Hao OuYang(欧阳豪) Qing-Xin Dong(董庆新) Yi-Fei Huang(黄奕飞)Jun-Sen Xiang(项俊森) Li-Bo Zhang(张黎博) Chen-Sheng Li(李晨圣)Pei-Jie Sun(孙培杰) Zhi-An Ren(任治安) and Gen-Fu Chen(陈根富)

1Institute of Physics,and Beijing National Laboratory for Condensed Matter Physics,Chinese Academy of Sciences,Beijing 100190,China

2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

3Songshan Lake Materials Laboratory,Dongguan 523808,China

Keywords: thermoelectric,topological insulator,crystal growth

1. Introduction

Thermoelectric(TE)materials have attracted widespread research interest in the development of potential applications for waste heat-to-electricity conversion, or solid-state refrigeration. The efficiency of thermoelectric energy conversions is characterized by the dimensionless parameter[1]ZT=S2σT/κ,whereσ,S,T,andκare the electric conductivity, Seebeck coefficient, Kelvin temperature, and thermal conductivity, respectively. However, the strong coupling[2–4]amongS,σandκleads to a finite improvement of conversion efficiency, preventing the common use of thermoelectric devices. How to eliminate or weaken the coupling among these three parameters is of great significance for further applications of TE materials. Topological materials are highly expected to do so, namely, decoupling the electron and phonon in transport process,[5–9]due to the topologically protected band structure and unconventional electronic properties,such as the strong spin-orbit coupling(SOC)and the inverted band structure. Indeed,Bi2Te3,Bi2Se3and its alloying derivatives,famous for their excellent thermoelectric properties, turn out to be the three-dimensional topological insulators(TIs),[10–12]which inspire us to find other excellent thermoelectric candidates in the nontrivial topological materials.

LiMgBi, which is half-Heusler structured (MgAgAstype) and crystallizes in the cubicF¯43mspace group, was recently identified as a high symmetry point topological semimetal,[13–15]while the latest first-principles calculations by Sattigeriet al.[16]have shown that LiMgBi would be a weak TI or band insulator, which could undergo the topological phase transition and transform into a Dirac semimetal driven by the volume expansive pressure. Additionally,the title compound is also predicted as a promising thermoelectric candidate with a large Seebeck coefficient.[17,18]In this work,we have grown the single crystals of LiMgBi and implemented a detailed study on electric and thermal transport properties on it. Our results reveal that LiMgBi is a TI with a multiband feature,and the hole-type carriers dominate the transport. Moreover,LiMgBi possesses a large Seebeck coefficient and a moderate thermal conductivity at room temperature,which provide a good platform to study thermoelectric properties and make it potential in energy-conversion applications.

2. Experiment

High-quality single crystals of LiMgBi were grown by the self-flux method with an optimized molar ratio of Li:Mg:Bi=1:1:10. Mg and Bi powders were mixed thoroughly in a mortar with pestle. Then the powder was placed into an alumina crucible together with Li flakes, covered with quartz wool and sealed into a quartz tube. The sealed quartz ampoule was heated to 873 K,kept at this temperature for 10 h,and then cooled down to 623 K at 2.5 K/h. At this temperature, the quartz ampoule was taken out of the muffle furnace and put into a centrifuge to separate the LiMgBi crystals from the Bi flux, then LiMgBi single crystals with typical size of 4 mm×2 mm×1 mm could be obtained. X-ray diffraction(XRD)patterns of polycrystalline and single crystal were collected by a PANalytical x-ray diffractometer with CuKαradiation(λ=1.541874 ˚A)at room temperature. Powder XRD Rietveld refinement was performed using the GSAS program.[19]Electric and thermal transport property measurements were used with four-probe method and mainly carried out in a Quantum Design physical property measurement system (QD PPMS-9T). Particularly, to adopt different sizes of a single crystal sample, we performed the thermal transport measurements on both homemade and QD’s puck.

3. Results and discussion

LiMgBi (Fig. 1(a)) adopts a filled zinc-blende-type structure.[20]As shown in Fig. 1(b), the elements Mg and Bi occupied the 4aand 4cWyckoff sites,respectively,composing the zinc tetrahedrons frame structure;while Li atoms,located at 4bWyckoff site,fill in the cage as the interstitial atoms and form chain along the [110] direction. Meanwhile, this crystal structure is the same as the Half–Heusler phase (XYZ),

Fig.1. (a)The crystal structure of LiMgBi. (b)Project view of the lattice along the[110]direction. (c)Powder XRD pattern of LiMgBi and refinements result. (d)Single crystal XRD pattern of LiMgBi. Inset shows the grown crystal on millimeter paper.

where Li,Mg,and Bi serve asX,Y,Zelements,respectively.The main panel of Fig. 1(c) shows the powder XRD pattern and Rietveld refinement result of the LiMgBi powder sample. The diffraction patterns can be well indexed using theF¯43m(No. 216) space group, except some very weak peaks from the residual Bi. The refinement smoothly converges toRwp=6.48%,Rp=4.23%, the determined lattice parametera=b=c=6.75 ˚A, which is in agreement with the previous result.[21]As shown in the inset of Fig.1(d),the obtained LiMgBi single crystal is black in color with the metallic luster and has a triangle shape. Single crystal XRD pattern reveals that the natural growth crystal surface is(h h h)crystallographic plane.

The temperature-dependent resistivityρxx(T) measured on LiMgBi single crystal under several magnetic fields is shown in Fig. 2(a). At zero filed, the resistivityρxx(0)first decreases linearly with decreasing temperature, exhibiting a metallic behavior until∼160 K. Thereafter the resistivity starts to increase, reaching a maximum at about 50 K,and finally drops slightly with further cooling. The metal-tosemiconductor-like transition with a low temperature plateau has often been observed in many topological materials,such as SmB6[22]Bi2Te2Se[23]and Bi2Te3,[24]which has been taken as a transport signature of conducting surface states of a TI protected by time reversal symmetry. With applied magnetic fields, the resistivity has a moderate increase above∼130 K,but shows a drastic up-turn below this temperature. This behavior is very similar to other recognized topological materials,such as LaBi[25]and LaSb.[26]

Fig.2. (a)Temperature dependence of resistivity at different magnetic fields. The electric current is parallel to the(111)plane and magnetic field is perpendicular to the electric current.Inset shows the enlarged part of ρxx(T)between 140 and 180 K.(b)The MR at various temperatures for magnetic field is perpendicular to(h h h)plane. Inset: the weak antilocalization effect fitting between −1 and 1 T,at 2 K.The blue dots and the red line represent the experimental data and the fitting curve, respectively. (c)Magnetic field dependence of MR at selected angular 2 K with magnetic field rotated in the plane perpendicular to the current for I‖y. Here ψ is defined as the angle between B and z-axis. (d)Angular dependent MR with keeping magnetic field perpendicular to electric current,at 2 K for selected magnetic field.

whereσWALandσNare the electric conductivity from the contribution of quantum interference corrections associated with spin orbital scattering and conventional bands;σ0andρ0are the electric conductivity and resistivity at zero field. The inset of Fig. 2(b) displayed the experimental data (blue solid dot)and fitting curve (red line) at 2 K. We can see that the low field MR data could be fitted well with the WAL semiclassical formula, which suggests the large intrinsic SOC in LiMgBi arising from Bi. Such behavior is widely observed in some heavy element Bi-based materials.[30–32]Figure 2(c)presents the magnetic field dependence of MR at 2 K for selected angles. There is no significant variation indicating a very weak anisotropy in LiMgBi. To further verify this character, the measurements of angular dependent MR were performed under several magnetic fields at 2 K, as displayed in Fig. 2(d).As the angle changes, the magnetoresistance forms a nearly circular shape, which is consistent with the highly symmetrical cubic crystal structure of LiMgBi.

We performed Hall measurement at various temperatures for the purpose of investigating the different type carrier’s contribution to transport process in this system, as shown in Fig. 3(a). Evidently, the positive Hall coefficientRxy=ρxy(µ0H)/Bwithin the measured temperature range indicates that hole-type carriers are dominant in the transport process.Furthermore,the deviation from the linear behavior of the Hall resistivity at low fields implies that LiMgBi is a multiband system. Thus, according to the above results, we analyzed the Hall resistivityρxy(µ0H)using the semiclassical two-band model with the following formula:

wherene,µe,nh,µhare the carrier density and mobility of electron and hole,respectively. The temperature dependences of the carrier density and mobility extracted from the Hall resistivity fitting are shown in Figs. 3(b) and 3(c). The estimatedne,nh,µe,µhat 2 K are 1.07×1014cm−3, 3.86×1018cm−3, 5.37×103cm2/(V·s), 0.02×103cm2/(V·s),respectively. When the temperature increases, the hole density increases while the electron density is substantially unchanged below 50 K.As the temperature rises further,the hole density decreases significantly together with a sharp increasing of electron density until both of them reach the minimum(1.18×1018cm−3for hole)and maximum(3.52×1014cm−3for electron) values at 200 K. Additionally, the evolution trends of hole mobility(0.06×103cm2/(V·s)the maximum at∼200 K)is the same as that of electron density. The electron mobility has a slight augment below 50 K,but a continuous decrease until room temperature(2.06×103cm2/(V·s)at 300 K).Remarkably,the density of hole-type carries is in order of 1018cm−3,which have the same magnitude order as typical TI materials, such as Bi1−xSbx,[33]Sb2Te3.[12,34]It is two or even more orders of magnitude lower than the carrier density of typical topological semimetals (1020–1021cm−3) such as WC,[35]WTe2,[36]and gray As,[37]which implies that LiMgBi prefers to be a TI rather than a topological semimetal. Noticeably, the hole density is four orders of magnitude larger than that of electron in all measured temperature range,it is reasonable that the transport properties are dominated by holes,and the high mobility of electron(two orders of magnitude larger than that of hole)may originate from the nontrivial topological metallic surface state,similar to Bi2Se3.[38,39]

Fig. 3. (a) The magnetic field dependent Hall resistivity at various temperatures. Inset: two-band model fitting of ρxy(µ0H) at selected temperatures. (b)and(c)The density and mobility of electron and hole versus temperature,respectively.

In order to evaluate the potential of the utilization of this thermoelectric candidate, we performed the thermoelectric transport measurements on the polycrystalline and single crystal of LiMgBi, respectively, as presented in Fig. 4.As the temperature rises, the single crystal Seebeck coefficient of LiMgBi increases rapidly from 21.6µV/K at 2 K to 380.7 µV/K at 75 K, and then undergoes a moderate ascension up to 440 µV/K at room temperature after the stationary range. By contrast, the Seebeck coefficient of the polycrystalline is basically temperature independent below 125 K and begins to increase enormously and reaches the maximum of 276.1 µV/K at 363 K. The difference of Seebeck coefficient between single crystal and polycrystalline should be attributed to the influence of grain boundaries scattering or carries densities.[40,41]In addition, both of them exhibit positive values in the measurement temperature range,further confirming that the hole-type carries play a dominant role in the thermoelectric transport process,and the derailment from linearly increasing behavior also verifies the multiband system.Figure 4(b) presents the thermal conductivityκof LiMgBi polycrystalline and single crystal. The thermal conductivity of single crystal has a tremendous variation. As the temperature rises,it quickly reaches the peak(68.1 W·K−1·m−1at 12 K)and then drops rapidly to the 5.2 W·K−1·m−1at 300 K.On the contrary,the thermal conductivity of polycrystalline always maintains a steady change between 2 and 3 W·K−1·m−1when temperature is above 100 K.The weak upturn may come from heat radiation at high temperatures.The inset of Fig.4(b)shows the comparison of total thermal conductivityκtotand electron portionκefor single crystal, which can be extracted from theκtotusing the Wiedemann–Franz(W-F)law

whereL0is Lorenz number(2.44×10−8W·Ω·K−2),σis the electric conductivity andTis Kelvin temperature. It can be seen theκeis almost three orders of magnitude smaller thanκtot, indicating that the most contribution to the transport of heat is mainly derived from lattice thermal conductivity.There are a lot of margins to reach the amorphous limit to further improve thermoelectric performance.

What we should pay attention to are the following points:(1)The large Seebeck coefficient. LiMgBi possesses the large Seebeck coefficient∼440 µV/K at 300 K, it is even larger than that of the optimized traditional commercial alloy of Bi2Te3and Sb2Te3[42](∼230 µV/K at 300 K). What’s more noteworthy is that it maintains continuously the large thermoelectric coefficient value in a wide range (above 75 K). (2)The comparable thermal conductivity (5.2 W·K−1·m−1at 300 K) with Sb2Te3[42](∼4.5 W·K−1·m−1at 300 K) and SiGe (∼3 W·K−1·m−1at 300 K)[43]inspire us to optimize the thermal conductivity by doping, nanosizing and thin-film superlattices or other methods to enhance the thermoelectric performance. (3) Unique properties of topological materials. LiMgBi,a TI candidate,has the unconventional electronic structure and specific electronic properties, and it is possible to considerably decouple the electron and phonon transport,reducing its lattice thermal conductivity while retaining the moderate electric conductivity of topological metallic surface states. Therefore, LiMgBi provides a good topological material platform to enhance thermoelectric performance.

Fig. 4. (a) and (b) The temperature dependence of Seebeck coefficient and thermal conductivity for single crystal and polycrystalline of LiMgBi. Inset: the photo image of the sample mounted on a sample holder. (Single crystal and polycrystalline measurement are performed on homemade instrument and QD-PPMS 9T).

4. Conclusion

In summary,we have successfully grown the single crystals of LiMgBi and its electric and thermal transport properties have been studied systematically. The electric resistivity shows a metal-to-semiconductor-like transition at∼160 K.While below 50 K, the resistivity tends to saturation, which may be rooting in the competition between bulk state and topological metallic surface state. The WAL effect was clearly observed in MR measurements, implying the large intrinsic SOC in LiMgBi. Hall measurements indicate that LiMgBi is a multiband system, which is dominated by the hole-type carriers in the transport process. The thermoelectric transport measurement states clearly a larger Seebeck coefficient(∼440µV/K)and a moderate thermal conductivity,which are worthy of further studies to assess the potential as a thermoelectric material candidate.