Extremely large spin hall angle in topological insulator pn junction

#Since their theoretical prediction and experimental verification in quantum wells and bulk crystals. Topological Insulators (TIs) have been of great interest in condensed matter physics, even prompting their classification as a new state of matter [Document 1]. The large spin orbit coupling in a TI leads to an inverted band separated by a bulk bandgap. Symmetry considerations dictate that setting such a TI against a normal insulator (including vacuum) forces a band crossing at their interface, leading to gapless edge (for 2D) and surface (for 3D) states protected by time reversal symmetry. At low energies, the TI surface Hamiltonian H=vF{circumflex over (z)}(σ×p) [Document 1] resembles the graphene Hamiltonian H=vFσ·p except that the Pauli matrices in TI represent real-spins instead of pseudo-spins in graphene. This suggests that the chiral tunneling (the angle dependent transmission) in a graphene pn junction [Documents 2-5] is expected to appear in a TI pn junction (TIPNJ) as well. Although TIPNJs have been studied recently [Documents 6-8], the implication of chiral tunneling combined with spin-momentum locking in spintronics has received little attention.

#The energy dissipation of a spintronic device strongly depends on the efficiency of spin current generation. The efficiency is measured by the spin-charge current gain

#β = 2 ⁢ I s / ℏ I q / q , where Is and Iq are the non-equilibrium spin and charge currents respectively. Increasing β reduces the energy dissipation quadratically. The gain for a regular magnetic tunnel junction is less than 1 [Document 9]. The discovery of Giant Spin Hall Effect (GSHE) [Document 10] shows a way to achieve β>1 by augmenting the spin Hall angle θH with an additional geometrical gain [Document 11]. The intrinsic gain θH for various metals and metal alloys has been found to vary between 0.07-0.3 [Documents 10, 12, 13]. Recently. Bi2Se3-based TI has been reported to have ‘spin torque ratio’ (a quantity closely related to θH) of 2-3.5 [Document 14] and has been shown to switch a soft ferromagnet at low temperature [Document 15]. An oscillatory spin polarization has also been predicted in TI using a step potential [Document 16].

#For a better understanding of the aforementioned embodiments of the invention as well as additional embodiments thereof, reference should be made to the Description of Illustrative Embodiments below, in conjunction with the following drawings in which like reference numerals refer to corresponding parts throughout the figures.

#FIG. 1. illustrates (a) cross section of the TIPNJ, (b) top view of the device showing the directions of incident, reflected and transmitted electrons and their spins, and (c) linear approximation of potential energy profile in accordance with some embodiments.

#FIG. 2. illustrates charge and spin current vs. gate voltage on the p-side (Vp) at Vn=0.15 V in accordance with some embodiments.

#Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

#The interplay between the chiral tunneling and spin momentum locking in TIPNJ shown in FIG. 1 leads to an extremely large, electrically tunable spin-charge current gain β even without utilizing any geometric gain. The chiral tunneling in TIPNJ only allows electrons with very small incident angle to pass through and all other electrons are reflected back to the source in the same way as graphene. As a result, charge current going through the junction decreases. Due to spin-momentum locking, the injected electrons have down spin but the reflected electrons have up spin, which enhances the spin current at the source contact. These result in a gate tunable, extraordinarily large spin-charge current gain. In a split-gate, symmetrically doped TIPNJ, the spin-charge current gain is,

#β ≈ 1 + R av 1 - R av ≈ π ⁢ qV o ⁢ d ℏ ⁢ ⁢ v F ( 1 ) at the source contact for small drain bias. Here, Rav is the reflection probability averaged over all modes, V, is the built in potential of the TIPNJ and d is the split between the gates. For large bias, Eq. (1) can be approximated as β≈2√{square root over (qVodvF)}. In a typical TIPNJ with d=100 nm, Vo=0.3 V and vF=0.5×106 m/s, β at source is ˜30 for small bias and ˜20 for large bias. At drain, β remains close to 1. Therefore, β is approximately between 1 and 20. The p region is highly spin polarized since only the small angle modes (with spin-y) exist there. The large β in a TIPNJ does not require any geometrical gain and can potentially be larger than the net gain in GSHE systems like β-Ta and W [Document 17] that rely on the additional geometrical gain. In addition, it is gate tunable, meaning that it is possible to turn its value continuously from 1.5 to 20. The flows of spin and charge are parallel in TIPNJ, as opposed to the transverse flow in GSHE.