Supplementary Information for SUPPLEMENTARY INFORMATION · conduction band (BVB/BCB) varies dramatically with photon energy from Fig. 2S (a – j). Besides the dispersion along the

Discovery of a single topological Dirac fermion in the strong inversion asymmetric compound BiTeCl

Supplementary Information for

Discovery of a Single Topological Dirac Fermion in a Strong

Inversion Asymmetric Compound BiTeCl

Y. L. Chen, M. Kanou, Z. K. Liu, H. J. Zhang, J. A. Sobota, D. Leuenberger, S. K.

Mo, B. Zhou, S.-L. Yang, P. S. Kirchmann D. H. Lu, R. G. Moore,

Z. Hussain, Z. X. Shen, X. L. Qi, T. Sasagawa

This file includes:

Part A: More measurements showing asymmetric electronic structures between

opposite crystal surfaces.

Part B: Surface nature of the Dirac cone and more details on the band structure of

BiTeCl

Part C: Fermi-surface across multiple Brillouin zones (BZs) of BiTeCl

Part D: ARPES circular dichroism

Part E: Calculation on the charge distribution of Bi2Te3 and HgTe

Part F: Rashba band structure occasionally observed and calculations

Part G: Effect of unpassivated surface charges on cleaved crystal in UHV

Part H: Rashba splitting of BiTeI bulk valence band (BVB)

Figures: Fig. S1 to Fig. S7

Movie clips: Movie_S1.mov and Movie_S2.mov

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS2768

NATURE PHYSICS | www.nature.com/naturephysics 1

http://www.nature.com/doifinder/10.1038/nphys2768

Figure. S1: (a-c) Band structures observed from the opposite crystal surfaces of three additional samples besides Fig. 2 in the main text. The measurement photon energy was 25, 45, and 50eV for samples 2, 3, 4, respectively; and the dispersions in (a - c) are along the K--K, M--M, and K--K directions. Top row: n-type band structures showing a clear Dirac fermion around the point in the bulk gap. Bottom row: p-type band structures showing the bulk valance band. Acronyms: BCB: Bulk conduction band, BVB: Bulk valance band, SSB: Surface state band.

Note: 1: The slight difference of the band structure between panels (a) and (c) (both along the K--K direction) is due to the different photon energy, making (a) and (c) probe bulk band structures at different kz’s in the momentum space. Thus the shape of the BCB and BVB is different. The intensity variation of SSB in (a) and (c) is due to the matrix element effect.

Note 2: The association of the termination surface of the top and bottom rows is discussed in main text (Fig. 3) and below (Fig. S4)

Part A: More measurements showing asymmetric electronic structures between opposite crystal surfaces.

In addition to Fig. 2 in the main text, the anisotropy of the band structures from opposite

crystal surfaces are observed in different samples measured at different synchrotron facilities with

different experiment conditions (e.g. photon energies, polarizations, measurement geometry, etc.),

as shown in Fig. S1.


2 NATURE PHYSICS | www.nature.com/naturephysics


Figure. S2: Energy dependence of the band structure (along the K--K direction) from the n-type surface of BiTeCl. From panel (a - j), the photon energy varies from 45eV – 63eV. Despite the dramatic change of the shape of the BCB and BVB, the SSB dispersion shape remains the same. The variation in the intensity of the SSB is due to the matrix elment effect at different photon energies.

Part B: Surface nature of the Dirac cone and more details on the band structure of BiTeCl

A set of energy dependent n-type band structure measurements near EF is shown in Fig.

S2. In the whole energy range (45~63eV), the linear dispersion of the Dirac cone remains

unchanged, proving its 2D (surface) nature, while the dispersion of the bulk valance and

conduction band (BVB/BCB) varies dramatically with photon energy from Fig. 2S (a – j).

Besides the dispersion along the K-Γ-K and M--M directions, a short movie clip is

included to illustrate the complete band dispersion along different k-space directions:

Movie_S1

which demonstrates the evolution of the band dispersion of BiTeCl along different azimuthal

angles with respect to the Γ-K direction. Movie_S1 clearly shows the conical shape of the linear

dispersion of the SSB along all directions.

A second movie,

Movie_S2




Figure S3: Measured wide-range FS map covering three BZs, where the red hexagons represent the surface BZs.

illustrates the evolution of the constant energy contours of the band structure of BiTeCl from the

binding energy Eb=0.8eV to the Fermi-energy (EF). In this energy region, the band structure

evolves from the BVB to SSB (through the Dirac point), then to the region where the SSB and

BCB coexist.

Part C: Fermi-surface across multiple Brillouin zones (BZs) of BiTeCl

The Fermi-surface (FS) across three BZs of BiTeCl is demonstrated in Fig. S3, where one

can clearly see that there is only one Dirac cone around the point in each BZ; and the

anisotropy between the two opposite crystal surfaces (panel a and b) is again clearly seen. The

uneven intensity of the FSs from different BZs is due to the matrix element effect.

Part D: ARPES circular dichroism

ARPES circular dichroism (CD) measurements were performed using 6eV photons

derived from the frequency-quadrupled output of a Ti:Sapphire laser. To generate left (right) –




Figure S4: (a, b) Ab initio calculations confirm the overlapping of the positive and negative charge centers of Bi2Te3 (a) and HgTe (b). Left panels of (a, b): Charge distribution overlaid on the atoms in the crystals. Right panels of (a, b): Integrated charge distribution along c-axis; red and blue filling indicates the positive and negative charge accumulation, respectively. The plus and minus signs over the black broken lines indicate the center of the positive and negative charges in each unit cell, respectively. (c): Crystal structure of HgTe. In each unit cell, the centers of the cations and anions coincide at the center of the unit-cell.

hand circular polarization, the light was passed through a quarter-wave plate with the fast axis

oriented 45° (-45°) with respect to the linear polarization axis of the incoming light.

The K--K spectrum shown in the main text (Fig. 3e) was measured in a plane normal to

the plane of incidence of the light. The photoelectrons were collected by a Scienta R4000

analyzer with total energy and angle resolutions of ~20meV and 0.2°, respectively. The intensity

changes of the Dirac cone are about ±50% when the light is switched between left and right-hand

circular polarizations.

Part E: Calculation on the charge distribution of Bi2Te3 and HgTe

As a comparison to Fig. 3 in the main text, we plot the bulk charge distribution obtained

by ab initio calculations of topological insulators Bi2Te3 and HgTe in Fig S4. The positive and




negative charge centers of both materials locate at the center of each unit cell and thus overlap,

resulting NO charge polarization in the bulk. This is distinct to the BiTeCl case in Fig. 3d of the

main text (where the positive and negative charge centers are clearly shifted).

For Bi2Te3, this overlap is natural due to its inversion symmetric crystal structure; while

for the HgTe, although it breaks inversion symmetry, the Zinc-Blend structure still guarantees the

coincidence of the opposite charge centers in each unit cell (Fig. S4b, c) – making the BiTeCl the

only topological insulator discovered with bulk charge polarization up to date.

Part F: Rashba band structure occasionally observed and calculations

In addition to typical band structure shown in Fig. 2-3 in the main text, we occasionally

obtained (once in several cleaves) very different band structures (main text Fig. 4b-d), which can

result from the free standing BiTeCl thin film loosely laid on the bulk BiTeCl crystal (Fig. S5a).

To determine the thickness of the free standing BiTeCl thin film on the top, we

performed ab initio calculations for 0.5-, 1-, 2-, 3-unit BiTeCl free standing films (note that each

unit-thick film corresponds to two Te-Bi-Cl layers - see the crystal structure in Fig. 1f in the main

text). The results of films with different thickness are summarized in Fig. S5b. One clearly sees

that the band gap magnitude decreases quickly with the increased thickness. Evidently, the results

from 0.5-unit and 1-unit thick films agree best with the measurements (Fig. S5b, c), given that the

band gap from experiments is ~0.8eV (see Fig. 4d in main text). In Fig. S5c, we show detailed

electronic structures of the 0.5-unit film including the band dispersions, band gap magnitude and

the FS shape, all of which agree perfectly with our measurements (e.g. the band gap is 0.8eV in

both theory and experiment; the kF size at the degenerate point along the -M direction is 0.19/Å

in theory and 0.2/Å in experiment; and the conduction band bottom position is 0.5eV from the




Figure S5: (a) Shematic shows how free standing BiTeCl thin films can be formed during the cleaving process. (b) Comparision of the band structrues from ab initio calculations for 0.5-, 1-, 2- and 3-units thick films. For 1-, 2- and 3-units’ results, the bold and thin curves are the bands projected to the Cl- and Te- termination surfaces, respectively. (c) Detailed band dispersions (note EF is shifted to match the experiments) and FS perfectly reproduce the ARPES measurements (Fig. 4b-d from the main text).

degenerate point in both theory and experiment). We thus conclude that the results in Fig. 4b-d in

the main text are most likely from the 0.5-unit thick film.

Part G: Effect of unpassivated surface charges on cleaved crystal in UHV

We performed ARPES measurements on freshly cleaved BiTeCl samples in the ultra-

high vacuum (p~2×10-11Torr) environment. Under such high vacuum level, the sample surface

remained clean (thus not passivated) during the measurement period as we can see below:

As a conservative estimation, we assume that the sample surface has sticking coefficient

S = 1 for residue gas molecules in the UHV chamber that touch the sample surface (i.e. every

molecule or atom impinging onto the cleaved surface will stick there) - although typically the

sticking coefficient S <<1. Even with this generous assumption, the time that it takes to form a

monolayer coverage of gas molecules on the sample surface to passivate it isR1: t = 3 × 10-6/p =




Figure S6: Illustartion of the electric field generated by the polarized surafce charge, which can generate effective pressure around the 109 Pa range.

1.5×105 seconds, which is much longer than our measurement period (~3 hrs, or 104 seconds)

after sample cleavage – suggesting that the sample surface we studied remained unpassivated

during the measurements.

The unpassivated charges on the polar sample surfaces can thus generate electric field

across the sample (see Fig. S6), which can in turn interact with the surface charges and result in

effective pressure. By assuming a 0.5e remaining charge in each 2D lattice unit cell (the unit cell

area A=15.58Å2), the effective pressure (P) generated is then (using parallel plate capacitor

approximation and dielectric constant ~15R2): ≈ 109 Pascal, which is in the

same order of pressure needed to introduce the topological phase transition suggested in a recent

calculation (reference 13 in the main text).

Part H: Rashba splitting of BiTeI bulk valence band (BVB)

In addition to the strong Rashba splitting in the bulk conduction band (BCB), we

observed clear Rashba splitting in the bulk valence band (BVB), which can be seen in Fig. 4 in

the main text and Fig. S7 below. The characteristic parameters quantifying the strength of the

Rashba splitting, the Rashba energy ER and the coupling constant R can be fitted from our

experimental band dispersion: and , respectively. The fitted parameters are

thus determined (Fig. S7) as: k0≈0.09/Å, m*≈0.2me0, ER≈0.14eV and R≈3.43eV•Å.




Figure S7: Rashba splitting of BiTeI bulk valance band and the characteristic parameters. The

experimental dispersion (two branches) can be fitted by the model: , from which

we get: k0≈0.09/Å, m*≈0.2me0, thus =0.14eV and . The red

dotted lines are the fitted dispersions.

[R1] A. Chambers, et al., "Basic Vacuum Technology", Institute of Physics Publishing, UK,

(1989)

[R2] I. P. Rusinov, et al., “Many-body effects on the Rashba-type spin splitting in bulk

bismuth tellurohalides”, preprint available at: http://arxiv.org/pdf/1303.4987.pdf




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Supplementary Information for SUPPLEMENTARY INFORMATION · conduction band (BVB/BCB) varies dramatically with photon energy from Fig. 2S (a – j). Besides the dispersion along the