Uncovering and tailoring hidden Rashba spin–orbit splitting in centrosymmetric crystals

Abstract

Hidden Rashba and Dresselhaus spin splittings in centrosymmetric crystals with subunits/sectors having non-centrosymmetric symmetries (the R-2 and D-2 effects) have been predicted theoretically and then observed experimentally, but the microscopic mechanism remains unclear. Here we demonstrate that the spin splitting in the R-2 effect is enforced by specific symmetries, such as non-symmorphic symmetry in the present example, which ensures that the pertinent spin wavefunctions segregate spatially on just one of the two inversion-partner sectors and thus avoid compensation. We further show that the effective Hamiltonian for the conventional Rashba (R-1) effect is also applicable for the R-2 effect, but applying a symmetry-breaking electric field to a R-2 compound produces a different spin-splitting pattern than applying a field to a trivial, non-R-2, centrosymmetric compound. This finding establishes a common fundamental source for the R-1 effect and the R-2 effect, both originating from local sector symmetries rather than from the global crystal symmetry per se.

Unveiling giant hidden Rashba effects in two-dimensional Si2Bi2

“…As expected, SOC weakens the SL-SL interaction, but strengthens α R , which was calculated to be 2.16 eVÅ at λ = λ 0 . This value is much larger than those observed in metal surfaces, for example, Au(111) (0.33 eVÅ) 24 , Bi(111) (0.55 eVÅ) 25 , as well as other materials exhibiting the R-2 SOC such as BaNiS 2 (0.24 eVÅ) 26 , and is also comparable with conventional giant Rashba system, such as hybrid perovskites (1.6 eVÅ) 27 , BiSb monolayer (2.3 eVÅ) 28 , or BiTeI (3.8 eVÅ) 29 . Therefore, we may classify our system into the giant hidden Rashba material.…”

“…To verify the SLL in our system, we quantify the spatial spin separation by introducing the degree of wavefucntion segregation (DWS) Dðψ σ k Þ defined as 26 Dðψ σ nk Þ ¼ P ψ σ nk ðS α Þ À P ψ σ nk ðS β Þ P ψ σ nk ðS α Þ þ P ψ σ nk ðS β Þ ;…”

The Rashba Scale: Emergence of Band Anti-crossing as a Design Principle for Materials with Large Rashba Coefficient

“…We focus on compounds with intrinsic dipoles (''bulk Rashba effect,'' 13 denoted as R-1). We exclude (1) magnetic compounds (no time-reversal-symmetry) in which the Zeeman effect is observed instead, 37,38 (2) surfaces or interfaces induced Rashba effects (the ''R-0'' effect), 7,39 which require non-bulk symmetry breaking, and (3) centrosymmetric compounds with local sectors that have noncentrosymmetric point groups (''hidden Rashba effect'' 8,9 or R-2). Figure 1A shows the existence of a significant range of a R and a general delineation (marked approximately by the blue hatched lines) into small versus large band edge Rashba effects, which are based on a R and hereafter referred to as weak versus strong Rashba, respectively.…”

“…Symmetry wise, the existence of a Rashba effect of arbitrary magnitude a R requires a compound with non-centrosymmetric structures having local electric dipoles induced by polar atomic sites that add up over the unit cell to a non-zero. 8,9 Despite the fact that large Rashba effect is needed for facile spintronic generation and detection of spin-polarized states [10][11][12][13] as well as for the detection of Majorana fermions, 14,15 the principles determining the magnitude of this functionality (''the Rashba scale'') has not been established. Indeed, the discovery of new compounds with large Rashba coefficient (e.g., GeTe [R3m], 16,17 BiTeI [P3m1], 18,19 and metallic PtBi 2 [P3m1] 20 ) is invariably greeted as a pleasant surprise.…”

Direct observation of hidden spin polarization in 2H−MoTe2

“…Spin polarization in nonmagnetic materials originates from the break of inversion crystalline symmetry [1][2][3][4][5] that could occur globally [1,2] or locally [3][4][5][6]. Such spin polarization can induce an effective magnetic field [7] for operating electron's spin in the absence of magnetic ions or field.…”