Hyperfine coupling and spin polarization in the bulk of the topological insulatorBi2Se3

Abstract

Nuclear magnetic resonance (NMR) and transport measurements have been performed at high magnetic fields and low temperatures in a series of n-type Bi2Se3 crystals. In low density samples, a complete spin polarization of the electronic system is achieved, as observed from the saturation of the isotropic component of the 209 Bi NMR shift above a certain magnetic field. The corresponding spin splitting, defined in the phenomenological approach of a 3D electron gas with a large (spinorbit-induced) effective g-factor, scales as expected with the Fermi energy independently determined by simultaneous transport measurements. Both the effective electronic g-factor and the "contact" hyperfine coupling constant are precisely determined. The magnitude of this latter reveals a non negligible s-character of the electronic wave function at the bottom of the conduction band. Our results show that the bulk electronic spin polarization can be directly probed via NMR and pave the way for future NMR investigations of the electronic states in Bi-based topological insulators. Bismuth selenide, Bi 2 Se 3 , known for years as a narrow gap semiconductor, has recently appeared as one of the first examples of "3D topological insulators"[1-3]. As such unique state of matter, it 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 field of spintronic [4] and quantum computation [5], have recently raised a considerable interest (see Ref. 6 for a review). 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 Bi 2 Se 3 , this originates from a parity inversion of the valence and conduction band in the presence of a large spin-orbit coupling [1].In an effort to deepen our understanding of the spin properties of topological insulators, a characterization of the coupling between the charge carriers and the nuclei in the Bi 2 Se 3 matrix is of high importance. Indeed, nuclear spins can inherently couple to the topologically protected electronic states and limit their coherence time. On the other hand, this hyperfine coupling can be efficiently exploited to probe the electronic system via NMR techniques. In particular, an electronic system bearing nonzero spin polarization acts as an effective local magnetic field which modifies the nuclei resonance frequency. This so-called "Knight shift" has previously been extensively studied to probe the electronic spin polarisation [7] as well as the spatial symmetry of the wave functions [8, 9] in some semiconductor-based bulk or low dimensional systems. A couple of recent works have investigated the NMR properties of Bi 2 Se 3 samples and revealed signatures of the bulk electronic states [10, 11]. These measurements were however l...

Se77nuclear magnetic resonance of topological insulatorBi2Se3

“…Unusually large 209 Bi linewidths have been noticed in previous works [14,[19][20][21], but indirect coupling was not invoked as a possible origin. Besides, rather fast 209 Bi NMR spin echo decays were observed, in particular in the central region of the spectra, but could not be explained.…”

“…In the supplement of Ref. [21], a single crystal 77 Se NMR spectrum consisting of one line with a field-independent ∼12 kHz linewidth is reported. This suggests the authors observed only Se out , while Se in was missing, probably due to noise.…”

“…Although NMR parameters such as shifts, linewidths, relaxation are sensitive to the electronic structure, e.g., through the local spin and orbital susceptibilities, it is unclear what NMR can contribute to the understanding of the topological surface states or to any special bulk properties of TIs (note, however, that NMR has been proposed [18] as a probe of the pairing symmetry in topological superconductors). So far, there have been few NMR studies of TIs: 209 Bi NMR of Bi 2 Se 3 single crystals and powders [14,[19][20][21], 125 Te NMR of Bi 2 Te 3 [22][23][24][25], and 77 Se NMR of Bi 2 Se 3 powder [22]. While all of these confirm bulk conductivity qualitatively from fast longitudinal nuclear relaxation (1/T 1 ), they leave many questions unanswered.…”

Hole Fermi surface inBi2Se3probed by quantum oscillations

“…This is accompanied by an increasing anisotropy of the Fermi surface observed as the Fermi level increases in the conduction band. More recent transport, 7-9 NMR, 9 and magneto-optics 10 measurements have confirmed the original parameters phenomenologically describing the bulk conduction band, and in some cases 10 connected them to the 3D Dirac Hamiltonian for massive fermions applied to topological insulators.…”

Nanoscale β-nuclear magnetic resonance depth imaging of topological insulators

“…The only NMR studies of TI surface states published to date were done on nanocrystals (7) and nanowires (8), by inferring the TI properties in the limit of high surface-tovolume ratios. A recent study on Bi 2 Se 3 performed at high magnetic fields provides the means of approaching the quantum limit in TIs via NMR (9). Because films grown by molecular beam epitaxy (MBE) and cleaved surfaces from single crystals are universally studied by most researchers, NMR experiments that directly interrogate TI properties in a depth-resolved manner beneath the surface of epitaxial TI films would be preferred, as they would enable comparison with the literature.…”