Resolving Dirac electrons with broadband high-resolution NMR

Abstract

Detecting the metallic Dirac electronic states on the surface of Topological Insulators (TIs) is critical for the study of important surface quantum properties (SQPs), such as Majorana zero modes, where simultaneous probing of the bulk and edge electron states is required. However, there is a particular shortage of experimental methods, showing at atomic resolution how Dirac electrons extend and interact with the bulk interior of nanoscaled TI systems. Herein, by applying advanced broadband solid-state 125 Te nuclear magnetic resonance (NMR) methods on Bi 2 Te 3 nanoplatelets, we succeeded in uncovering the hitherto invisible NMR signals with magnetic shielding that is influenced by the Dirac electrons, and we subsequently showed how the Dirac electrons spread inside the nanoplatelets. In this way, the spin and orbital magnetic susceptibilities induced by the bulk and edge electron states were simultaneously measured at atomic scale resolution, providing a pertinent experimental approach in the study of SQPs.

Proton-detected fast-magic-angle spinning NMR of paramagnetic inorganic solids

“…This is provided by a 2D sideband separation experiment such as the adiabatic Magic Angle Turning (aMAT) sequence, 14 which uses a train of adiabatic refocusing pulses 46 with unique timings in order to result in pure isotropic evolution in the indirect dimension. The experiment, originally developed for lower-g nuclei in the context of energy storage materials, [47][48][49][50] achieves a 2D spectrum correlating pure isotropic to anisotropic frequencies (Fig. 1d), with a projection along the indirect dimension (Fig.…”

Crystal and Electronic Facet Analysis of Ultrafine Ni2P Particles by Solid-State NMR Nanocrystallography

“…Furthermore, the pDOS values are in accordance with the calculated total (isotropic) 31 P NMR Knight shift, referenced according to the relation K=σrefσcalc. In this formula σref=220.23 ppm is the reference 31 P NMR shielding, calculated with the procedure used by Mayo et al 29 (see Supplementary Figure 10), and σcalc is the total DFT calculated 31 P NMR shielding in Ni2P, which is equal to σcalc = σFC+ σdip+σorb 16 . According to the DFT calculations, the Fermi-Contact shielding σFC is the primary contribution responsible for the large NMR shift difference between the two non-equivalent sites (σFC is equal to -4085 ppm for P(1) and -1061ppm for P(2)), while the orbital contribution is smaller (σorb = 70.72 ppm for P(1) and -150.29 for P(2)), and the dipolar term σdip is negligible (of the order of a few ppm for both P(1) and P(2)).…”

“…As solid-state nuclear magnetic resonance (ssNMR) is sensitive to the structure and electronic environment at the atomic (local) scale, it is able to determine the distinct surface facets in nanosized particles as well as distinguish between these and the bulk-like interior of the nanoparticle [16][17][18][19] . In the case of nanocrystalline metallic powders, the strength of ssNMR lies in its ability to probe the interactions which couple the conduction electrons with the nuclear spins, via the Knight shift 20 K= KFC+ Kdip+Korb.…”

Resistively detected NMR as a probe of the topological nature of conducting edge/surface states

“…The technique has been applied to study the physics of quantum Hall effect, and electronic polarization in quantum wells of 2D electron gases and in quantum wires [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] . NMR has also been used to investigate bulk properties of topological materials with non-local order [37][38][39][40][41][42][43] . The use of traditional NMR techniques to study properties of reduced dimensionality systems, such as GaAs heterostructures and surface states, is precluded as relatively few nuclear spins participate making the signal of RF response weak.…”