Nonmagnetic band gap at the Dirac point of the magnetic topological insulator (Bi1−xMnx)2Se3

Magnetic doping is expected to open a band gap at the Dirac point of topological insulators by breaking time-reversal symmetry and to enable novel topological phases. Epitaxial (Bi1−xMnx)2Se3 is a prototypical magnetic topological insulator with a pronounced surface band gap of ∼100 meV. We show that this gap is neither due to ferromagnetic order in the bulk or at the surface nor to the local magnetic moment of the Mn, making the system unsuitable for realizing the novel phases. We further show that Mn doping does not affect the inverted bulk band gap and the system remains topologically nontrivial. We suggest that strong resonant scattering processes cause the gap at the Dirac point and support this by the observation of in-gap states using resonant photoemission. Our findings establish a mechanism for gap opening in topological surface states which challenges the currently known conditions for topological protection.

of the main text, we showed a modified Arrot plot according to a 3D Heisenberg ferromagnet [2,3] normalized to the mass of the sample with the exponents = 0.348 and  = 1.41, from which we deduce a T C of 5.5 K. Here we show for the same data a conventional mass-normalized Arrott plot. A similar presentation was used previously [4] for the determination of the ferromagnetic Curie temperature in (Bi 1-x Mn x ) 2 Te 3 . From the present plot, we deduce a by 2 K higher T C .
Supplementary Figure 5: Temperature-dependence of the bulk magnetization. Comparison between field-cooling (FC) and zero-field-cooling (ZFC) measurements obtained using SQUID magnetometry for (a) 4% and (b) 8% Mn doping. The temperature dependence of both the in-plane (ip) and out-ofplane (oop) components of the magnetization is shown. The FC measurements are performed under an applied magnetic field of 10 mT parallel and perpendicular to the surface. The ZFC and FC results are very similar for each composition, and compare well to the surface-sensitive XMCD measurements shown in the main text (see Supplementary Note 2 for details).
Supplementary Figure 6: Surface-sensitive XMCD measurements for 8% Mn-doped Bi 2 Se 3 . The spectra were obtained at the Mn L 3 -edge and a temperature of 20 K under an applied magnetic field of -2T parallel (red circles) and perpendicular to the surface (black solid line). The x-ray beam impinged the sample in normal incidence (black solid line) and at a gracing incidence angle of 30° with respect to the surface plane (red circles); see Supplementary Notes 2 and 4 for details. . Panels (i) and (l) show the average XMCD and XMCD profile, respectively. The scale bar (horizontal white-solid line) shown in (a) is 500 m and applies to all panels. Note the absence of correlation between the different individual measurements as well as the contrast decrease after averaging, indicating absence of ferromagnetic domains at room temperature; see Supplementary Note 3 for more details.
Supplementary Figure 9: Simulations of spectral weight at the Dirac point. (a) Schematic of a topological insulator hosting bulk magnetic impurities (green spheres) with random magnetic moments represented by green arrows. (b) A random magnetic moment in our simplified model is illustrated as a green arrow in the three-dimensional space. The in-and out-of-plane projection of the magnetic moment varies only with the polar angle θ and a randomized collection of magnetic impurities covers the whole polar and azimuthal (φ) range. The dashed line indicates the in-plane projection of the magnetic moment while the dashed circle encloses the full solid angle covered by a specific polar value. (c) Evaluation of the spectral weight using our model for different constraints in the magnetic moment orientation, plotted as a function of the energy away from the Dirac point (E-E D ). The constraints are chosen in accordance with the results of our magnetic characterization, which reveals either preferentially-oriented inplane magnetic moments below T c or random orientations of the Mn magnetic moments above T c . The black curve corresponds to a fully randomized population after integration across all possible values of θ and φ. Blue, green, red and pink curves correspond to randomized magnetic moments constrained by symmetric polar angles with respect to the x-y plane which add up to the total solid angle indicated in the legend.  Figure 14: Spin-resolved measurements. Out-of-plane spin polarization measurements obtained at zero momentum (k II =0) from (a) the (Bi 1-x Mn x ) 2 Se 3 sample with 8% Mn content (x = 0.08) and (b) the (Bi 1-x In x ) 2 Se 3 sample with 2% In content (x = 0.02). No spin polarization perpendicular to the surface is observed in both cases. Measurements in (a) were taken at 20 K, while measurements in (b) at room temperature. In the case of the 8% Mndoped Bi 2 Se 3 sample, a magnetic field of +0.3 T was applied perpendicular to the surface plane at 20 K right before the acquisition of the data (similar results were obtained at room temperature).
Supplementary Figure 15: Photon-energy dependence of the surface gap. Data as in Fig. 5 of the main text for more photon energies. Electronic band dispersions of (a-f) undoped Bi 2 Se 3 , (g-l) 2% and (m-r) 8% Mn-doped Bi 2 Se 3 . The photon energy changes between 16 and 21 eV as indicated in each panel. The red curves are the corresponding energy-distribution curves in normal-emission. The conduction band (CB) and valence band (VB) quantum-well states (QWS) are used to track changes of the bulk band gap. The M-shaped band at higher binding energy has been assigned to a surface state (SS) [5]. The SS may not track the band bending [5] but it tracks here clearly the Mn-induced hole doping. We rely, therefore, on the positions of the most intense CB QWS and VB QWS as observed for similar photon energies before [5]. Here, the separation between CB QWS and VB QWS stays constant within a few meV for 18 eV and within 20 meV when other photon energies are taken into account (horizontal blue, green and pink solid lines). This means that the bulk band gap does not change due to the Mn. The horizontal black-dashed lines in each panel highlight the minimum size of the surface band gap after taking into account the contribution from the linewidth broadening.

Supplementary Note 1: Determination of the surface band gap
To determine the size of the surface band gap for different Mn concentrations, we have fitted the experimental energy-distributions curves (EDCs) at zero momentum extracted from the ARPES spectra acquired at different photon energies. In Supplementary Fig. 2, we show the fit results (black solid lines) of the EDCs (red circles) acquired at 50 eV photon energy and 12 K temperature as an example. Panels (a) to (d) display the fit results from 2 up to 8% Mn, respectively. The size of the surface band gap obtained from the fits is shown in Supplementary Fig. 2d.
Where E i , ω i , and the matrix elements M i are fitting parameters corresponding to the binding energy, width, and intensity of each Lorentzian peak, and f(E,T) is the Fermi function. The spectral function A i (E i ,ω i ) is approximated by Lorentzian functions, and B(E) is assumed to be a Shirley-like background [1]. The full width at half maximum (FWHM) of the Gaussian slit function G(hν) corresponds to the total energy resolution E of the experiment, which is photon-energy dependent.

Supplementary Note 2: Field-cooling, zero-field cooling and XMCD above T c
In Supplementary Fig. 5, we show field-cooling (FC) and zero-field-cooling (ZFC) measurements obtained using SQUID magnetometry for the Mn-doped Bi 2 Se 3 samples with (a) 4% and (b) 8% Mn content. The temperature dependence of both the in-plane and outof-plane components of the magnetization is shown. The FC measurements are taken under an applied magnetic field of 10 mT parallel and perpendicular to the surface. It is clearly seen that the FC and ZFC measurements follow each other for each Mn concentration. In addition, the measured magnetization is always larger or equal for an in-plane magnetic field as compared to an out-of-plane magnetic field at all temperatures. Therefore, there is no sudden change in the orientation of the easy axis above T c , while below T c the easy axis is clearly parallel to the sample surface.
We point out that the SQUID results are sensitive to the magnetization of the bulk, and thus cannot generally be used to rule out static short-range magnetic order above T c at the surface. Nevertheless, we emphasize that one of the main outcomes of our magnetic characterization is that both surface and bulk have basically the same magnetic properties (note the small surface T c enhancement by ≤ 4 K).
In order to further address the possibility of static short-range magnetic order above T c at the surface, in Supplementary Fig. 6 we show XMCD measurements taken for 8% Mn-doped Bi 2 Se 3 at a temperature of 20 K and under an applied magnetic field of -2T parallel (red circles) and perpendicular to the sample surface (black solid lines). Similar results were obtained for 4% Mn doping. Note that even for an applied magnetic field of 2 T, below T c the system is not magnetically saturated irrespective of the Mn concentration (see, e.g., inset of Fig. 4b of the main text), thus it cannot be saturated at 20 K. Moreover, the x-ray beam impinged the sample in normal (black solid lines) and grazing incidence (red circles), meaning that the XMCD measurements shown in Supplementary Fig. 6 are sensitive to the out-ofplane and in-plane components of the magnetization, respectively. In the presence of shortrange static magnetic order, the application of a magnetic field is crucial to verify if above T c a preferential orientation of the Mn magnetic moments perpendicular to the surface exists, which is one of the preconditions for a local band gap opening. However, above T c such a preferential orientation is neither observed in our XMCD nor in our SQUID results described above, indicating that short-range static magnetic order at the surface or in the bulk with preferentially oriented Mn magnetic moments perpendicular to the surface is not responsible for the opening of the large surface band gaps that we observe. Taking into account that under an applied magnetic field above T c there is no such preferential orientation, and that the corresponding XMCD signal without an applied magnetic field is zero, we can conclude that above T c the system is characterized by random orientations of the Mn magnetic moments. We have to stress that in ARPES, static magnetic moments pointing along random directions within the probed area can be viewed as a superposition of different photoemission signals that are spatially averaged (gapped vs. non-gapped states). As canted magnetic moments introduce a gap which varies in size depending on the magnitude of their perpendicular component [6], it is straightforward to demonstrate that in the case of random Mn magnetic moments most of the contributions to the ARPES intensity will be concentrated near the Dirac point (see Supplementary Note 4 for further discussion and analysis).

Supplementary Note 3: Magnetic imaging at the Mn L 3 -edge
To additionally address whether magnetic domains might form, we performed x-ray photoelectron emission microscopy (X-PEEM) experiments at room temperature. The circularly-polarized (90% polarization) x-ray beam impinged the sample at a gracing incidence angle of 16°. With such geometry the experiment is sensitive to both, in-plane and out-of-plane components of the magnetization since both present a projection along the xray beam propagation direction. The lateral resolution is ̴ 20 nm. For magnetic imaging, we exploited the element and magnetic sensitivity of x-ray circular magnetic dichroism (XMCD). In Supplementary Fig. 7, we show a typical absorption spectrum measured for the (Bi 1- x Mn x ) 2 Se 3 sample doped with 8% Mn using X-PEEM. The spectrum is obtained across the Mn L 2,3 -edges from the same region of the sample shown in the XMCD images of Supplementary  Fig. 8, and plotted as the result of the sum of two absorption spectra recorded with opposite light helicity. The lineshape is consistent with the absorption spectra obtained without lateral resolution shown in the main text, revealing a predominant d 5 configuration.
In panels (a), (b), (c), (g) and (h) of Supplementary Fig. 8, we show a total of five consecutive XMCD-PEEM measurements, where the magnetic contrast from exactly the same region of the sample is shown. Each measurement consisted of 160 images (3 seconds integration time each); 80 at the Mn L 3 -edge (40 per helicity) and 80 at the pre-edge (40 per helicity). After normalization to a bright-field the sequence was drift-corrected, and frames recorded using the same photon energy and helicity of the circularly-polarized light were averaged. In order to optimize the magnetic sensitivity, the pre-edge data was subtracted from that measured at the Mn L 3 -edge. The Mn magnetic contrast is then plotted as the difference between the two resulting average images with opposite helicity (after pre-edge subtraction), divided by their sum. The results reveal that there is no correlation between the different images. This can also be clearly seen in the curves plotted below each XMCD image, which correspond to XMCD profiles extracted across the same line [blue dotted line drawn on panel (a)]. Panels (i) and (l) of Supplementary Fig. 8 show the XMCD-PEEM image and the corresponding XMCD profile that result from the average of all individual measurements, respectively. The XMCD contrast for the average XMCD image has decreased by more than a factor five, and lies below the ±1% range. The absence of correlation between measurements, as well as the contrast decrease after averaging indicates that the XMCD signal spans over statistical noise, i.e. there are no ferromagnetic domains with full or partial in-plane or out-of-plane magnetization.

Supplementary Note 4: Short-range magnetic fluctuations and Dirac point spectral weight
As discussed in Supplementary Note 2, our SQUID and XMCD measurements establish that above T c short-range static magnetic order does not play a role in the bulk and at the surface, respectively. We have further supported this conclusion by XMCD-PEEM measurements revealing the absence of short-range inhomogeneous magnetic order, at least within the lateral resolution of our experiment. In this respect, we believe that the agreement and consistency of all individual experiments taken as a whole strongly supports our conclusions, rather than focusing on the individual outcome of a single experiment utilizing a specific technique.
Having said this, the only remaining possibility for a local band gap opening due to magnetism would be magnetic short-range fluctuations. However, we have to stress that for a local band gap opening to fully develop due to short-range magnetic fluctuations above T c , one would again require a preferential orientation of the fluctuating magnetic moments perpendicular to the surface. In this scenario, the argumentation is very similar to the one given in Supplementary Note 2. By applying a magnetic field parallel and perpendicular to the surface above T c , it is in principle possible to determine the existence of such an anisotropy using a slow probe such as XMCD. Our XMCD measurements shown in Supplementary Fig. 6, however, indicate that if short-range magnetic fluctuations are at play above T c , these are not preferentially oriented perpendicular to the surface plane. We emphasize again that under the conditions of the measurements shown in Supplementary  Fig. 6, the system is not magnetically saturated. Taking into account that above T c and without an applied magnetic field the resulting XMCD signal disappears, if short-range magnetic fluctuations are present without an applied magnetic field, these are likely to be random. Moreover, based on the SQUID measurements shown in Supplementary Fig. 5, a similar conclusion can be drawn in the case of magnetic fluctuations in the bulk. We point out that in ARPES, the effect of magnetic fluctuations would similarly result in a complex redistribution of the Dirac point spectral weight, regardless of whether ARPES is a slower or faster probe compared to the time scale of the magnetic fluctuations. The reason is that a large amount of fluctuating magnetic moments pointing along different directions within the probed area can be viewed as a superposition of different photoemission signals that are averaged in space and time (gapped vs. non-gapped states). These signals would emerge with different relative statistical weights depending on how long and which part of the fluctuating magnetic moments is preferentially oriented perpendicular or parallel to the surface. Without a preferential orientation of the fluctuating magnetic moments perpendicular to the surface, most of the contributions to the ARPES intensity will be concentrated near the Dirac point. Note that this is also true for static random Mn magnetic moments, where only the spatial average of the individual signals is important. Using a simplified model, it is possible to show that the same conclusion holds in the case of shortrange random magnetic fluctuations.
For this purpose, we have developed an ergodic model to simulate the spectral weight in the vicinity of the Dirac point for a randomized population of Mn magnetic moments ( Supplementary Fig. 9a). In our model, canted magnetic moments introduce a gap which varies in size from zero to Δ max depending on the magnitude of their out-of-plane component [6] (Supplementary Fig. 9b). For simplicity, we have not considered the additional smearing of the Dirac point intensity along the momentum direction due to inplane magnetic moments. We represent the electronic bands by Gaussian peaks with a fullwidth at half-maximum which is about 30% of the maximum value of the band-gap size located symmetrically with respect to the Dirac point when the gap opens. Note that our model works for any possible generic value of Δ max . In addition, by increasing the broadening of the bands in our model, even when the surface-state linewidth is larger than the maximum possible gap, we obtain very similar results. Supplementary Fig. 9c depicts the evolution of the spectral weight at zero momentum (k II =0) from a fully randomized population of magnetic moments (black line) to configurations where the magnetic moments are restricted to polar angles  around the x-y plane (colored lines), in correspondence with the results of our magnetic characterization. For the sake of clarity, a Shirley-like background has not been considered in this representation. The resulting spectral weight is obtained after integrating all allowed polar angles  over the full range of azimuthal angles in accordance with the rotational symmetry of our problemsee Supplementary Fig. 9b).
We clearly observe that the magnetic moment randomization smears the intensity along the energy axis across the whole gap range. This is due to the fact that the intensity around the Dirac point spans over all possible gaps due to the weighted contributions from random magnetic moments. In particular, the randomization leads to the largest intensity around the Dirac point, while the weakest intensity appears away from the Dirac point near the maximum possible gap corresponding to a purely perpendicular moment, in contrast to our observations. Finally, we would like to stress that based on the results of Ref. 7, and taking into account the small predicted gap size from ab-initio calculations (Δ max 9 meV for Co on Bi 2 Se 3 (Ref. 8) and Δ max 16 meV for Mn in Bi 2 Te 3 (Ref. 9), it is difficult or almost impossible to anticipate static short-range magnetic order or short-range magnetic fluctuations as the reason for the large 100 meV gap observed in our work and in Ref. 10.

Supplementary Note 5: X-ray diffraction
From the x-ray diffraction data taken in symmetric  scans we determined the c-lattice parameter and estimated also the changes in the bilayer distances within the Bi 2 Se 3 quintuplets. In Supplementary Figs. 10 -13 we present the measured and simulated  scans (upper panels) as well as their details around the diffraction maxima 000.12 to 000.21 (lower panels). The values of the c-lattice parameters determined from the positions of the diffraction maxima are presented in Supplementary Table 1.
As expected, the c-lattice parameter increases with increasing Mn content. We have simulated the diffraction curves using standard x-ray kinematical diffraction theory, including the effects of partial polarization of the primary beam, absorption correction and the correction to the irradiated sample surface. The aim of the simulation was to compare the heights of the measured diffraction maxima with the theoretical prediction, since the heights are proportional to the square of the (Bi 1-x Mn x ) 2 Se 3 structure factor that sensitively depends on the distance of individual bilayers.
In the simulations we assumed nominal bilayer distances relative to the measured c values, these relative distances were taken from the PDF-4 database [11], the results of the simulations are plotted by blue lines. As we demonstrated in our previous paper [12], the quasi-forbidden diffraction maximum 000.12 is extremely sensitive to the bilayer spacings. From our simulations it follows that even for pure epitaxial Bi 2 Se 3 , the individual bilayer distances in the unit cell do not correspond to the values in Ref. 11, which were determined from the diffraction data on bulk single crystals. We tried to improve the correspondence of the measured and simulated diffraction curves by changing the values of the bilayer distances keeping their sum d Se-Se +2(d Se-Bi +d Bi-Se ) within one quintuplet constant and equal to c/3, since three quintuplets create one Bi 2 Se 3 elementary unit cell.
The best correspondence (yet not good enough) was achieved by changing the Se-Se distance by d Se-Se and that of the first neighboring Se-Bi bilayer by d Se-Bi ; their values are summarized in Supplementary Table 2.
The modified calculation results are denoted by red curves in Supplementary Figs. 10 -13. With increasing Mn content the diffraction maxima get broader and for the highest Mn content of 8% the maxima are deformed so that an exact determination of the d values is not possible. However, the table clearly indicates a possible expansion of the van der Waals Se-Se bilayer due to the Mn atoms. The broadening of the maxima is caused with a deterioration of the crystal quality with increasing x Mn . The nature of the structure defects is not clear, most likely planar defects like stacking faults or Bi-Bi bilayers randomly placed in the lattice are responsible for this broadening. In the simulations this effect was included by decreasing the mean number of quintuple layers creating one coherently diffracting domain (see Ref. 12 for details).

Supplementary Note 6: One-step model calculations
Using the results of ab-initio theory within the coherent potential approximation as an input, we have performed additional calculations within the one-step model of photoemission [13]. The calculations are based on multiple scattering theory including wave-vector and energydependent transition matrix elements [14]. We use a fully relativistic version which is part of the Munich SPR-KKR program package [15], with spin-orbit coupling included by solving the four-component Dirac equation. In particular, the one-step model photoemission calculation for Mn-doped Bi 2 Se 3 was done using the implemented version for disordered magnetic materials [16], while the calculation for the undoped Bi 2 Se 3 system was done using the implemented version for ordered materials in its spin-density matrix formulation [17].
In Figure 17, We attribute the additional deviations between experiment and theory to the fact that we use an atomic-sphere approximation in the electronic structure calculation which, moreover, leads to an overestimation of the surface contribution. Considering that the calculated dispersions are very sensitive to the geometrical structure of the first few layers, a fullpotential electronic structure calculation would improve the agreement. Nonetheless, we emphasize again that these deviations do not prevent us from capturing the main physics underlying the origin of the gap in the calculations. In the framework of a fully selfconsistent full-potential electronic structure calculation an even closer agreement between experiment and theory concerning the electronic structure is expected. To obtain an even higher level of agreement in a spectroscopical calculation, a fully relativistic full-potential photoemission theory that is intimately based on the corresponding input from a selfconsistent SPR-KKR half-space calculation would be needed, which is still an important task for future studies. It would be a very important step forward to implement such a photoemission theory in the framework of the one-step model, as it has not been done so far. In this way, future spectroscopical calculations could probably deal with full-potential based electronic structure inputs.

Supplementary Note 7: Non-magnetic impurities
As mentioned in the main text, we have performed additional control experiments using nonmagnetic Sn and In impurities in Bi 2 Se 3 . These experiments have been performed for both epitaxial films and bulk single crystals, from which we have obtained similar results for both types of impurities. In Supplementary Fig. 18  It can be clearly seen that after doping with Sn ( Supplementary Fig. 18b), no surface band gap opens at the Dirac point, a result that we can confirm up to high-levels of Sn concentrations. On the other hand, our Bi 2 Se 3 sample doped with 2% In (Supplementary Fig.  18d) clearly exhibits the opening of a large surface band gap, which is of the order of 100 meV, a result that is completely in contrast to the case of the sample doped with 4% Sn concentration. Interestingly, the size of the surface band gap for the In-doped Bi 2 Se 3 sample is of the same order of the gap observed for the 8% Mn doped Bi 2 Se 3 sample. This indicates that the concentration range at which the large surface gap develops varies from dopant to dopant, a fact which based on the ideas proposed in papers like Refs. 18,19 might be associated with the impurity-dependent strength of the Coulomb U, regardless whether the dopant is magnetic or not.
As mentioned in the main text, we emphasize that in the case of In-doped Bi 2 Se 3 samples a topological to trivial quantum-phase transition is known to exist (see, e.g., Ref. 20). Therefore, we have examined the bulk band gap in a wide range of In concentrations across the quantum-phase transition. The results are shown in Supplementary Fig. 18e, where in addition to the bulk band gap (red solid symbols) we plot the size of the surface band gap (green solid symbols). The size of the bulk band gap is obtained from photon-energy dependent ARPES measurements as they track the dispersion of the bulk-bands perpendicular to the surface. In the ARPES measurements, we typically observe that the bulk band gap decreases progressively up to concentrations of about 5% In. The ARPES spectra reveal that above 5% In the bulk band gap increases again, and finally reaches a value above 0.4 eV for 8% In doping which is larger than the bulk band gap in pure Bi 2 Se 3 . The bulk band gap extracted from the ARPES spectra reveals a clear minimum somewhere around 4 to 5% In concentration. This can be obtained with some degree of accuracy by a parabolic fit of the bulk band dependence with In concentration. Moreover, the concentration at which the bulk band inversion occurs fits well with our preliminary optical measurements. Thus, in Supplementary Fig. 18e, we reverse the sign of the bulk band gap for In concentrations above 5% to illustrate the inversion of the bulk bands more clearly, and mark the region of the inversion point by a red colored area. The changes are also highlighted by a red-dashed line, which is a guide to the eye, as the bulk band dependence with In concentration might not be necessarily linear. These results are very reproducible, cleavage-to-cleavage, and confirm the existence of an inversion point, in addition to the fact that the large surface gap opening observed in Supplementary Fig. 18d for 2% In doped-Bi 2 Se 3 samples occurs in the topological side of the quantum-phase transition. Our control experiments demonstrate the existence of a novel mechanism for surface band gap opening which is not directly connected to long-range or local magnetic properties.
Another interesting aspect is related to the linewidth broadening of the surface states near the Fermi level. If we compare the ARPES spectra shown in panels (a) and (c) of Supplementary Fig. 18 for Bi 2 Se 3 epitaxial layers and bulk crystals, respectively, we can observe that the linewidth of the MBE-grown films is larger than the one of the bulk crystals, which is always the case for samples measured under the same experimental conditions. We attribute the additional broadening in the MBE-grown films to surface disorder, since disorder degrades the surface quality. At the same time, this means that surface disorder does not open a surface band gap at the Dirac point, otherwise it should have been observed in Supplementary Fig. 18a for pure Bi 2 Se 3 films. Moreover, note that at 4% Sn doping in Supplementary Fig. 18b the broadening does not increase substantially, in contrast to the case of 2% In doping ( Supplementary Fig. 18d), where in addition to the opening of a surface band gap the broadening increases drastically. These differences suggest that an important contribution to the linewidth broadening originates from the surface band gap opening. This result motivates us to examine more closely the relation between the linewidth broadening and the size of the surface gap opening in both In-doped and Mn-doped samples, as the additional broadening can also be observed for the Mn-doped Bi 2 Se 3 films.
In Supplementary Fig. 19 respectively. This similarity strongly suggests that the mechanism underlying the surface band gap opening in both Mn and In-doped samples has the same origin, namely that the additional linewidth broadening is most likely caused by resonant processes of non-magnetic scattering for both types of impurites. This conclusion is further supported by the fact that our spin-resolved ARPES measurements shown in Supplementary Fig. 14 reveal that the outof-plane spin polarization measured at zero momentum is zero for both gapped Dirac cones in Mn-doped ( Supplementary Fig. 14a) and In-doped ( Supplementary Fig. 14b) samples. The absence of a hedgehog spin texture in Mn-doped films and the similarity to the results for Indoped samples pinpoints a non-time reversal symmetry breaking mechanism underlying the origin of the surface band gap, a fact that is also consistent with our conclusions derived from the magnetic properties of the Mn-doped films.

Supplementary Note 8: Sample Growth and Structural Characterization
The In-doped bulk crystals were grown from the melt by the Bridgman method, and the growth time including cooling was about 2 weeks for a ∼50 g crystal. Mn-doped Bi 2 Se 3 layers were grown by molecular beam epitaxy (MBE) on cleaved (111) BaF 2 substrates, and a similar growth procedure as the one described here was employed for Sn-doped Bi 2 Se 3 films. For the growth of Mn-doped Bi 2 Se 3 samples, the molecular beams were generated using a compound bismuth selenide effusion cell, a Mn cell, and an additional selenium cell for stoichiometry control. A whole series of samples was grown in which the Mn concentration was varied between 0 and 8%. The MBE growth was carried out at a substrate temperature of 380°C and growth rates around 0.2 QL/sec or ∼2Å/sec at a background pressure ≤ 5×10 −10 mbar. The flux rates from the individual sources were precisely measured using a water cooled quartz crystal microbalance moved into the substrate position. The resulting mass deposition rates were converted into flux rates of atoms arriving at the surface per unit area using the densities and molar masses of the different constituents. The Mn concentration x Mn was determined from the obtained Mn to Bi 2 Se 3 flux ratio, i.e., the ratio of arriving Mn atoms relative to the number of (Bi + Mn) atoms. The concentrations derived in this way were in good agreement with the concentrations determined by electron microprobe x-ray analysis as well as the concentrations determined from the core-level peaks in the photoemission spectra. A high excess of Se flux above 2 Å/sec was provided for all samples, which corresponds to an overall Se-to-Bi(Mn) flux ratio of ∼ 5:1.
As shown by the reflection high-energy electron diffraction patterns and atomic force microscopy images presented in Supplementary Fig. 20, under these conditions the growth of (Bi 1-x Mn x ) 2 Se 3 proceeds in a pure 2D mode irrespective of the Mn concentration, resulting in 2D diffraction streaks normal to the surface as well as a terraced surface structure mostly exhibiting quintuple layer steps. According to our x-ray diffraction results presented in Supplementary Figs. 10 -13, the crystal structure of the epilayers exclusively shows a c-axis orientation perpendicular to the surface. The bulk cubic lattice constant of BaF 2 is 6.200 Å and the in-plane lattice constant of the (111) surface 4.384 Å compared to a = 4.138 Å for Bi 2 Se 3 . In spite of this lattice mismatch, our layers are found to be fully relaxed from x-ray diffraction. All (Bi 1-x Mn x ) 2 Se 3 epilayers exhibit n-type conduction with electron densities in the range of 1-5×10 19 cm −3 that only gradually increases with increasing Mn content.

Supplementary Note 9: Core-level photoemission
In Supplementary Fig. 21, we show x-ray photoemission (XPS) spectra of the Mn-doped sample with 8 % concentration. The XPS measurements were taken at an electron kinetic energy of 70 eV for (a) Mn 2p, (b) Se 3d and (c) Bi 5d core levels. The Mn 2p core level clearly contains dominant Mn 2+ (d 5 ) contributions. We observe a Mn 2+ (d 5 ) component (640.7 eV) with some other contributions of Mn +1 (639.6 eV) and Mn +3 (641.7eV) which are not well resolvable, plus a pronounced Mn 2+ (d 5 ) satellite. Both Se 3d and Bi 5d high-resolution spectra demonstrate a multicomponent structure as compared to clean Bi 2 Se 3 , with two additional components being related to the chemical bonds to Mn atoms. Similar measurements were carried out for other Mn concentrations. The composition of the samples was confirmed by the XPS measurements with an accuracy of 1 mole %. The composition was quantified using atomic sensitivity factors and taking into account the calibration of the analyzer transmission function. For x=0.08 we found Mn/Bi=0.074, for x=0.04 Mn/Bi=0.044 correspondingly.