Spintronics with topological insulator Takehito Yokoyama, Yukio Tanaka *, and Naoto Nagaosa Department of Applied Physics, University of Tokyo, Japan * Department of Applied Physics, Nagoya University, Japan arXiv:

Edge states From

Quantum Spin Hall state Kane and Mele PRL 2005 Generalization of quantum Spin Hall state to 3D Fu, Kane & Mele PRL 07 Moore & Balents PRB 07 Roy, cond-mat 06 One to one correspondence between spin and momentum B. A. Bernevig and S.-C. Zhang PRL2006 Spin filtered edge states

3D Topological insulator Bi 1-x Sb x D. Hsieh et al. Nature (2008) & Science (2009) Observation of Dirac dispersion!

In topological insulator, electrons obey Dirac equation 2.Zeeman field acts like vector potential 1.This corresponds to the infinite mass Rashba model Therefore, spintronics on topological insulator seems promising! Motivation We study magnetotransport on topological insulator.

Current Setup

Formalism Hamiltonian Wavefunctions Boundary condition gives Conductance Fermi energy

Magnetoresistance Azimuthal angle of F1 Polar angle of F1

Magnetoresistance in pn junction Azimuthal angle of F1 Polar angle of F1

F2 F1 F2 F1 F2 Band gap Fermi level Continuity of wavefunction Parallel configurationAnti-parallel configuration nn junction pn junction

Inclusion of barrier region We find that transmission coefficient is π-periodic with respect to Z Due to mismatch effect, some barrier region may be formed near the interface. This indicates spin rotation through the barrier

Magnetoresistance in pn junction Opposite tendency due to spin rotation through the barrier region

Discussion Typical value of induced exchange field due to the magnetic proximity effect would be 5 ∼ 50 meV (from experiments in graphene and superconductor) H. Haugen,et al, Phys. Rev. B 77, (2008). J. Chakhalianet al., Nat. Physics 2, 244 (2006). E can be tuned by gate electrode or doping below the bulk energy gap ( ∼ 100 meV) Ferromagnet breaks TRS, which would tame the robustness against disoder. However, high quality topological insulator can be fabricated Y. S. Hor et al., arXiv: v2 Fermi velocity Mean free path Localization does not occur and surface state is stable for exchange field smaller than the bulk energy gap The characteristic length of the wavefuction Thomas-Fermi screening length for Bi 2 Se 3 H. Zhang et. al, Nat. Phys. 5, 438 (2009). forThus, we have

Conclusion We investigated charge transport in two-dimensional ferromagnet/feromagnet junction on a topological insulator. The conductance across the interface depends sensitively on the directions of the magnetizations of the two ferromagnets, showing anomalous behaviors compared with the conventional spin-valve. The conductance depends strongly on the in-plane direction of the magnetization. The conductance at the parallel configuration can be much smaller than that at the antiparallel configuration. This stems from the connectivity of wavefunctions between both sides.

Overlap integral nn junctionpn junction Incident wavefunction Transmitted wavefunction