Acknowledgements The spin-resolved ARPES measurements are supported by NSF through the Center for Complex Materials (DMR-0819860) and Princeton University; the use of synchrotron X-ray facilities (ALS-LBNL Berkeley) is supported by the Basic Energy Sciences of the U.S. Depart- ment of Energy (DE-FG-02-05ER46200) and by the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. Author information Correspondence and requests for materials should be addressed to M.Z.H (mzhasan@princeton.edu). Spin-integrated ARPES data were taken at beamlines 12.0.1 and 7.0.1 of the Advanced Light Source in Lawrence Berkeley National Laboratory with 29 eV to 100 eV photons. Typical energy and momentum resolutions were 15 meV and 1% of the surface BZ and 50 meV and 2% of the surface BZ respectively. Spin-resolved ARPES measurements were performed at the SIS beamline at the Swiss Light Source using the COPHEE spectrometer, which consists of two 40 kV classical Mott detectors that measure all three spatial components of spin polarization. Spin-resolved mea- surements were taken with 20 eV to 22 eV photons with energy and momentum resolutions of 80 meV and 3% of the surface BZ respectively. Spin-integrated data were collected on Bi$_{2}$$_{−}$$_{δ}$Ca$_{δ}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ single crystals cleaved in ultra high vacuum pressures better than 5 × 10 − 11 torr and maintained at a temperature of 10 K unless otherwise specified. Spin-resolved data were collected at 50 K. Adsorption of NO$_{2}$ molecules on Bi$_{2}$$_{−}$$_{δ}$Ca$_{δ}$Se$_{3}$ was achieved via controlled exposures to NO$_{2}$ gas (Matheson, 99.5%). The adsorption effects were studied under static flow mode by expos- ing the cleaved sample surface to the gas for a certain time then taking data after the chamber was pumped down to the base pressure. Spectra of the NO$_{2}$ adsorbed surfaces were taken within min- utes of opening the photon shutter to minimize photon exposure related effects. The calculations were performed with the LAPW method in slab geometry using the WIEN2K package. METHODS [1] Day, C. Exotic spin textures show up in diverse materials. Phys. Today 62 , 12-13 (2009). http://dx.doi.org/10.1063/1.3120883 10