Surface Electronic Structure of Cr Doped Bi₂Se₃ Single Crystals

Abstract

Here, by using angle-resolved photoemission spectroscopy, we showed that Bi_2−xCr_xSe₃ single crystals have a distinctly well-defined band structure with a large bulk band gap and undistorted topological surface states. These spectral features are unlike their thin film forms in which a large nonmagnetic gap with a distorted band structure was reported. We further provide laser-based high resolution photoemission data which reveal a Dirac point gap even in the pristine sample. The gap becomes more pronounced with Cr doping into the bulk of Bi₂Se₃. These observations show that the Dirac point can be modified by the magnetic impurities as well as the light source.

1. Introduction

Topological insulators (TIs) gained great attention due to their peculiar electronic structure characterized by strong spin-orbit coupling [1,2]. These materials are insulating in the bulk while hosting metallic topological surface states (TSSs) with a chiral spin texture at the boundary. TSSs are described by the massless Dirac equation and are protected against non-magnetic perturbations by time-reversal symmetry (TRS) [1,2]. Novel magnetic states of matter can be realized in TIs through the interaction between the TSSs and the internal magnetic exchange field. In particular, the ferromagnetic order can break TRS and open a magnetic gap at the Dirac point (DP) by lifting the spin degeneracy, and hence the dissipationless chiral edge state propagating along the sample edge can emerge without the need for the external magnetic field [3,4]. Such a state of matter is known as the quantum anomalous Hall effect (QAHE). Accordingly, the QAHE was experimentally realized in V- and Cr-doped (Bi, Sb)₂Te₃ thin films, but at temperatures far below the ferromagnetic transition temperature [5,6]. Since then, there have been intensive studies to resolve these obstacles and increase the onset temperature for the QAHE. It has been recognized that the fundamental drawbacks are the dopant-induced disorder in the lattice and unfavorable distortion of the band structure [7,8,9,10,11,12,13]. So far, most of the transport and photoemission experiments have been conducted on magnetic topological insulators (MTIs) prepared as thin films, based on the expectation that the thinner samples can be less disordered. This has made molecular beam epitaxy (MBE) a primary technique to grow MTI materials. However, MBE may not be an ideal method to prepare MTIs because of the low growth temperature required for chalcogenides which may form the clustering of dopants. On the other hand, abundant vacancies form at high growth temperatures which can induce disorders and strongly modify the chemical potential of the system [14]. Therefore, fabricating MTIs with the lowest density of defects and desired electronic structure is still one of the critical steps in facilitating future studies and applications. Among many TIs, Bi₂Se₃ is one of the most promising systems due to its simple electronic structure with a large bulk band gap where the DP is located [2]. This leads to extensive theoretical studies of the impact of transition metal doping on its magnetic and electronic structures. However, dopants induce a prominent lifetime broadening in ARPES spectra of Bi₂Se₃ which makes it difficult to catch the details of the band structure [9,10,11,12,13]. Therefore, experimental studies have often adopted (Bi,Sb)Te-based TIs. However, in this material, an unavoidable bulk band crossing at the binding energy of the DP causes non-trivial magnetic quantum states to appear only below a few K [15]. On the other hand, a more robust surface electronic structure and high crystalline quality of Bi₂Se₃ could make it a promising pathway to the realization of a high-temperature QAHE.

Unlike the thin film samples, there are only a few band structure studies on magnetic-impurity-doped Bi₂Se₃ single crystals [16] although their magnetic and transport properties are investigated in more detail [17,18,19]. In this article, we study the electronic structure of Cr-doped Bi₂Se₃ single crystals grown using the floating zone method. We confirmed their high crystal quality by performing high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM), X-ray photoemission spectroscopy (XPS), and micro-spot low energy electron diffraction (µLEED) experiments. Our angle-resolved photoemission spectroscopy (ARPES) experiments show that the surface electronic structure of Cr-doped Bi₂Se₃ single crystals is free of large Dirac gaps and significant lifetime broadening. These enhanced structural and electronic features facilitate the study of the Dirac cone in detail. Hence, our synchrotron-based ARPES experiments show that Bi₂Se₃ has robust gapless surface states against Cr doping. On the other hand, the same samples exhibit a Dirac gap even in the pristine form when the electronic structure is recorded with a laser source and the gap can be further modified with Cr doping. This interesting observation reveals an interplay mechanism between magnetic impurities, light source, and the Dirac cone electronic structure.

2. Materials and Methods

Single crystals with nominal composition Bi_1−xCr_xSe₃ were grown by a modified floating-zone method. Bi, Se, and Cr of 6N purity were loaded into double-walled quartz ampules and sealed under vacuum. The materials first were melted at 900 °C in a box furnace and fully rocked to achieve a homogeneous mixture. A 12 mm diameter pre-melted ingot rod in a sealed quartz tube was mounted in a floating-zone furnace in which the pre-melted ingot rod was first pre-melted at a velocity of 200 mm/hr and then grown at 1.0 mm/hr. ARPES experiments were performed at 21-ID-1 ESM beamline of National Synchrotron Light Source II (NSLS-II) by using a DA30 Scienta electron spectrometer (Scienta Omicron, Uppsala, Sweden). The pressure in the photoemission chamber was 1 × 10⁻¹⁰ Torr and samples were kept at 15 K during the experiment by a closed-cycle He cryostat. The angle between the incident beam and the surface normal of the sample at normal emission was 55°. Incident beam spot-size was set to be ~10 × 10 μm²). Single crystals were cleaved in the ARPES chamber at 15 K. High symmetry points in the BZ were calculated by using the free electron final state approximation $ħ{\mathrm{k}}_{\mathrm{z}}=\sqrt{2{\mathrm{m}}_{\mathrm{e}}({\mathrm{E}}_{\mathrm{k}\mathrm{i}\mathrm{n}}{\mathrm{c}\mathrm{o}\mathrm{s}}^2\mathsf{\theta }+{\mathrm{V}}_{\mathrm{o}})}$ where ${\mathrm{m}}_{\mathrm{e}}$ is the free electron mass, ${\mathrm{E}}_{\mathrm{k}\mathrm{i}\mathrm{n}}$ is the kinetic energy of a photoelectron, and ${\mathrm{V}}_{\mathrm{o}}$ is the inner potential which is 11.8 eV for Bi₂Se₃ [20]. The laser ARPES experiments were carried out with hv = 6.3 eV and R4000 Scienta electron spectrometer (Uppsala, Sweden) at the Hiroshima Synchrotron Radiation Center (HiSOR) [21]. Samples were cleaved in ARPES chamber and experiments were conducted at 11 K. XPS experiments were carried out in an ultrahigh vacuum (UHV) system with base pressures < 2 × 10⁻⁹ Torr equipped a SPECS, PHOIBOS 100 (Berlin, Germany) hemispherical electron energy analyzer and twin anode X-ray source (SPECS, XR50) (Berlin, Germany). Mg K_α (1253.6 eV) radiation was used at 10 kV and 30 mA. The angle between the analyzer and X-ray source was 45° and photoelectrons were collected along the sample surface normal. The total experimental resolution in XPS was ~1 eV. Depth profile XPS was carried out by sputtering the sample at room temperature. Then, the sample was annealed at 225 °C for 30 min after each sputtering. Sputtering was performed by using SPECS PU-IQE 11/35 (Berlin, Germany) sputtering at 1 W power and P_Ar = 2 × 10⁻⁵ Torr in the experimental chamber. The sputtering rate was calibrated as 2 Å/min. The magnetic properties of the crystals were measured by using a superconducting quantum interference device (SQUID) (San Diego, CA, USA) at Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory. HAADF-STEM images were acquired with dedicated Hitachi HD2700C (Hitachi, Tokyo, Japan) STEM with a probe Cs corrector operating at 200 kV at room temperature. Samples were prepared using the in situ lift-out method on the FEI Helios 600 Nanolab dual-beam FIB (Peabody, MA, USA). Final milling was completed at 2 keV. HAADF-STEM experiments were conducted at the Center for Functional Nanomaterials, Brookhaven National Laboratory. µLEED experiment was performed at XPEEM/LEEM endstation of the ESM beamline (21-ID-2). Samples were cleaved in air and rapidly loaded into the system.

3. Results

We present a HAADF-STEM image of the Bi_1.78Cr_0.22Se₃ single crystal sample in Figure 1a for structural characterization. The high crystalline quality of the sample is clear in its highly ordered periodically aligned atomic lattices and the van der Waals (vdW) gaps between the individual quintuple layers (QLs). This finding is also supported by sharp diffraction patterns in µLEED (Figure 1b). In addition to probing the local atomic layered structure using HAADF-STEM and surface structure with µLEED, we also characterize the local electronic structure with XPS. Figure 1b,c show the core levels of the Bi_1.78Cr_0.22Se₃ single crystal at different depths. The Bi⁺³ 5d_5/2 and Bi⁺³ 5d_3/2 peaks are located at 25 eV and 28.1 eV, respectively, for the cleaved sample. Furthermore, the Cr 2p_3/2 and 2p_1/2 peaks are located at the 575.6 eV and 585.5 eV binding energies, respectively, corresponding to the Cr⁺³ valence state [13,22]. This indicates the isoelectric substitution of Bi with the Cr atoms. The core levels obtained from the different depths with respect to the cleaved surface do not show any prominent differences in the width or the binding energy which confirms the chemical uniformity of the sample. Also, unlike the case of surface doping in thin films [13], the transition metal incorporation into the bulk does not induce any new local electronic structure evident from the Bi 5d and Cr 2p peak shapes. These findings show the single chemical state of the sample as well as the absence of the Cr impurity clusters.

To investigate the magnetic properties of the Cr-doped Bi₂Se₃ single crystal, we carried out the superconducting quantum interference device (SQUID) magnetometry measurement. Figure 2a depicts the zero-field-cooled (ZFC) and field-cooled (FC) magnetization (M) curves under the 500 Oe applied field (H) for a Bi_1.78Cr_0.22Se₃ single crystal. The plot shows signatures of three magnetic transitions at ~160 K (T₁), ~120 K (T₂), and ~20 K (T₃). This indicates the coexistence of the different magnetic states as seen in (MnBi₂Te₄) (Bi₂Te₃)_m [23]. It is also noteworthy that the M-T curve does not exhibit the characteristics of Cr_xSe_y compounds and/or Cr clusters [24,25]. This suggests that the magnetic responses are the intrinsic property of the sample. Moreover, the M–H curves of the Bi_1.78Cr_0.22Se₃ single crystal at 10 K, 100 K, and 150 K are given in Figure 2b. The expanded scale of M-H curves in the inset of the figure shows a clear hysteresis loop at 10 K. This hysteresis loop weakens at higher temperatures, but it is persistent even at 150 K as a very weak feature suggesting the possible high-temperature ferromagnetic order. Also, M does not saturate even at high fields as an indication for antiferromagnetic or paramagnetic order [26]. Antiferromagnetic TIs are also extremely rare materials which can host axion electrodynamic and quantized magnetoelectric coupling effects. One of the known examples of this class is the recently discovered MnBi₂Te₄ single crystal with a Néel temperature (T_N) of 25.4 K [27]. Furthermore, ferromagnetic order has been observed only in thin films of Cr-doped Bi₂Se₃ [28], while a single crystal of the same sample is antiferromagnetic [19]. The magnetic order in this film is previously attributed to multimers of several substitutional Cr atoms [29]. Therefore, multiple magnetic transitions and ordering in our sample could be due to the presence of multimer clusters with different arrangements and sizes. Thus, the complex magnetic nature of Cr-doped Bi₂Se₃ single crystals might open possibilities to discover other quantum states in addition to the QAHE.

In earlier studies, the drastic change in the band structure of a TI due to impurity doping hindered the investigation of the evolution of the TSSs and the bulk bands. In particular, sudden lifetime broadening and an unexpected large gap at the DP were observed in Dy-, V-, Mn-, and Cr-doped Bi₂Se₃ samples grown by MBE [9,10,11,12,13]. On the other hand, the high crystalline quality of the samples studied here can overcome these issues. Figure 3 shows the ARPES momentum (k)–Energy (E) maps of the Bi_2−xCr_xSe₃ single crystals for different x values. The pristine Bi₂Se₃ displays the gapless surface Dirac cone with the DP at 0.36 eV binding energy (Figure 3a). The Cr doping does not lead to a prominent modification on the surface electronic structure of Bi₂Se₃ as seen in Figure 3b,c, which show the ARPES maps for x = 0.1 and 0.22. Even though the ferromagnetic order should open an energy gap at the DP, the energy distribution curves (EDCs) along the k_x = 0 Å⁻¹ superimposed in Figure 3 exhibit the DP without a notable energy gap for any doping level. This might be due to the predicted size of the gap of <10 meV [30], which is beyond our experimental detection limit. In contrast to our observation, a 50 meV gap at the DP of the Bi_1.993Cr_0.007Se₃ sample is reported in a recent synchrotron-based ARPES study [16]. We will later discuss that the light source is also an effective way of manipulating the DP. Therefore, experimental parameters used in photoemission correlated with the distribution of magnetic impurities could be the main sources of difference. In our samples, the only noticeable impact of Cr doping is a slight downward band bending. This shifts the DP to 0.43 eV binding energy for x = 0.22 (Figure 3c). The electron doping can be estimated from the Fermi surface areas enclosed by the TSSs (A_SS) and the bulk bands (A_BB) [31]. The total charge per surface unit cell is given by q = (A_BB + A_SS)/A_BZ, where A_BZ = 2.662 Å⁻² is the area of the surface Brillouin zone (BZ) of Bi₂Se₃. At x = 0.22, nearly ~0.013 e⁻ per unit cell is transferred from Cr atoms into the surface and the bulk bands. The surface charge density (n_e) is then computed by employing n_e = q/A_UC, where A_UC = 44.487 Ų is the area of the unit cell of Bi₂Se₃ in real space and n_e is found ~4.3 × 10¹² cm⁻² for pristine Bi₂Se₃ and ~7.2 × 10¹² cm⁻² for Bi_1.78Cr_0.22Se₃. The ARPES maps in Figure 3 also allow us to estimate the bulk carrier concentration (n_3D) by using the bulk Fermi wave vector k_F where the bulk band crosses the Fermi level. According to n_3D = ${\mathrm{k}}_{\mathrm{F}}^3$/(3 π²) and with k_F = ~0.08 Å⁻¹, n_3D is computed as ~1.7 × 10¹⁹ cm⁻³ for Bi_1.78Cr_0.22Se₃.

We also studied the dispersion of the bulk and surface states of the Bi_1.78Cr_0.22Se₃ single crystal along the perpendicular wave vector (k_z) by varying the incident photon energy (hv); thus, we studied them at different k_z values (Figure 4). TSSs are expected to be k_z-independent due to their 2D nature. This can be seen in the ARPES maps shown in Figure 4a–d where the dispersion remains unchanged under varied hv. The linear TSSs are also clear in the constant energy cuts of the 3D band structure where they form the circular momentum surfaces (Figure 4e). The dispersions of the bulk bands, however, are modified by the incident hv. At hv = 30 eV (k_z = 3.12 Å⁻¹) corresponding to the Γ-point, BCB has a maximum at the binding energy of ~0.24 eV, while it is smeared out from the ARPES map at hv = 50 eV (k_z = 3.87 Å⁻¹) corresponding to the Z-point. Similarly, in the k_z-dispersion of BVB, it is also evident that it reaches the minimum binding energy of ~0.6 eV at hv = 60 eV (k_z = 4.2 Å⁻¹). This gives a large bulk band gap of 0.36 eV where the DP is located. These electronic characteristics are the most important prerequisites for the transport properties to be governed only by TSSs when the DP is pushed to the charge neutral point.

Another advantage of hv-dependent ARPES is to identify the impurity states in the band structure. These states can reshape the Dirac cone and even open a non-magnetic gap at the DP [32,33,34,35]. To exclude this scenario, we recorded the photoemission spectra of the Bi_1.78Cr_0.22Se₃ single crystal at the Cr resonance. In the resonant photoemission process, core level electrons are photoexcited to empty d-derived states above the Fermi level followed by the relaxation process which resonates with direct d-band photoemission, enhancing the density of states of the d-bands. Figure 4f shows the EDCs taken from the Bi_1.78Cr_0.22Se₃ single crystal both on-resonance (hv = 50 eV) [36] and off-resonance (hv = 40 eV) to study the Cr 3p–3d absorption edge. The spectral shape in the vicinity of the DP marked with a dashed red square does not exhibit a prominent modification when hv is switched from on- to off-resonant. The only difference between the spectra arises from the k_z dispersion of the bulk bands located above and below the DP. This shows the absence of the Cr 3d impurity states within the energy interval of the DP. However, we should emphasize that Bi₂Se₃ single crystals have been shown to host additional states at the DP for the different dopants which have been proposed by theoretical works [32,33,34,35], though the inability to resolve the details of the band structure in current MTI thin films hinders confirmation of these predictions.

Due to the strong distortion on the band structure of the transition-metal-doped TIs, the possible magnetic gap at the DP has not been reliably studied in previous works. These difficulties are not present in the MTI single crystals. Therefore, we searched for the magnetic gap by conducting high-resolution laser-based ARPES experiments from the pristine and Cr-doped Bi₂Se₃ single crystals shown in Figure 5a,b, respectively. The spectral feature of the DP was examined in detail by fitting the EDC cuts obtained along the $\overline{\mathsf{\Gamma }}$ point of each spectrum (superimposed in the corresponding figures). Interestingly, the fittings yielded an estimated 16 meV gap even at the DP of the pristine Bi₂Se₃ (Figure 5a). To our knowledge, this anomalous gap was only addressed in TlBiSe₂ TI [8]. One scenario for the non-magnetic gap could be the detachment of the top QLs from the rest of the material during the cleaving which could open a hybridization gap at the DP [37,38]. However, such a scenario would also result in stronger band bending and the formation of quantum well states which we did not observe. Based on our photoemission and structural characterization data, the vacancy-induced modification of the band structure can also be excluded from being a mechanism for opening a non-magnetic gap [35]. We suggest that it is an intrinsic electronic property of Bi₂Se₃ but the understanding of its nature requires more elaborate and detailed study. Whatever its origin is, it is another fertile parameter to engineer the TSSs, modifying the spin texture of the TSSs in the vicinity of the DP.

We also analyzed the EDC cuts along the $\overline{\mathsf{\Gamma }}$ direction in the Bi_1.78Cr_0.22Se₃ ARPES map superimposed in Figure 5b. The Voigt profile fitting of the lower and the upper branch of the DP gives a 30 meV gap at the DP. It is difficult to attribute this gap completely to the magnetic origin since the DP of the pristine sample is already gapped and it is interesting that the gap is not resolved in ARPES experiments conducted with synchrotron radiation at higher photon energies even though the size of the gap for pristine and Cr-doped samples is within our experimental resolution. This suggests that the gap at the DP is correlated with the light source as well as magnetic impurities.

4. Conclusions

In summary, our results reveal that the Cr-doped Bi₂Se₃ single crystals exhibit a well-ordered crystal structure and are free of unexpected distortions on the band structure. We believe that single crystal growth minimizes the dopant clustering and prevents the formation of the other chemical compounds (i.e., Cr_xSe_y). It is also possible to obtain the different structural forms by adopting different growth temperatures and atomic stoichiometry. Similar growth advantages were also utilized in magnetic (MnBi) (Bi₂Te₃)_m self-organized single crystal heterostructures [39]. However, this system still exhibits QAHE only up to a few K, far below the Néel temperature of 23 K [40]. This is possibly due to the bulk band mixing with the TSSs and the involvement of additional symmetry protection of the gapless Dirac cone [41]. Therefore, the absence of these complexities in the surface electronic structure of Bi₂Se₃ makes it one of the most promising candidates for high-temperature QAHE. By taking advantage of the well-defined Dirac cone electronic structure, we have studied the energy gap opening at the DP and found that it exhibits dependence on the photon source and magnetic impurities. Therefore, these results provide new insight into the reshaping of the TSSs in MTIs.