Infrared study of the multiband low-energy excitations of the topological antiferromagnet MnBi2Te4

PHYSICAL REVIEW B 103, L121103 (2021) Letter Infrared study of the multiband low-energy excitations of the topological antiferromagnet MnBi2Te4 Bing Xu ,1Y. Zhang,2E. H. Alizade ,3Z. A. Jahangirli ,3,4F. Lyzwa,1E. Sheveleva ,1P. Marsik,1Y. K. Li,5,6 Y. G. Yao,5,6Z. W. Wang,5,6,*B. Shen ,2,†Y. M. Dai,7V. Kataev ,8M. M. Otrokov,9,10 E. V. Chulkov,11,12,13 N. T. Mamedov ,3,‡and C. Bernhard1,§ 1University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland 2Sate Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China 3Institute of Physics, Azerbaijan National Academy of Sciences, Baku AZ1143, Azerbaijan 4Baku State University, Z. Khalilov str. 23, AZ1148, Baku, Azerbaijan 5Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China 6Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing 100081, China 7National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China 8Leibniz Institute for Solid State and Materials Research IFW Dresden, 01069 Dresden, Germany 9Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Basque Country, Spain 10IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Basque Country, Spain 11Donostia International Physics Center, 20018 Donostia-San Sebastian, Basque Country, Spain 12Departamento de Física de Materiales UPV/EHU, 20080 Donostia-San Sebastian, Basque Country, Spain 13Saint Petersburg State University, Laboratory of Electronic and Spin Structure of Nanosystems, 198504 Saint Petersburg, Russia (Received 19 September 2020; accepted 5 February 2021; published 3 March 2021) With infrared spectroscopy, we studied the bulk electronic properties of the topological antiferromagnet MnBi2Te4with TN≃25 K. With the support of band-structure calculations, we assign the intraand interband excitations and determine the band gap of Eg≈0.17 eV. We also obtain evidence for two types of conduction bands with light and very heavy carriers. The multiband free-carrier response gives rise to an unusually strong increase of the combined plasma frequency, ωpl, below 300 K. The band reconstruction below TNyields an additional increase of ωpl and a splitting of the transition between the two conduction bands by about 54 meV. Our study thus reveals a complex and strongly temperature-dependent multiband low-energy response that has important implications for the study of the surface states and device applications. DOI: 10.1103/PhysRevB.103.L121103 The research effort on topological quantum materials [1–4] has recently been extended to systems with magnetic order, which enable a variety of field-controlled quantum states [5–13], such as the quantum anomalous Hall (QAH) effect [6–8], the topological axion state [9–12], and Majorana fermions [2,13]. Such materials have been obtained, e.g., by creating heterostructures from magnetic and topological materials or by adding magnetic defects to topological materials. With the latter approach, the QAH effect was realized for the first time in Cr-doped (Bi,Sb)2Te3films [7]. The ideal candidates, however, are bulk topological materials with intrinsic magnetic order for which various problems inherent to thin film growth and defect engineering can be avoided. A promising candidate is MnBi2Te4(MBT), which is a topological insulator with A-type antiferromagnetic (AFM) order as predicted by theory [14–17] and recently confirmed *[email protected] †[email protected] ‡[email protected].az §[email protected] by experiments [18–31]. Notably, the bulk AFM transition at TN≃25 K has been predicted to strongly affect the electronic states at the (0001) surface, since it creates a gap on the Dirac cone [14–16,18]. Moreover, for thin films the topological properties should depend on the number of MBT layers such that an axion insulator or a QAH insulator appears for even and odd numbers, respectively [14,15]. A quantized Hall conductance has indeed been observed in few-layer MBT films [26–28], albeit only in magnetic fields of 5–10 T that change the magnetic order to a ferromagnetic one [27,28]. The properties of the surface of MBT single crystals are also debated. For example, the formation of a gap below TNof the Dirac cone at the (0001) surface is seen in some angle-resolved photoemission spectroscopy (ARPES) studies [18–21] but not in others [32–36]. This calls for further studies of the surface structural and magnetic properties [33]. Likewise, the bulklike low-energy excitations and their modification in the AFM state are still not fully understood. Here we study the bulk electronic properties of MnBi2Te4 crystals with infrared spectroscopy. In combination with band-structure calculations, we assign the intraand interband excitations and estimate the inverted bulk band gap and the 2469-9950/2021/103(12)/L121103(6) L121103-1 ©2021 American Physical Society BING XU et al. PHYSICAL REVIEW B 103, L121103 (2021) FIG. 1. (a) T-dependent resistivity of the MnBi2Te4sample A. The arrow marks the AFM transition at TN≃25 K. (b) Hall resistance Rxy of sample A at 30 K. (c) Tdependence of the reflectivity up to 6000 cm−1.Inset:Spectrumupto50000cm −1at 300 K. (d) T dependence of the real part of the dielectric function ε1(ω). Inset: Screened plasma frequency obtained from the zero crossing of ε1(ω). chemical potential. We also study the excitations of the free carriers and determine their plasma frequency. The latter has a surprisingly low value and an unusual Tdependence, with a pronounced anomaly below TN. We show that this anomalous behavior can be explained in terms of two conduction bands with largely different effective masses. Below TNwe also identify a splitting of the transitions between the light and heavy conduction bands (by about 54 meV) that arises from the magnetic coupling between the conduction electrons and the localized Mn moments and agrees with the one seen with ARPES [34–37]. This information about the multiband nature of the free carriers and their low-energy excitations is a prerequisite for understanding the plasmonic properties in the bulk as well as of the surface states and their eventual device applications. In the first place, it calls for attempts to reduce the defect concentration and thus the n-type doping such that a simpler single band picture applies. Two batches of MBT single crystals were grown with a flux method [31] at Sun Yat-Sen University (Sample A) and Beijing Institute of Technology (Sample B). Both have a metallic in-plane resistivity with an anomaly around TN≃25 K, as shown in Fig. 1(a) for sample A. The negative Hall-resistivity ρxy of sample A in Fig. 1(b) indicates electronlike carriers with a concentration of n=1.7×1020 cm−3, in agreement with most previous studies [21–23,38,39]. Details about the infrared reflectivity measurements and the Kramers-Kronig analysis are given in Sec. A of the supplemental material (SM) [40]. FIG. 2. (a) T-dependent optical conductivity of MnBi2Te4up to 8000 cm−1. The symbols on the yaxis denote σDC at 10 and 300 K from the transport data in Fig. 1(a). Inset: Spectrum up to 50 000 cm−1at 300 K. (b) T-dependent spectra of 2 2(ω). The dashed line shows a linear extrapolation toward the zero crossing of 2 2(ω) to obtain the onset of the direct interband transitions, Edir.(c)T dependence of the spectral weight for different cutoff frequencies. (d) Tdependence of Edir. Figure 1(c) shows for sample A the temperature (T)- dependent reflectivity R(ω) up to 6000 cm−1.Theinsetshows the room-temperature spectrum up to 50 000 cm−1.Below about 1500 cm−1there is a sharp upturn of R(ω) toward unity that is characteristic of a plasma edge due to the itinerant carriers. This plasma edge shifts to higher frequency as the T decreases, indicating an enhancement of free carrier density, n, or a reduction of effective mass, m∗. Very similar spectra have been obtained for sample B (see Sec. B in the SM [40]), thus the following discussion is focused on sample A. Figure 1(d) displays the Tdependence of the real part of the dielectric function ε1(ω). The spectra reveal an inductive behavior with a downturn of ε1(ω) toward negative values at low frequency that is another hallmark of a metallic response. The sharp features at 47, 84, and 133 cm−1are infrared-active phonons that are not discussed further here. The horizontal dashed line shows the zero crossing of ε1(ω), which marks the screened plasma frequency ωscr pl =ωpl/√ε∞, where ε∞is the high-frequency dielectric constant and ωpl =ne2/0m∗ is the free-carrier plasma frequency. The inset details the T dependence of ωscr pl , which reveals an unusually large increase from about 750 cm−1at 300 K to 880 cm−1at 30 K. There is also a sudden, additional increase below TNto about 910 cm−1at 10 K, which provides a first spectroscopic indication that the AFM order has a pronounced effect on the electronic properties. Figure 2(a) displays the Tdependence of the real part of the optical conductivity σ1(ω) up to 8000 cm−1.Theinset shows the 300 K spectrum up to 50 000 cm−1which is dominated by two interband transitions with bands around 12 500 and 20 000 cm−1, in agreement with Ref. [45]. The optical response below 8000 cm−1consists of a Drude peak with a tail extending to about 2000 cm−1that is well separated from the onset of strong interband transitions above 3000 cm−1. L121103-2 INFRARED STUDY OF THE MULTIBAND LOW-ENERGY … PHYSICAL REVIEW B 103, L121103 (2021) FIG. 3. (a) Schematic of the band structure of MnBi2Te4in the paramagnetic (upper panel) and AFM (lower panel) states. (b) DrudeLorentz fit of the conductivity at 30 K around the lowest interband-transition. (c) T-dependent spectra showing the anomaly below TN≃25 K. (d) Difference plots of σ1(ω) and corresponding fits of the band splitting. Lorentz fits of the low-energy interband transition at 30 and 10 K and of the split bands at 10 K assuming (e) a symmetric and (f) an asymmetric band splitting. Tdependence of the fit parameters of the split bands obtained (g) and (h) with the symmetric and (i) the asymmetric model. The Drude peak grows upon cooling, consistent with the increase of ωscr pl in Fig. 1(d). The dc conductivity data at 10 and 300 K from Fig. 1(a) (squares on the y-axis) agree with the zero-frequency extrapolation of σ1(ω). The width of the Drude peak of about 500 cm−1is nearly T-independent and much larger than, e.g., in Bi2Te3[46]. The scattering thus seems to be dominated by disorder effects, e.g., due to Mn-Bi antisite defects [19]. The Tdependence of the onset of the strong interband transitions, Edir, that are most likely direct transitions across the band gap, Eg, between the valence band (VB) and the conduction band (CB), has been obtained with a linear extrapolation of 2 2(ω), as shown in Fig. 2(b).It increases toward low T, but it decreases suddenly below TN [see Fig. 2(d)]. The spectral changes have been further analyzed by calculating the evolution of the spectral weight (SW), S(ωc)= ωc 0σ1(ω)dω, for different cutoff frequencies ωc. Figure 2(c) shows the Tdependence of the ratio S(ωc,T)/S(ωc,T= 300 K) at representative cutoffs. At ωc=500 and 2000 cm−1, where the free-carrier response dominates, the SW increases toward low Tand exhibits an additional upturn below TN,in agreement with the trend of ωscr pl in Fig. 1(d). At the higher cutoffs, this increase becomes less pronounced until at ωc= 8000 cm−1(1 eV) it is almost constant. This confirms that the SW redistribution is confined to energies below 1 eV. Next, we analyze in more detail the response below 2000 cm−1, which contains in addition to the Drude response a weak band due to a low-energy interband transition. This is evident in Fig. 3(b), which displays the σ1(ω) spectrum at 30 K together with a Drude-Lorentz fit. It reveals a band centered around 1100 cm−1that overlaps with the tail of the Drude response. The fit function contains two Drude-terms with different plasma frequencies and scattering rates of ωpl,1=6215 cm−1,1/τ1=520 cm−1and ωpl,2=1870 cm−1,1/τ2=150 cm−1, respectively. The band at 1100 cm−1is described by a Lorentz function. Details about the Drude-Lorentz analysis are given in Sec. C of the SM [40]. Figure 3(a) shows a schematic of the band structure in the vicinity of the chemical potential that is consistent with our optical data, with our band calculations along the -Y direction (see Sec. E in the SM [40]) and also with reported ARPES data [33–35]. In addition to a pair of conduction and valence bands that is forming an inverted band gap (CB1 and VB1), it contains a second conduction band (CB2) that is located slightly above CB1 and has a very flat bottom and thus a very large effective mass. As shown in the following, our optical data suggest that the chemical potential, μ, is crossing both CB1 and CB2 (at low temperature). This assignment is consistent with the use of two Drude-peaks in fitting the low-energy response in the previous paragraph. It also accounts for the weak band around 1100 cm−1in terms of the interband transitions between CB1 and CB2 (red arrow). The optical excitations at higher energy involve transitions across the direct band gap Eg, from the VB to the empty states in CB1 and CB2, as illustrated in Fig. 3(a) by the orange arrows. Note that if μwould not be crossing CB2, the transition between the top of VB1 and the bottom of CB2, which are both rather flat and optically allowed, would give rise to a strong peak near Edir that is clearly not seen in the spectra of Fig. 2(a). On the other hand, a pronounced peak around 3350 cm−1(415 meV) has been observed in the corresponding spectra, which were taken on the as-grown surface of the same sample (see Sec. D in the SM [40]). This implies that for the as-grown surface, the chemical potential is somewhat lower, such that it falls below CB2. Such a reduction of the free-carrier concentration might be caused, for example, by the localization of carries on extrinsic defects or by a lower L121103-3 BING XU et al. PHYSICAL REVIEW B 103, L121103 (2021) concentration of intrinsic defects that are responsible for the n-type doping. With this band assignment, we can estimate for the cleaved MBT surfaces the low-Tvalue of the chemical potential μby using the expressions μ=¯h2k2 F/2m∗= (¯h2/2m∗)(6π2n/gsgb)2/3, with the Fermi vector kF, the carrier density n=1 (2π)34 3πk3 Fgsgb, and the spin and band degeneracies gs=2 and gb=2[15,16,47]. Using n1=0.517 × 1020 cm−3and n2=1.183 ×1020 cm−3(see Sec. C in the SM [40]),aswellasm∗ 1=0.12meand m∗ 2=3meaccording to the band-structure calculations (see Sec. E in the SM [40]), we derive μ1=0.266 eV and μ2=0.019 eV for CB1 and CB2, respectively. Accordingly, with an estimate of Edir ≃ 0.415 eV for the direct interband transition between VB1 and CB2 around the point, we derive a band gap of Eg≈ Edir +μ2−μ1=0.17 ±0.02 eV at 30 K (as explained in Sec. F of the SM [40], the largest uncertainty arises from the estimate of μ2), which agrees well with the reported values from band calculations and ARPES [15–21,33–35]. Next, we focus on the band reconstruction below TN,especially on the anomalous changes of the interband transition at 1100 cm−1, which provide evidence for a magnetic splitting of CB1. In the paramagnetic state, the σ1(ω) spectra in Fig. 3(c) exhibit a monotonic increase in this frequency range that arises mainly from the growth of the Drude SW, as shown in Figs. 1(d) and 2(c).BelowTN, this trend is suddenly interrupted, i.e., σ1(ω) decreases from about 500– 1200 cm−1whereas it gets anomalously enhanced between 1200 and 2000 cm−1. These anomalous changes, which are detailed in Fig. 3(d) in terms of the difference spectrum of σ1(ω) at 30 and 10 K, are characteristic of a splitting of the conduction band CB1 into CB1a and CB1b, as indicated in the lower panel of Fig. 3(a). An additional contribution that arises from a much weaker and almost featureless Tdependent change of the background, which occurs also above TN, has been corrected using the difference between 30 and 50 K (olive line). This band splitting, which is caused by the exchange interaction of the conduction electrons with the Mn moments, which lifts the band degeneracy due to the unit cell doubling in the AFM state, is also seen in recent ARPES studies [34–37]. Note that the magnetic splitting of CB2 is assumed to be much smaller and thus is neglected. This assumption is supported by ARPES data [34–37], and also by a comparison of the density of states at the Fermi level derived from our optical data with the Korringa-slope of the ESR data in Ref. [18], as outlined in Sec. H of the SM [40]. The successful modeling of the data in Fig. 3(d) confirms that the spectral changes below TNarise from a corresponding splitting of the interband transitions from CB1a to CB2 and CB1b to CB2. It has been obtained with the function σ1(ω)=La(ωa,γ a,Sa)+Lb(ωb,γ b,Sb)−L(ω0,γ,S), for which Lrepresents the Lorentz function, and the subscripts aand bdenote the interband transitions from the split bands. The parameters in the paramagnetic state have been obtained from a Drude-Lorentz fit at 30 K. We have used two different approaches to model the changes below TN. The first one assumes a symmetric splitting of the bands with |ωa−ω0|=|ωb−ω0|,γa=γb=γ, and S2 a+S2 b=S2. The second one allows for an asymmetric band splitting but fixes their spectral weights to |ωa−ω0| =|ωb−ω0|,γa= γb=γ, and S2 a=S2 b=S2/2. The orange and red curves in Fig. 3(d) show that both models allow us to reproduce the S-shaped feature of σ1(ω, 10 K) −σ1(ω, 30 K). The contributions of the individual bands CB1a and CB1b as obtained from the two models are shown in Figs. 3(e) and 3(f), respectively. The symmetric model yields a splitting of |ωa−ω0|= |ωb−ω0|=27 meV at 10 K, and for the asymmetric one it amounts to |ωb−ω0|=32 meV and |ωa−ω0|=17 meV. The Tdependence of the obtained fit parameters is displayed in Fig. 3(g) for the weights S2 aand S2 bobtained with symmetric band splitting and in Figs. 3(h) and 3(i) for the corresponding positions ωaand ωbfor the symmetric and asymmetric models, respectively. Note that the splitting of CB1 (and likely a corresponding splitting of VB1) can also account for the anomalous decrease of Edir below TN, since it reduces Eg. Finally, we return to the unusually large increase of ω2 pl toward low Tand its pronounced anomaly below TN.The ∼20% increase between 300 and 30 K can hardly arise from a volume contraction effect that would imply a giant expansion coefficient of 4 ×10−3K−1. Likewise, the anomalous increase of ω2 pl below TNwould require unrealistically large magnetostriction effects. Instead, we propose that the strong increase of ω2 pl toward low Tresults from an exchange of conduction electrons between the light and very heavy states in CB1 and CB2 [48–52]. Due to their largely different effective masses, the distribution of electrons is strongly dependent on the relative position of CB1 and CB2 with respect to the chemical potential. Accordingly, the Tdependence of the chemical potential accounts for the observed change of ω2 pl in the paramagnetic state (see Sec. F in the SM [40]). The anomalous increase of ω2 pl below TNrequires in addition a small shift of the center of CB1a and CB1b against CB2 of ∼10 meV (see Sec. G in the SM [40]), which is indeed comparable to the shift obtained with the asymmetric band-splitting model in Figs. 3(f) and 3(i). Note that the corresponding effect of the magnetic slitting of CB1a and CB1b is weaker and of the opposite sign (see Sec. G in the SM [40]). We would also like to mention that for the majority of degenerate doped narrow gap semiconductors, ωpl exhibits a much weaker Tdependence and usually decreases upon cooling due to the freeze-out of carriers. Interestingly, another rare exception, for which ω2 pl exhibits a similarly strong increase toward low T,isBi 2Te3. While the samples studied in Ref. [53] were hole-doped, in analogy to MBT, they may also have light and very heavy valence electrons. In summary, we determined the bulk, optical properties of the AFM topological insulator MnBi2Te4. In combination with band-structure calculations, we assigned the intraand interband excitations and obtained a bulk band gap of Eg≈0.17 eV. We also provided evidence for two conduction bands with largely different effective masses of 0.12 and 3 me and chemical potentials of 0.266 and 0.019 eV (at 30 K). A T-dependent transfer of electrons between these conduction bands and the subsequent change of the average effective mass can account for an unusually strong Tdependence of the free-carrier plasma frequency, ωpl.BelowTN≃25 K, we observed clear signs of a band reconstruction in terms of an additional, anomalous increase of ωpl and a splitting of L121103-4 INFRARED STUDY OF THE MULTIBAND LOW-ENERGY … PHYSICAL REVIEW B 103, L121103 (2021) the transition between the conduction bands. This detailed information about the bulk band structure and the multiband charge-carrier response is a prerequisite for the understanding of the plasmonic properties of the bulk and surface states and their device applications. We acknowledge discussions with A. Akrap, G. Khalliulin, and Z. Rukelj. The work in Fribourg was supported by the Schweizerische Nationalfonds (SNF) through Grant No. 200020-172611. V.K. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) through Grant No. KA1694/12-1. N.M. acknowledges the support of the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. E˙ IF-BGM-4-RFTF1/2017-21/04/1-M-02). The work at Beijing was supported by the Natural Science Foundation of China (NSFC Grant No. 11734003), the National Key R&D Program of China (Grants No. 2016YFA0300600 and No. 2020YFA0308800), and the Beijing Natural Science Foundation (Grant No. Z190006). Z.W. acknowledges the support from Beijing Institute of Technology Research Fund Program for Young Scholars. B.S. acknowledges the support of the Fundamental Research Funds for the Central Universities, Grant No. 19lgpy260. E.V.C. acknowledges Saint Petersburg State University (Grant No. ID 73028629). Y.M.D. acknowledges the support of the Natural Science Foundation of China (Grant No. 11874206). M.M.O. acknowledges the support by Spanish Ministerio de Ciencia e Innovación (Grant No. PID2019-103910GB-I00). [1] M. Z. Hasan and C. L. Kane, Rev. Mod. 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