Free-electron creation at the 60° twin boundary in Bi2Te3

Interfaces, such as grain boundaries in a solid material, are excellent regions to explore novel properties that emerge as the result of local symmetry-breaking. For instance, at the interface of a layered-chalcogenide material, the potential reconfiguration of the atoms at the boundaries can lead to a significant modification of the electronic properties because of their complex atomic bonding structure. Here, we report the experimental observation of an electron source at 60° twin boundaries in Bi2Te3, a representative layered-chalcogenide material. First-principles calculations reveal that the modification of the interatomic distance at the 60° twin boundary to accommodate structural misfits can alter the electronic structure of Bi2Te3. The change in the electronic structure generates occupied states within the original bandgap in a favourable condition to create carriers and enlarges the density-of-states near the conduction band minimum. The present work provides insight into the various transport behaviours of thermoelectrics and topological insulators.


Supplementary Note 1.
It is necessary to rule out other possible scenarios affecting the increasing carrier concentration of our Bi2Te3 thin films with the increasing H2 flow rate (growth rate). , the other possible candidates are the reduction effect of the film surface and the bulk doping effect through the formation of point defects by the different growth rate.
We measured the carrier density of an isolated single-domain area in two ways: by fabricating single-domain Bi2Te3 films grown under the same MOCVD growth condition, and by fabricating a micro-Hall bar pattern to access a single-domain region in the original two-domain sample. In the below, experimental results on these two cases will be discussed.

Twin-free, single-domain Bi2Te3 films
We were able to fabricate twin-free, single-domain, epitaxial (001) Bi2Te3 thin films using 4 o miscut (001) GaAs substrate. The other growth conditions of MOCVD are all the same as we used to grow samples shown in the main text. Due to the unique van der Walls epitaxy nature of Bi2Te3 material, (001) epitaxial Bi2Te3 films with 3-fold symmetry can be grown on (001) GaAs substrate with 4-fold symmetry, which is not possible in the normal epitaxial films. Moreover, the vicinal surface of 4 o miscut (001) GaAs substrate allows us to grow a single-domain, twin boundary-free, epitaxial Bi2Te3 film. Supplementary Figure 3a and b show the out-of-plane θ-2θ scan and the azimuthal φ scan of (105) plane of Bi2Te3 film as well as (202) plane of GaAs substrate, respectively. These results indicates that the (001) epitaxial Bi2Te3 film is grown with a single domain structure, i.e. without twin boundaries.
The out-of-plane and in-plane EBSD images also confirm that the Bi2Te3 film grown on 4 o miscut (001) GaAs substrate is twin-free as shown in supplementary Figure 3c and d, respectively. Such a single-domain structure is maintained for all H2 flow rates we used to control the growth rate.
Supplementary Figure 3e shows the temperature-dependent carrier concentration of the twin-free (001) Bi2Te3 film grown at the two extreme H2 flow rates. It is noted that the variation of the carrier concentration of them is very small with a level of approximately1×10 18 cm -3 . This indicates that other potential mechanisms such as the surface reduction effect and the bulk doping by the point defect generation by the H2 flow variation cannot explain our observation of the carrier density changes with a level of approximately 1×10 19 cm -3 .

Micro-Hall bar pattern measurement on a single-domain region in the two-domain sample
We also compared the carrier density of the following cases in the same sample: a large area including twin boundaries and a small region without boundaries, i.e., a singledomain area. For this comparison, we patterned the two different-sized Hall bars with 1 μm × 1 μm and 50 μm × 50 μm on the same sample as shown in Supplementary Figure 4a Figure 4b). The lowtemperature measurement shows that the electron carrier density at 10 K of the single-domain region is 7.73 ×10 18 cm -3 while that of the area having twin boundaries is 1.48×10 19 cm -3 . This is a direct evidence that the 60 o twin boundary in Bi2Te3 can be a source of free electrons.
In conclusion, we directly showed that the carrier concentration of the twin-free, single-domain Bi2Te3 is much lower than that of the Bi2Te3 having twin boundaries. We have shown this by two different ways: using the as-grown, single-domain sample, and using a selectively-patterned, single-domain region in the two-domain sample. Our results clearly exhibit that other possibilities such as the surface reduction effect and the bulk doping effect via non-stoichiometry and point/antisite defects do not affect our conclusion that the free electron carriers can be created at the 60 o twin boundary in Bi2Te3, as their contribution is low.

Supplementary Note 2. Carrier concentration calculation based on DFT results
Carrier concentration of n-type semiconductor can be calculated as the equation (1 We carried out the same DFT calculations on two-different-sized supercells, as shown in supplementary Figure 5. The supercell b has a shortened length by 2/3 along xdirection compared to the supercell a. Thus, the density of twin boundary in the supercell a (632.1 μm -1 ) is 33% larger than that in b (424.9μm -1 ). The calculated carrier concentration of the supercell a is approximately 1.30×10 20 cm -3 while that of the supercell b is approximately 1.03×10 20 cm -3 . This indicates that the carrier concentration of Bi2Te3 is proportional to the density of the twin boundary, which is the same trend as observed in the experiment.