1. Half-Heusler Compounds for Topological Insulators Joshua Sayre Materials 286G May 26, 2010

2. Outline Hall effect → Quantum Hall effect → Quantum Spin Hall effect HgTe quantum wells Half-Heusler opportunities

3. Hall effect J. D. Livingston, “Electronic Properties of Engineering Materials,” Wiley (1999). Discovered in 1879 by Edwin Hall, 18 years before the electron was discovered Allows for the mobility (μ), carrier density (N), and charge (q) to be determined

4. Quantum Hall effect Discovered in 1980 by Klaus von Klitzing (1985 Nobel Prize in Physics) For semiconductors, apply a magnetic field (at low T) and observe flow of charges in opposite directions at the surface of a material (topologic) The conduction has quantized energy levels

5. Quantum spin Hall insulator Edges of insulators (in the absence of a magnetic field), develop helical domains where charge carriers travel in opposite directions M. König, S. Wiedmann et. al Science, 318, (2007) 766-770. Backscattering effects are forbidden by time reversal symmetry Magnetic field can transform the material from conducting to insulating X.-L. Qi and S.-C. Zhang, Physics Today, 63, (2010) 33.

6. HgTe F-43m (#216), a=6.46Å Quantum wells sandwiched between CdTe barriers Wells must be >6.3nm, to invert the band structure at Γ Conduction band from p-states of the VI atom (Te) and valance band from the s-states of II atom (Hg) at low T (~10 K), inverted from typical S/C A. Bernevig, T. Hughes, S.C. Zhang, Science, Physics Today, 314, (2006) 1757-1761.

7. HgTe, topological insulator M. König, S. Wiedmann et. al Science, 318, (2007) 766-770. Possible applications in new spintronic devices if QSH can be observed at room temperature

8. Heusler Compounds Characterized by 4 interpenetrating FCC lattices, X 2 YZ (18 or 24 valence electrons) Half-Heusler has 3 interpenetrating FCC lattices, XYZ (18 valence electrons) Stuffed Zincblende structure Over 500 Heusler compounds containing more than 200 S/C Half-Heusler Half-Heusler compounds such as YPtSb, YPdBi and ScAuPb have experimental lattice constants near the border between trivial and topological insulator at room temperature Tuning via strain proposed as a means to make a material a topological insulator

9. Half-Heusler S. Chadov, X. Qi, et. al, ArXiv e-prints, 1003.0193, (2010). ←Region of inverted band gaps at experimental lattice constants

10. Half-Heusler H. Lin, L. A. Wray, et. al, ArXiv e-prints, 1003.0155, (2010).