Large magnetoresistance and Fermi surface study of Sb$_2$Se$_2$Te single crystal

TL;DR

This study investigates the magnetoresistance and Fermi surface of Sb$_2$Se$_2$Te single crystals, revealing large, non-saturating MR and three Fermi surface pockets with trivial topology, relevant for electronic applications.

Contribution

The paper provides the first detailed analysis of the magnetotransport properties and Fermi surface topology of Sb$_2$Se$_2$Te single crystals, including SdH oscillations and Berry phase calculations.

Findings

Magnetoresistance reaches 1100% at 31 T with no saturation.

Three Fermi surface pockets identified via SdH oscillations.

Confirmed trivial topology of the prominent Fermi pocket.

Abstract

We have studied the magnetotransport properties of a Sb$_2$Se$_2$Te single crystal. Magnetoresistance (MR) is maximum when the magnetic field is perpendicular to the sample surface and reaches to a value of 1100\% at $B$=31 T with no sign of saturation. MR shows Shubnikov de Haas (SdH) oscillations above $B$=15 T. The frequency spectrum of SdH oscillations consists of three distinct peaks at $\alpha$=32 T, $\beta$=80 T and $\gamma$=117 T indicating the presence of three Fermi surface pockets. Among these frequencies, $\beta$ is the prominent peak in the frequency spectrum of SdH oscillations measured at different tilt angles of the sample with respect to the magnetic field. From the angle dependence $\beta$ and Berry phase calculations, we have confirmed the trivial topology of the $\beta$-pocket. The cyclotron masses of charge carriers, obtained by using the Lifshitz-Kosevich formula, are found to be $m^{*}_{\beta}=0.16m_o$ and $m^{*}_{\gamma}=0.63m_o$ for the $\beta$ and $\gamma$ bands respectively. Large MR of Sb$_2$Se$_2$Te is suitable for utilization in electronic instruments such as a computer hard disc, high field magnetic sensors, and memory devices.

Equations

$$R_T=\frac{\lambda (T/B)}{sinh[\lambda (T/B)]},$$

Full text

I Introduction

The recently discovered topological insulators have garnered enormous attention because of their unique surface properties, known as topological surface states or edge states, which arise from the non-trivial topology of the bulk state wave functions in Hilbert spaceHasan and Kane (2010); Qi and Zhang (2011); Ando (2013); Ando and Fu (2015); Cava et al. (2013). The surface or edge states in topological insulators are important not only for understanding fundamental physics but they also have great technological value for future electronicsAnalytis et al. (2010). To exploit the surface states of these materials in future technology, we must first detect and understand their physical properties. Several experimental techniques have been employed to detect topological surface states and understand their properties. Angle-resolved photoemission spectroscopy (ARPES) experiments allow one to observe a Dirac cone due to its surface states and a well defined bulk band structureHasan and Kane (2010); Qi and Zhang (2011); Ando (2013). From a technological point of view, transport characteristics of surface states are important. However, the bulk conduction channel interferes with the surface states which makes transport studies of topological surface states challengingQu et al. (2010); Analytis et al. (2010); Eto et al. (2010); Cao et al. (2013). Two transport methods, quantum oscillations and weak antilocalization (WAL), have been widely used for studying topological surface statesTaskin et al. (2011); Shrestha et al. (2014); Bao et al. (2012); He et al. (2011). In the presence of magnetic fields, the electrical resistivity shows quantum oscillations, known as Shubnikov-de Haas (SdH) oscillations, due to the quantization of carrier states into Landau levelsShrestha et al. (2017a); Kittel ; Ashcroft and Mermin . The angle dependence of the frequency of SdH oscillations helps to map the cross section of the Fermi surface and its possible origin to either surface or bulk states. Topological materials possess the strong spin-orbit interactions that are often reflected as a cusp or dip in magnetoconductivity at low magnetic fields, known as a weak antilocalizationHe et al. (2011), Chen et al. (2014); Shrestha et al. (2017b). As a quantum correction to the classical conductivity, a WAL effect could be due to spin-orbit interactions in the surface or bulk states. The scaling of WAL curves with the normal field components provides evidence of the dominance of surface states in magnetoconductivity. Also, a large non-saturating magnetoresistance (MR) and high mobility have been seen in many topological systems, and the observation of these properties has been taken as a signature of the existence of a linear dispersion relation of the surface statesWang et al. (2012); Yan et al. (2013).

Recently, we have investigated magnetotransport properties of $p$-type metallic Sb2Te2Se single crystalShrestha et al. (2017c) in fields up to 31 T. From the angle dependence of quantum oscillations and Berry phase calculations, we have confirmed the existence of a 2D Fermi surface in Sb2Te2Se. In the search of a new topological system, we have extended our study to an isostructural compound Sb2Se2Te.

Sb2Se2Te is a structural analogue of the ternary tetradymite-likeXu et al. compound Sb2Te2Se with a “Se” atom in the place of a “Te” atom. First principles calculation shows that a topological phase transition (from non-trivial to trivial) takes placeZhang et al. (2010) in Sb2(Te1-xSex)3 while going from x=0 to x=1. Also, band structure calculationsMenshchikova et al. (2013) show that Sb2Se2Te is a topologically trivial system with a narrow band gap of 100 meV (direct). Despite these theoretical reports, there are only few transport studies on the Sb2Se2Te compound. Recently, Huang $et$ $al.$Huang et al. (2016) reported a large non-saturating linear MR of Sb2Se2Te that reaches up to 120% at 9 T. However, due to low field range they could not observe quantum oscillations and study Fermi surface properties. Here, we have studied MR and Fermi surface properties of a Sb2Se2Te single crystal in the extended field range of 31 T. The Fermi surface is three dimensional and has three pockets ($\alpha$, $\beta$ and $\gamma$). Also, we have shown the trivial topology of the $\beta$ pocket using the angle dependence measurements of $\beta$ and Berry phase calculations.

II Experimental Procedure

High quality single crystals of Sb2Se2Te were grown by the modified Bridgman method. The synthesis was done by using stoichiometric quantities of the starting materials Sb, Se, and Te, each with purity of 99.9999%, mixed in quartz ampoules with diameters of 20 mm and vacuum pumped to 10*-6* torr. These ampoules were positioned in a Bridgman crystal growth furnace. In the furnace, the ampoules were heated to 700oC and homogenized for 48 hours. The crystal growth process was performed with temperature decreasing at 0.3oC per hour in the range of 700 $-$ 570 oC. The ampoules were further cooled from 570oC to room temperature at 10oC per hour.

Resistivity and Hall measurements were carried out using the ac-transport option of a physical property measurement system (PPMS, Quantum Design). Magnetoresistance measurements were performed at the National High Magnetic Field Laboratory (NHMFL), with fields up to 31 T. Six gold contacts were sputtered on a freshly cleaved crystal face for standard resistivity and Hall measurements. Platinum wires were attached using silver paint. The sample was then mounted on the rotating platform of a standard probe designed at NHMFL. Alternating current of 1 mA was passed through the sample using a Keithley (6221) source meter. The longitudinal and Hall resistances were measured using a lock-in amplifier (SR 830). The sample can be positioned at different angles with respect to the applied magnetic field. The measuring probe is then inserted into a 3He Janis cryostat that is mounted on the top of a resistive magnet (31 T). The position of the sample with respect to the applied field was calibrated using a Hall sensor.

III Results and Discussion

Figure [1] shows the longitudinal resistivity as a function of temperature for a Sb2Se2Te single crystal. The sample exhibits a metallic behavior below room temperature. The residual resistivity ratio RRR=$\rho_{xx}$(300 K)/$\rho_{xx}$(20 K) = 20 shows the high crystallinity of the single crystal. This value of RRR is nearly 3 times as large as the previous measurementHuang et al. (2016), RRR = $\rho_{xx}$(300 K)/$\rho_{xx}$(2 K) = 7. Hall measurements were carried out to determine the nature of the bulk charge carriers and their concentration. Non-linear field dependence of $R_{xy}$ near $B$ = 0 suggests the existence of a multiband effect (electron and hole bands)Qu et al. (2010); Ren et al. (2010). However, the overall positive slope of the Hall resistance (see inset, Fig. 1) shows the dominance of the hole-like bulk charge carriers. The bulk carrier concentration is estimated to be 3$\times$1019cm*-3* at 0.4 K.

The magnetoresistance of Sb2Se2Te is measured under high magnetic field up to 31 T at NHMFL. Figure [2(a)] shows magnetoresistance expressed in percentage, MR = $\frac{R_{xx}(B)-R_{xx}(0)}{R_{xx}(0)}\times$100%, measured at different temperature with $\theta$ = 0o. Here, $\theta$ is defined as the angle between the magnetic field direction and normal to the sample surface. MR is positive and increases linearly with applied field $B$, and it reaches to 312% at 9 T. At given field $B$=9 T and $T$=10 K, this MR value is significantly higher than the previous reportHuang et al. (2016) of MR=120%. The large MR response in our sample could be due to better crystallinity i.e. RRR=20 as compared to that of RRR=7 in Huang et al. (2016). MR decreases gradually with increasing temperature. MR increases linearly with $B$ and reaches $\approx$1100% at $T$=0.4 K and $B$=31 T. Under same magnetic field and temperature, this MR value is significantly higher than our previous reportShrestha et al. (2017c) of $\approx$98% increase for Sb2Te2Se single crystal. At $T$=50 K, MR reaches 560%, which is almost $\frac{1}{2}$ of the value at $T$=0.4 K. A system with large MR usually also possesses high mobility, as observed in many topological and Dirac systemsShekar et al. (2015); Liang et al. (2015). We have used the simple Drude model [$\mu(T)$=$R_{H}(T)/\rho_{xx}(T)$, where $R_{H}(T)$ is the Hall coefficient at temperature T] to estimate the effective mobility. From our calculations, we found \mu$$\approx700 cm*-2V-1s-1* at 20 K. It is important to note that MR shows Shubnikov de Haas (SdH) oscillations in the fields above 15 T as a result of the cyclotron motion of the charge carriers in a perpendicular magnetic field. The oscillations are clear at low temperatures and diminished at higher temperatures above $T$=15 K. The frequency of SdH oscillations is proportional to the cross-section area of the Fermi surface. Thus, in order to better understand the shape, size, and dimensionality of the Fermi surface in Sb2Se2Te, we have studied the angle dependence of the quantum oscillations. Figure [2(b)] shows the selected MR curves measured at different $\theta$ values. It is important to note that (1) SdH oscillations are present in all angles from $\theta$=0 to 90o and (2) the oscillations look complex which could be the mixture of multiple frequencies (will be discussed later). This scenario is different than what we observed in our previous studyShrestha et al. (2017c) on Sb2Te2Se where oscillations possess a single frequency and are diminished above $\theta$=40o. The presence of SdH oscillations even at $\theta$=90o indicates the presence of a 3D Fermi surface in Sb2Se2Te. Also, MR value depends on the tilt angle of the sample with respect to magnetic field. MR is maximum when magnetic field is perpendicular to the sample surface, i.e. at $\theta$=0o and it decreases with increasing $\theta$ as shown in Fig. [2(c)].

The frequency of SdH oscillations shown in Fig. [2(b)] were determined by taking the fast Fourier transform (FFT). Figure [3(a)] shows the FFT spectrum at $\theta$=0o. It consists of three major peaks at 32, 80 and 117 T, denoted as $\alpha$, $\beta$ and $\gamma$. There are two additional peaks, one at 160 T is the second harmonics of $\beta$ and another at 258 T is the sum of 2$\alpha$, $\beta$ and $\gamma$. A frequency of oscillations $f$ is linked to the cross-section of the Fermi surface by Onsagar’s relationShrestha et al. (2014) as $f=(\frac{h}{4\pi e})K^{2}_{F}$, where h is Planck’s constant and $K_{F}$ is the Fermi wave vector. The presence of $\alpha$, $\beta$ and $\gamma$ peaks in Fig. [3(a)] implies the presence of three Fermi pockets in Sb2Se2Te. Fig. [3(b)] shows the FFT of SdH oscillations at selected $\theta$ values. As compared to $\alpha$ and $\gamma$ peaks, the $\beta$ peak is prominent and convenient to track its position at different $\theta$ values, as pointed by black arrows. If quantum oscillations are originated from a 2D Fermi surface, the SdH oscillations or their frequency scale with the normal component of magnetic fieldsAndo (2013); Ando and Fu (2015). Here, the position of $\beta$ changes with $\theta$ but it does not show any systematic $\theta$ dependence as shown in Fig. [3(c)]. This suggests that the $\beta$ pocket of Fermi surface has a trivial topology.

In order to provide further evidence for the bulk states origin of the $\beta$ peak, we have estimated the Berry phase, $\phi$, by using the Landau level (LL) fan plot, which should be $\phi$=0.5 for Dirac particles and 0 for normal fermions. To calculate Berry phase of the $\beta$ oscillations it has to be resolved separately, without the interference from the oscillations of the $\alpha$ and $\gamma$ branches. Figure 4(a) shows the SdH oscillations in magnetic field range (7 $-$ 11) T. In this field range, there exists only one frequency $\beta$ as shown in inset, implying that the contribution from $\alpha$ and $\gamma$ oscillations is completely eliminated. We let 1/$B_{max}$ and 1/$B_{min}$ represent the positions of maxima and minima of the SdH oscillations. The positions of minima and maxima were assigned integer and half integer values respectively to construct the LL fan diagram shown in figure [4(b)]. In the limit 1/$B$ $\rightarrow$0, we have obtained Berry phase, $\phi$=$-$0.04 $\pm$ 0.06. This value is very close to the theoretical value 0 for normal fermions. This further confirms the trivial topology of the $\beta$ pocket.

The effective mass $m^{*}$ of charge carriers of Fermi surface pocket can be determined by employing the Lifshitz-Kosevich (LK) formula to temperature dependence data of quantum oscillations. Figure [5(a)] shows SdH oscillations obtained after subtracting a smooth polynomial background at different temperatures. The amplitude of oscillations decreases with increasing temperature. According to LK theory, the oscillation amplitude at fixed magnetic fields can be described by thermal damping factor $R_{T}$Qu et al. (2010); Ando (2013) as

[TABLE]

where $\lambda(T/B)={2\pi^{2}k_{B}\over{\hbar e}}m^{*}{T\over B}$. Due to the presence of multiple oscillation frequencies, it difficult to exactly extract the oscillation amplitude from the raw data in Fig. [5(a)]. That is why, we have taken temperature dependence of the peak height on the FFT spectra of $\Delta R_{xx}$ versus 1/$B$ curves as shown in Fig. [5(b)]. The inset of Fig. [5(b)] shows the LK fitting using Eq.(1) for $\beta$ and $\gamma$ pockets. The parameter $B$ used in LK formula fitting is taken as the average inverse fields of the FFT interval. From the best fit, we have estimated cyclotron masses of $\beta$ and $\gamma$ bands to be $m^{*}_{\beta}=0.16m_{o}$ and $m^{*}_{\gamma}=0.635m_{o}$, where $m_{o}$ is the rest mass of electron. Due to limited temperature dependence data of $\alpha$ peak in the FFT spectrum, we could not use LK formula to determine effective mass of the $\alpha$ pocket.

IV Summary

Here, we have studied magnetoresistance (MR) of a Sb2Se2Te single crystal in magnetic fields up to 31 T. MR is large and reaches up to 1100% under $T$ = 31 T at $B$=0.4 K and does not show any sign of saturation. MR is maximum when magnetic field is perpendicular to sample surface. In order to study Fermi surface properties of Sb2Se2Te, we have measured Shubnikov de Haas (SdH) oscillations at different tilt angles of sample with respect to magnetic field. Unlike the 2D Fermi surface of Sb2Te2Se compound, Sb2Se2Te has the 3D Fermi surface with three surface pockets ($\alpha$, $\beta$ and $\gamma$). From the angle dependence of frequency and the Berry phase calculations, we have confirmed that the $\beta$ pocket has the trivial topology. Using Lifshitz-Kosevich analyses, we have estimated the cyclotron masses of $\beta$ and $\gamma$ pockets as $m^{*}_{\beta}=0.16m_{o}$ and $m^{*}_{\gamma}=0.63m_{o}$.

acknowledgements

This work is supported in part by the U.S. Air Force Office of Scientific Research, the T. L. L. Temple Foundation, the J. J. and R. Moores Endowment, and the State of Texas through the TCSUH. V. Marinova acknowledges support from the Bulgarian Science Fund, project FNI-T-02/26. A portion of this work was performed at NHMFL, which is supported by the NSF co-operative Agreement No. DMR-1157490 and the State of Florida. Work at Idaho National Laboratory is supported by the Department of Energy, Office of Basic Energy Sciences, Materials Sciences, and Engineering Division.