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We reported the first spin potentiometric measurement to electrically detect spin polarization arising from spin-momentum locking in topological insulator (TI) surface states using ferromagnet/tunnel barrier contacts [1]. This method has been adopted to measure the current generated spin in other TI systems [2-10], albeit with conflicting signs of the measured spin voltage [1,2,4,6-10]. Tian et al. wish to use their model as presented in Ref. [4] to determine the sign of the induced spin polarization, and thereby determine whether the claims of various groups to have sampled the topologically protected surface states in bulk TIs are correct. The central point of our Reply is that the model as presented is incapable of doing so because it fails to include separate physical contributions which independently effect the sign of the spin polarization measured.
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Several recent experiments on three-dimensional topological insulators claim to observe a large charge current-induced non-equilibrium ensemble spin polarization of electrons in the helical surface state. We present a comprehensive criticism of such claims, using both theory and experiment: First, we clarify the interpretation of quantities extracted from these measurements by deriving standard expressions from a Boltzmann transport equation approach in the relaxation-time approximation at zero and finite temperature to emphasize our assertion that, despite high in-plane spin projection, obtainable current-induced ensemble spin polarization is minuscule. Second, we use a simple experiment to demonstrate that magnetic field-dependent open-circuit voltage hysteresis (identical to those attributed to current-induced spin polarization in topological insulator surface states) can be generated in analogous devices where current is driven through thin films of a topologically-trivial metal. This result *ipso facto* discredits the naive interpretation of previous experiments with TIs, which were used to claim observation of helicity, i.e. spin-momentum locking in the topologically-protected surface state.
Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and time-reversal symmetry (TRS) breaking. In most cases, one could break the TRS of time-reversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. Conventional topological phase transition induced by external field/stimulus needs a route along which the bandgap closes and re-opens. Hence, the phase transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work we propose that using gapless surface states, the transition can happen at arbitrarily weak (but finite) external field strength. This can be regarded as an unconventional topological phase transition, where the bandgap closing is guaranteed by bulk-edge correspondence and symmetries, while the bandgap reopening is induced by external fields. We demonstrate this concept on the 2D surface states of 3D topological insulators like $rm Bi_2Se_3$, which become 2D QAH insulators once a circularly polarized light is turned on, according to van Vlecks effective Hamiltonian in Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamical approach to trigger topological phase transitions and create QAH insulators.
High resolution spin- and angle-resolved photoemission spectroscopy (spin-ARPES) was performed on the three-dimensional topological insulator Bi$_2$Se$_3$ using a recently developed high-efficiency spectrometer. The topological surface states helical spin structure is observed, in agreement with theoretical prediction. Spin textures of both chiralities, at energies above and below the Dirac point, are observed, and the spin structure is found to persist at room temperature. The measurements reveal additional unexpected spin polarization effects, which also originate from the spin-orbit interaction, but are well differentiated from topological physics by contrasting momentum and photon energy and polarization dependencies. These observations demonstrate significant deviations of photoelectron and quasiparticle spin polarizations. Our findings illustrate the inherent complexity of spin-resolved ARPES and demonstrate key considerations for interpreting experimental results.
Non-invasive local probes are needed to characterize bulk defects in binary and ternary chalcogenides. These defects contribute to the non-ideal behavior of topological insulators. We have studied bulk electronic properties via $^{125}$Te NMR in Bi$_2$Te$_3$, Sb$_2$Te$_3$, Bi$_{0.5}$Sb$_{1.5}$Te$_3$, Bi$_2$Te$_2$Se and Bi$_2$Te$_2$S. A distribution of defects gives rise to asymmetry in the powder lineshapes. We show how the Knight shift, line shape and spin-lattice relaxation report on carrier density, spin-orbit coupling and phase separation in the bulk. The present study confirms that the ordered ternary compound Bi$_2$Te$_2$Se is the best TI candidate material at the present time. Our results, which are in good agreement with transport and ARPES studies, help establish the NMR probe as a valuable method to characterize the bulk properties of these materials.
The spin-momentum locking at the Dirac surface state of a topological insulator (TI) offers a distinct possibility of a highly efficient charge-to-spin current (C-S) conversion compared with spin Hall effects in conventional paramagnetic metals. For the development of TI-based spin current devices, it is essential to evaluate its conversion efficiency quantitatively as a function of the Fermi level EF position. Here we exemplify a coefficient of qICS to characterize the interface C-S conversion effect by using spin torque ferromagnetic resonance (ST-FMR) for (Bi1-xSbx)2Te3 thin films whose EF is tuned across the band gap. In bulk insulating conditions, interface C-S conversion effect via Dirac surface state is evaluated as nearly constant large values of qICS, reflecting that the qICS is inversely proportional to the Fermi velocity vF that is almost constant. However, when EF traverses through the Dirac point, the qICS is remarkably suppressed possibly due to the degeneracy of surface spins or instability of helical spin structure. These results demonstrate that the fine tuning of the EF in TI based heterostructures is critical to maximizing the efficiency using the spin-momentum locking mechanism.
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