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Phase-coherent transport in catalyst-free vapor phase deposited Bi$_2$Se$_3$ crystals

Free-standing Bi$_2$Se$_3$ single crystal flakes of variable thickness are grown using a catalyst-free vapor-solid synthesis and are subsequently transferred onto a clean Si$^{++}$/SiO$_2$ substrate where the flakes are contacted in Hall bar geometry. Low temperature magneto-resistance measurements are presented which show a linear magneto-resistance for high magnetic fields and weak anti-localization (WAL) at low fields. Despite an overall strong charge carrier tunability for thinner devices, we find that electron transport is dominated by bulk contributions for all devices. Phase coherence lengths $ł_ϕ$ as extracted from WAL measurements increase linearly with increasing electron density exceeding $1 μ$m at 1.7 K. While $ł_ϕ$ is in qualitative agreement with electron electron interaction-induced dephasing, we find that spin flip scattering processes limit $ł_ϕ$ at low temperatures.