermoelectric generators and infrared detectors. Recent discoveries of novelstructural and electronic states and the latest realization of a new type of topologicalorder in SnTe have reinvigorated strong interest in this fascinating material. It haslong been known that SnTe undergoes pressure-driven phase transitions from theambient-pressure Fm-3m (B1) structure through an intermediate phase to the Pm-3m(B2) structure. However, structural determination of the intermediate phase hasremained an intriguing and longstanding mystery since x-ray diffraction (XRD) isoften insufficient by itself to resolve complex phases, especially those with lowsymmetries. Previous work proposed conflicting structures such as an orthorhombicGeS structure or a pseudo-tetragonal structure. Similar uncertainties exist for otherIV-VI compounds such as SnS, which was proposed to change under pressure fromGeS to monoclinic structure, which is in contradiction to another prediction oftransition to orthorhombic Cmcm structure. Meanwhile, several orthorhombic phaseshave been proposed for the intermediate phases of PbX (X=Te, Se, S) without aconsensus view. These structural uncertainties greatly impede further exploration ofthis important class of materials. Here we unravel the convoluted high-pressure phasetransitions of SnTe using angle-dispersive synchrotron x-ray diffraction combinedwith first-principles structural search. We identify three coexisting intermediate phases of Pnma, Cmcm, and GeS type structure and establish the corresponding phaseboundaries. We further unveil the intricate pressure-driven evolution of the energetics,kinetics and lattice dynamics to elucidate its distinct phase-transition mechanisms.These findings resolve structures of SnTe, which have broad implications for otherIV-VI semiconductors that likely harbor similar novel high-pressure phases.
Topological insulators are intriguing states of quantum matter characterized byan insulating gap in the bulk and conducting gapless edges or surface states in theboundaries. Their discovery has generated great interest because of the scientificimportance of the observed phenomena and promising potential of these materials forhigh-temperature spintronics applications. Search for additional members of this classof materials has been continuing. Recent theoretical work identified tin telluride(SnTe) as a distinct type of topological crystalline insulator, in which the metallicsurface states are protected by the mirror symmetry of the crystal, in contrast to thetime-reversal symmetry protection in the earlier identified Z2topological insulators.Subsequently, angle-resolved photoemission spectra (ARPES) detected surfaceelectronic states consisting of four Dirac cones (even number of so-calledband-inversion points) in the first surface Brillouin zone, providing experimentalevidence for the topological crystalline insulator phase in SnTe. Most recently, thetopological crystalline insulator phase and topological phase transition have also beenobserved in Pb1-xSnxTe by ARPES measurements. Following these excitingdiscoveries, a pressing task is to explore the behavior the recently identifiedtopological insulating state and characterize its response to external physicalconditions that may alter the underlying fundamental physics. Of particular interestare the possible changes in the stability of its cubic crystalline phase and the natureand size of its electronic band gap, which are essential ingredients for maintaining thetopological insulating state in SnTe. Tin telluride is a direct narrow band gapsemiconductor with a gap of0.18eV (0.30eV) at room (4.2K) temperature. It has been extensively studied over the past several decades, and it has remained a topic ofgreat interest because of its fundamental physics and potential applications inelectronic devices. An unusual feature of the electronic structure of SnTe is that theordering of its conduction and valence band near the Fermi energy is inverted relativeto a normal semiconductor like PbTe whose electronic band structure connects to theatomic limit smoothly. The so-called “negative band gap”(or band inversion) in SnTeoccurs between a valence band maximum near the L points in the Brillouin zone withL6-symmetry and the conduction band minimum with L6+symmetry, which areopposite to those in PbTe. A transition from the normal band structure in PbTe to thatof SnTe with the non-trivial inverted band gap has been illustrated by examining theband gap evolution in Pb1-xSnxTe as a function of alloy composition, which shows thatthe band gap of the alloy initially decreases with increasing value of x, leading to itsfull closure, and then reopens and increases in the inverted direction with furtherrising x. Moreover, ARPES and ab initio calculations revealed complex Fermi surfacestructure near the L points, showing topological changes in the constant-energysurface from disconnected pockets, to open tubes, and then to cuboids as the bindingenergy (or hole-doping) increases. The narrow band gap of SnTe is very sensitive tochanges of external conditions such as pressure, doping, or temperature. Given theessential role of the inverted band gap in the topological insulating state of SnTe, it iscrucial that we establish an understanding of its behavior under changing externalconditions. While the response of the electronic properties of SnTe to changingtemperature and hole-doping has been extensively studied, the effect of pressure onthe structural stability of the cubic phase of SnTe and its electronic properties remainslargely unexplored. In this paper, we present a systematic first-principles study of theinfluence of applied pressure on the structural and electronic properties of thetopological insulating state that exists in the cubic phase of SnTe. We have calculatedthe phonon dispersion curve to examine the dynamic stability of the cubic SnTestructure under pressure, and our results indicate that pressure suppresses a soft optical phonon associated with a structural instability, thus strengthening the cubicphase. Our electronic band structure calculations reveal significant pressure effect onthe topological structure of the Fermi surface and its impact on the chargeredistribution which, in turn, strengthens the bonding and structural stability of thecubic phase. The band structure calculations also show that the electronic band gap ofSnTe increases in size considerably with applied pressure, making the topologicalinsulating state more robust under pressure. These results show that pressure stabilizesand enhances the topological crystalline insulator state of SnTe and effectively tunesits electronic structure and Fermi surface, which are expected to have significantimpact on the transport and optical properties crucial for its applications.
The fundamental physics and potential application as thermoelectric energyconverters and electronic devices have made SnTe a subject of intense investigation.At ambient conditions, SnTe crystallizes in the face-centered cubic (B1, Fm-3m)structure, and it undergoes a rich variety of structural, electronic, and topologicalphase transitions under changing temperature and pressure conditions. At atmosphericpressure, a phase transition in the temperature range of30-100K is accompanied by acrystal symmetry change from cubic (B1, Fm-3m) to rhombohedral (R3m) driven by asmall dimerization in the unit cell, causing changes in the temperature dependence ofvarious physical properties, e.g., M ssbauer spectroscopy, Raman scattering, electricresistivity, and thermal expansion coefficient. At high pressure, SnTe transforms to abody-centered cubic (B2, Pm-3m) structure that is superconducting with a criticaltemperature (TC) that peaks at~7.5K and then decreases with further increase ofpressure. This result raises several fundamental questions concerning the underlyingmechanism, especially the relation between the pressure induced structural phasetransition and the evolution of the electronic structure and electron-phonon couplingthat is responsible for the observed superconductivity. The electronic band structure ofSnTe exhibits a peculiar behavior in that the ordering of its conduction and valence band near the Fermi energy is inverted relative to those in a normal semiconductor(e.g., PbTe). Recent theoretical predication and experimental angle-resolvedphotoemission spectra demonstrate that the narrow band gap semiconductor SnTe is atopological crystalline insulator, in which the topological nature of the electronicstructures arises from the crystal symmetry rather than the time reversal symmetry.Subsequent calculations show that high pressure can make the topological insulatingstate in SnTe more stable and robust, as evidenced by the hardening of all the phononbranches and the increase of the inverted (negative) band gap under pressure.Furthermore, pressure and doping induced electronic topological changes in theconstant-energy surface in the face-centered cubic structure of SnTe have beenuncovered by ARPES and first-principles calculations. These studies show thatpressure has a strong influence in tuning the electronic properties of SnTe. Thepressure induced B1-B2phase transition of SnTe goes through an intermediatepressure range where some lower-symmetry structures appear. However, an accuratedetermination of the intermediate phase(s) and the phase boundaries has been plaguedby uncertainties in structural identification and refinement. Recently, the highlyconvoluted structural transitions in SnTe at high pressure have been unraveled by anintegrated approach of synchrotron X-ray diffraction measurement combined with thelatest first-principles structural search technique. Among the structures identified inthe intermediate pressure range, two phases with Pnma and Cmcm symmetry aredynamically stable and exhibit interesting and different electronic properties,especially in terms of their band gap and Fermi surface topology. In this paper, wepresent a systematic study of the pressure effect on the electronic properties andelectron-phonon coupling (EPC) in SnTe using first-principles calculations. Our studyreveals a series of pressure-induced transitions of the electronic states in SnTe in thepressure range of0-60GPa between semiconducting, metallic, superconducting andtopological insulating states. In particular, our results show that SnTe becomessuperconducting in the intermediate pressure range well before the transition to the B2 phase occurs. Once the B2phase is established, the strong EPC produces asuperconducting state with a maximum critical temperature of7.16K which is inexcellent agreement with the experimental value of about7.5K. With increasingpressure, our calculations predict a steady decline of TC, which again is in agreementwith experimental observation. These results suggest that our calculations havecaptured the main physics concerning the EPC responsible for superconductivity inSnTe, which gives confidence in our prediction of additional superconducting states inthe intermediate phases, and it may stimulate further experimental investigation insearch of such states.
引文
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