Quantum Oscillations of Robust Topological Surface States up to 50 K in Thick Bulk-insulating Topological Insulator

As personal electronic devices increasingly rely on cloud computing for energy-intensive calculations, the power consumption associated with the information revolution is rapidly becoming an important environmental issue. Several approaches have been proposed to construct electronic devices with low energy consumption. Among these, the low-dissipation surface states of topological insulators (TIs) are widely employed. To develop TI-based devices, a key factor is the maximum temperature at which the Dirac surface states dominate the transport behavior. Here, we employ Shubnikov-de Haas oscillations (SdH) as a means to study the surface state survival temperature in a high quality vanadium doped Bi1.08Sn0.02Sb0.9Te2S single crystal system. The temperature and angle dependence of the SdH show that: 1) crystals with different vanadium (V) doping levels are insulating in the 3-300 K region, 2) the SdH oscillations show two-dimensional behavior, indicating that the oscillations arise from the pure surface states; and 3) at 50 K, the V0.04 single crystals (Vx:Bi1.08-xSn0.02Sb0.9Te2S, where x = 0.04) still show clear sign of SdH oscillations, which demonstrate that the surface dominant transport behavior can survive above 50 K. The robust surface states in our V doped single crystal systems provide an ideal platform to study the Dirac fermions and their interaction with other materials above 50 K.


Introduction
Since the concept of topology has been introduced into condensed matter physics, an exotic form of quantum matter, namely, the topological insulator (TI), has attracted much attention, in which there is no transport of electrons in the bulk of the material, while the edges/surface can support metallic electronic states protected by time-reversal symmetry. 1Theoretical predictions have revealed spin-moment locking, and linear-dispersion edge states can be addressed in a two-dimensional (2D) topological insulator. 2,3The experimental breakthrough leading to the 2D system was achieved in a strong spin-orbital coupled CdTe/HgTe quantum well, which gave rise to a quantum spin Hall state. 4Recently, 1T′-WTe2 monolayer 5- 7 has been proved to be a new quantum spin Hall insulator, with a conducting edge state that can survive to 100 K 8,9 , thereby offering a potential application for a 2D TI in ultra-low-energy electronics.
1][12][13] The unique conducting surface states offer a new playground for studying the physics of quasiparticles with unusual dispersions, such as Dirac or Majorana fermions, as well as showing promising capabilities for spintronics (e.g.efficient spin-torque transfer).2][13][14][15][16] In particular, a quantized anomalous Hall effect (QAHE) was found in a magnetic-ion-doped 3D TI thin film that presented a transverse current with extremely low dispersion. 17,18 achieve the QAHE, both the linearly dispersed topological surface states and ferromagnetic ordering are needed.More recently, X-ray magnetic circular dichroism (XMCD) results 19 have demonstrated that the ferromagnetic ordering of spin-spin related surface states survives better than in the bulk states, which might imply that the critical temperature of the surface states is the key to QAHE.
Since the surface states of a TI are very important, it is a great challenge to develop a system in which surface-dominated transport survives at high temperature.In fact, most of the known TI materials are not bulk-insulating, which hinders study of the transport properties of the surface states.Therefore, bulkinsulating TIs with high resistivity are still required to extend the topological states to the high temperature region.A good example of a wide-gap TI system is Bi2-xSbxTe3-ySey (BSTS) 10,11,[20][21][22][23] , which shows surface states that dominate the transport behavior at and below 30 K 10 .Since in bulk-insulating TIs, the Fermi surface is formed by pure Dirac dispersed surface states, the Shubnikov-de Haas (SdH) oscillations are strong evidence that can be used to evaluate the contribution of surface states.Tracing the SdH oscillations is an effective method to study the surface states in bulk-insulating 3D TIs.For example, the angular dependence of the SdH oscillations is key evidence that can be used to isolate surface-features.The oscillation magnitudes also provides insight into other properties of the electronic structure such as the effective mass.In realistic systems, the effective mass of a Dirac carrier is always nonzero instead of the ideal zero mass, and this causes temperature-induced damping of the amplitudes of SdH oscillations.One strategy that improves on BSTS, for which the surface band is not ideally linear, is to utilize a different TI: Sn-doped Bi2-xSbxTe2S, which has a wide bulk band gap [24][25][26][27] .In the latter compound, 2% tin is introduced to stabilize the crystal structure, and the corresponding material shows surface states with a linear dispersion over a large energy range. 24We therefore focus on further optimization of this particular system by adding V at the bismuth sites to tune the bulk band gap.In this work, we found that the SdH oscillations could survive up to 50 K in the V0.04 sample (Vx:Bi1.08-xSn0.02Sb0.9Te2S,where x = 0.04), which allows 3D TIbased study of this substrate above the 50 K region.A special feature of this material is that the SdH oscillations are found in 1 mm-thick bulk crystals, which present useable surface states, making these crystals suitable for the fabrication of further van der Waals heterostructures.

Results & Discussion
A single crystal exfoliated from the as-grown V0.04 ingot is shown in Fig. 1(a).The V:BSSTS single crystal shares the same crystal symmetry as its parent compounds Sb2Te3 and Bi2Te3, which belong to the R-3m space group, with quintuple layers piled up along the hexagonal c-axis (Fig. 1b).Traditionally, Se is widely used as a dopant to tune the band structure, which results in the (Bi,Sb)2(Te,Se)3 (BSTS) formula for the most popular topological insulator.Nevertheless, the defect chemistry limits our ability to grow large high-quality bulk single crystals of BSTS.Ideally, the new low-energy electronics industry requires wafer-size thick topological insulator materials with stable surface states and a large bulk band gap.Previous work by Kushwaha et al. demonstrated that Sn-doped Bi1.1Sb0.9Te2Ssingle crystal has a low carrier concentration with clean surface states at low temperatures.To further optimize this material, we have employed V as a Bi-site dopant, which, we discovered, has the effect of making the bulk states more insulating (as sketched in Fig. 1(d)), whilst having minimal effects on the surface states.This is a major step forward towards realizing an ideal TI material for the electronics.
Plots of the temperature dependence of bulk resistivity are presented in Fig. 2(a) for single crystal samples ~1 mm in thickness with different V doping levels.The resistivity curves for all of the vanadium doped samples show a steep upturn as the sample is cooled, indicating that the bulk V:BSSTS samples have become highly insulating.The residual resistance ratios (RRR), defined by RRR = ρ(3 K)/ρ(300 K) for the samples, where ρ is the resistivity, were 2.1, 9.4, and 127 for V0.02, V0.04, and V0.08, respectively.As the Vdoping level increases, the resistivity and the RRR increase dramatically, showing better insulating behavior, e.g., the maximum resistivity of the V0.02 sample is near 0.1 cm, but it can reach about 0.7 and 10 cm in the V0.04 and V0.08 samples, respectively.In the low temperature region below 10 K, the resistivity curves of the V0.02 and -V0.04 samples show an additional minor feature and a slight upturn, although this is negligible compared to the major transition at ~ 100 K.In the more highly insulating V0.08 sample, the low temperature resistivity slightly drops with cooling.The temperature at which the surface states finally dominate the bulk resistivity depends on intrinsic factors, but also varies with V doping.The ln versus T - 1 plots (shown in Fig. 1b) exhibit activated behavior, with the activation energy for transport at 110, 240 and 340 meV in the V0.02, V0.04, and V0.08 samples, respectively.We conducted measurements to determine the magnetoresistance (MR) ratio, MR = (R(H)-R(0))/R(0), for all three V-doped samples in the low temperature region in order to understand the magnetotransport properties.In the V0.02 sample, the MR curves first decrease in the low magnetic field region, and then increase with increasing magnetic field, up to about 16% at 3 K and 14 T. The maximum MR value at 14 T increases upon heating, so that it reaches 25% at 50 K.In the V0.04 and V0.08 samples, the MR values are always positive at all temperatures and under all magnetic field conditions, but they show temperaturedamping behavior, with maximum MR of 50% and 110% at 3 K, respectively.Although the single crystals are similar in size and shape, the MR curves for the 3 samples are quite different from one another.In the V0.02 crystal, the MR curves show a non-monotonic relationship with increasing magnetic field.Between 0 -1 T, the 3 K MR curves slightly decrease to about -0.7%, and they then show a weak field dependence until about 5 T, after which, obvious oscillation patterns are displayed in the quasi-parabolic curves.The aforementioned oscillations, denoted as Shubnikov-de Haas (SdH) oscillations, result from Landau quantization.Upon cooling to different temperatures, the phenomenon of low-field MR decrease shows a similar tendency, but with a larger change in the relative drop, e.g., the minimum MR value (appearing at 1 T) at 5 K is about 1%, but it is near 1.6% at 8 -50 K. Unlike the V0.02 sample, the V0.04 sample becomes more resistive with increasing field.Starting in the low-field region, the MR curves show a rapid increase at 3 K.Note that the total behavior of the V0.04 sample is linear-like with high field SdH oscillations, but it shows a faster-than-linear increase in applied fields below 0.5 T fields.This faster rate of increase is attributed to the contribution of surface conduction, denoted as the weak anti-localization effect. 22During heating, the low field behavior remains, but it becomes less significant and vanishes at 50 K.In the V0.08 sample, the MR shows a simple linear increase with magnetic field in the H < 6 T region, after which, the SdH oscillations occur and the MR values increase more slowly than the linear tendency before.
Let's then focus on the SdH oscillations in the MR curves, which are obtained via subtracting the smooth background and are plotted in Fig. 2(d, f, h).Since the bulk states are strongly insulating, the oscillation related Fermi surface is due to the contributions of the pure surface states.The oscillation patterns of each sample are almost the same, but with different amplitudes, which are damped during heating.Note that, in the V0.04 sample, the SdH oscillations survive at 50 K, which means that the surfaces states are quite mobile at this temperature and might still exist at even higher temperatures.The SdH oscillations for a semimetal can be described by the Lifshitz-Kosevich (LK) formula, with a Berry phase being taken into account for the topological system: Where   = /sinh(/) ,   = exp (−  /) , and   = cos (/2) .Here,  =  * / 0 is the ratio of the effective cyclotron mass  * to the free electron mass  0 ; g is the g-factor;   is the Dingle temperature; and  = (2 2    0 )/ℏ, where kB is Boltzmann's constant, ℏ is the reduced Planck's constant, and e is the elementary charge.The oscillation of  is described by the cosine term with a phase factor  − , in which  = 1/2 -B/2, where B is the Berry phase.From the LK formula, the effective mass of carriers contributing to the SdH effect can be obtained through fitting the temperature dependence of the oscillation amplitude to the thermal damping factor   .From the temperature damping relationship, we obtain the Dingle temperatures of the three samples: 4.7, 6.5, and 9.4 K for V0.02, V0.04, and V0.08, respectively.The effective masses for these crystals are 0.16 m0, 0.15 m0, and 0.13 m0, respectively, as shown in Fig. 3(c).The quantum relaxation time and quantum mobility can also be obtained by τ = ħ/2πkBTD and  = eτ/m * , respectively.According to the Onsager-Lifshitz equation, the frequency of quantum oscillation,  = ( 0 /2 2 )  , where AF is the extremal area of the cross-section of the Fermi surface perpendicular to the magnetic field, and 0 is the magnetic flux quantum.The cross-sections related to the 32, 30, and 25 T pockets are 0.34, 0.31, and 0.26  10 -3 Å -2 , respectively.The obtained parameters are summarized in Table 1 below.
The Berry phase can be obtained via the Landau fan diagram, which is shown in Fig. 3 2D-like relationship is strong evidence that the quantum oscillations are contributed by the topological surface states.

Conclusions
We employed a simple-melting -slow-cooling method to grow single crystals of V, Sn doped Bi1.1Sb0.9Te2Ssingle crystals.The R-T and Hall measurements that all three samples are insulating in the 3-300 K region, with low carrier concentrations.SdH oscillations can be detected in the low temperature region, which implies that our insulating single crystals possess Fermi surfaces.Furthermore, we find strong 2D-like behavior and a  Berry phase in all three samples, which provide compelling evidence that the bulks of these crystals are good insulators.Moreover, V dopant appears to tune both the type and the concentration of carriers in these TI systems, which provide us with an ideal platform to study their physical properties, as well as offering potential forMdevice fabrication related to their surface states.

Methods
To obtain bulk-insulating TIs, defect control is one of the most important factors in the crystal growth process.Here, we employ a simple melting-cooling method in a uniform-temperature vertical furnace to spontaneously crystallize the raw elements into a tetradymite structure (Vx:Bi1.08-xSn0.02Sb0.9Te2S,V:BSSTS for short).Briefly, high-purity stoichiometric amounts (10 g) of V, Bi, Sn, Sb, Te, and S powders were mixed via ball milling and sealed in a quartz tube as starting materials.The crystal growth was carried out using the following procedures: i) Heating the mixed powders to completely melt them; ii) Maintaining this temperature for 24 h to ensure that the melt is uniform; and iii) Slowly cooling down to 500 C to crystallize the sample.After growth, single crystal flakes with a typical size of 5 × 5 × 1 mm 3 could be easily exfoliated mechanically from the ingot.Naturally, the single crystals prefer to cleave along the [001] direction, resulting in the normal direction of these flakes being [001].
The electronic transport properties were measured using a physical properties measurement system (PPMS-14T, Quantum Design).Hall-bar contact measurements were performed on a freshly cleaved ab plane using silver paste cured at room temperature.The electric current was parallel to the ab plane while the magnetic field was perpendicular to the ab plane.The angle dependence of the magnetoresistance (MR) was also measured using a standard horizontal rotational rig mounted on the PPMS.

Fig. 1
Fig. 1 Atomic and electronic structures of single crystal V:BSSTS.(a) Typical size of V0.04 doped single crystal

Fig. 2
Fig. 2 Temperature dependence of the resistivity and the magnetoresistance (MR) of V:BSSTS.(a) The temperature

Fig. 3
Fig. 3 Carrier analyses of the single crystals with different V doping levels.(a) Landau fan diagram related to the

Fig. 4
Fig. 4 Angle dependent SdH oscillations at 3 K.(a) Angular dependence of the MR for the V0.04 sample at 3 K,

Table 1 .
(b).Since xx > xy, we assign the maxima of the SdH oscillation to integer (n) Landau levels, to linearly fit the n versus 1/H curve.As we can see in Fig.3(b), the intercept has a value of around 0.5for all three samples, which implies that these oscillations are contributed by the topological surface states.Parameters determined from the SdH oscillations.F is the frequency of quantum oscillation.m* is the effective mass.TD is the Dingle temperature.The 2D carrier's density and mobility are denoted by n and , respectively.