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Hyperfine coupling and spin polarization in the bulk of the topological insulator Bi2Se3

Bismuth selenide, Bi2Se3, known for years as a narrow-gap semiconductor, has recently appeared as one of the first examples of “3D topological insulators”. This unique state of matter is characterized by the coexistence of 2-dimensional conducting surface states with an insulating bulk material. The charge carriers at the surface behave as massless relativistic particles (Dirac fermions) with a spin locked to their translational momentum. These so-called “helical Dirac fermions,” which promise applications in the fields of spintronics and quantum computation, have recently raised considerable interest. As a matter of fact, the existence of gapless states at the boundary of the material is related to a well-defined change in the bulk band structure. In Bi2Se3, this originates from a parity inversion of the valence and conduction band in the presence of a large spin-orbit coupling, leading to the formation of 3D massive Dirac fermions in the bulk and “helical Dirac fermions” on the surface.


In an effort to deepen our understanding of the spin properties of topological insulators, we have recently focused on the characterization of the coupling between the charge carriers and the nuclei in the Bi2Se3 matrix. Nuclear Magnetic Resonance (NMR) has been known for a long time as a powerful tool to probe the spin polarization or spatial properties of electronic phases. However, the hyperfine coupling between electrons and nuclei can be very different in nature and strength depending on the host systems. In particular, the theoretically expected “p-like” wave functions characterizing both surface and bulk states in Bi2Se3 suggests that an anisotropic hyperfine coupling should dominate in this material. This would render the “NMR-access” to the electronic properties less straightforward than in the thoroughly studied “s-like” GaAs-based low dimensional systems.


In our work, we have combined NMR and transport measurements to show that the spin degree of freedom of bulk electronic states in Bi2Se3 can directly be probed via the hyperfine interaction with the Bi nuclei. In the lowest density samples, the complete spin polarization of the conduction electrons is indicated by a saturation of the isotropic component of the 209Bi NMR shift above a density-dependent magnetic field Bs (see Figure 1). This allows us to precisely estimate the “contact term” of the hyperfine coupling and to determine the amplitude and sign of an effective electronic g-factor describing the spin splitting in Bi2Se3. The observation of a large isotropic NMR shift reveals a non-negligible proportion of “s-like” electronic states near the bulk band gap of this topological insulator. Our findings pave the way for future sensitive NMR experiments (such as resistively-detected NMR) aiming at testing the spin physics of the surface states in Bi-based topological insulators.



Figure 1 : Magnetic field dependence of the isotropic component of the NMR Knight shift in a Bi2Se3 sample with a carrier concentration ne 7.5×1017cm-3. The isotropic component has been extracted from the angular dependence of Bi NMR spectra. Simulation based on the phenomenological approach of a 3D electron gas with a large (spin-orbit-induced) effective g-factor (red solid line). Inset : NMR spectrum at B=12T for the field applied along the c-axis of the crystal, where f0 = 209 gamma * B is the resonance frequency of the bare 209Bi nuclei. The spectrum consists of a central line (denoted by the vertical dashed line) and four pairs of quadrupolar satellites.



Related publication :

Hyperfine coupling and spin polarization in the bulk of the topological insulator Bi2Se3,

S. Mukhopadhyay, S. Krämer, H. Mayaffre, H. F. Legg, M. Orlita, C. Berthier, M. Horvatić, G. Martinez, M. Potemski, B. A. Piot, A. Materna, G. Strzelecka, and A. Hruban,

Phys. Rev. B 91, 081105(R) 2015

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