-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0 5 10 15 20 25 x = 0.005 Bi$_{2-x}$Ca$_{x}$Se 3 x = 0 n Hall (10 20 e / cm 3 ) x = 0.0025 p-type n-type Bi$_{1.9933}$Sn$_{0.0067}$Te$_{3}$ GLYPH<c114> 4 K (m GLYPH<c87> cm) Bi$_{0.9}$Sb$_{0.1}$ E$_{F}$ BCB BVB SS -0.1 0.0 0.1 -0.1 0.0 0.1 -0.1 0.0 0.1 -0.1 0.0 0.1 -0.4 -0.2 0.0 -0.1 0.0 0.1 -0.1 0.0 0.1 -0.1 0.0 0.1 k (Å ) -1 -0.1 0.0 0.1 IntensityGLYPH<.notdef>(arb.GLYPH<.notdef>units) E$_{F}$ (c)GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>0% (d)GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>0.25% (e)GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>1% Low High (f) (h) (g) (l) (m) BiGLYPH<.notdef>GLYPH<.notdef>Se 2 3+x BiGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>GLYPH<.notdef>Se 2-$_{GLYPH<c100>}$ GLYPH<c100> GLYPH<c100> =GLYPH<.notdef>0.0025 GLYPH<c100> =GLYPH<.notdef>0.005 xGLYPH<.notdef>=GLYPH<.notdef>0.03 BiGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>Sb 0.9 0.1 BiGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>Sn Te 1.9933 0.0067 3 (a) (b) BiGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>Se 1.9975 0.0025 3 CBM VBM z=0 EGLYPH<.notdef>GLYPH<.notdef>(eV) B (i) (j) (k) (n) E$_{B}$ crystal vac n-type Compensated insulator ChargeGLYPH<.notdef>compensation k (Å ) -1 k (Å ) -1 GLYPH<c100> =GLYPH<.notdef>0 TuningGLYPH<.notdef>throughGLYPH<.notdef>bulkGLYPH<.notdef>doping FIG. 5: Hsieh, Xia, Qian et al. , NATURE 460, 1101 (2009). FIG. 6: Hsieh, Xia, Qian et al. , NATURE 460, 1101 (2009). 16 GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s32> GLYPH<s32> GLYPH<s32> -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 400 350 300 250 200 150 x10 3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.2 0.0 0.2 SpinGLYPH<.notdef>polarization IntensityGLYPH<.notdef>(arb.GLYPH<.notdef>units) k (ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 k (ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 -0.2 -0.1 0.0 0.1 0.2 0.3 k (ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 2 3 4 P y P z P x (e) (f) EGLYPH<.notdef>GLYPH<.notdef>=GLYPH<.notdef>-20GLYPH<.notdef>meV B EGLYPH<.notdef>GLYPH<.notdef>=GLYPH<.notdef>-20GLYPH<.notdef>meV B I I$^{y}$ y -0.2 -0.1 0.0 0.1 0.2 -0.2 -0.1 0.0 0.1 0.2 EGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>(eV) B -0.3 M GLYPH<c71> M M Low High -0.1 0.0 0.1 -0.1 0.0 0.1 Bi Te 2 3 (g) -0.2 -0.1 0.0 -0.2 -0.1 0.0 0.1 0.2 -0.1 0.0 0.1 -0.4 -0.2 0.0 k (ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 k (ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 k (ÅGLYPH<.notdef>GLYPH<.notdef>) y -1 (d) TunedGLYPH<.notdef>BiGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>CaGLYPH<.notdef>GLYPH<.notdef>Se$_{3}$ k x k y M (h) K 5 86 90 5 2-$_{GLYPH<c100>}$ GLYPH<c100> (a) (b) (c) MomentumGLYPH<.notdef>distributionGLYPH<.notdef>ofGLYPH<.notdef>spin MomentumGLYPH<.notdef>distributionGLYPH<.notdef>ofGLYPH<.notdef>spin Spin-helicalGLYPH<.notdef>DiracGLYPH<.notdef>cones