Tunable spin-orbit coupling in two-dimensional InSe

Abstract

We demonstrate that spin-orbit coupling (SOC) strength for electrons near the conduction band edge in few-layer γ-InSe films can be tuned over a wide range. This tunability is the result of a competition between film-thickness-dependent intrinsic and electric-field-induced SOC, potentially, allowing for electrically switchable spintronic devices. Using a hybrid k • p tight-binding model, fully parameterized with the help of density functional theory computations, we quantify SOC strength for various geometries of InSe-based field-effect transistors. The theoretically computed SOC strengths are compared with the results of weak antilocalization measurements on dual-gated multilayer InSe films, interpreted in terms of Dyakonov-Perel spin relaxation due to SOC, showing a good agreement between theory and experiment. Ev −2.79 eV t Γ cc 0.34 eV mc 0.266 m0 t Γ vv −0.41 eV tcc 2 −3.43 eVÅ 2 Ev 1 −3.4 eV Ev 2 −3.5 eV t Γ cv 0.25 eV tcv 2 −3.29 eVÅ 2 Ecv 2.79 eV Ec 1 c 1.09 eV Evv 1 0.54 eV Evv 2 0.683 eV b54 10.54 eVÅ λ15 0.119 eV b16 −2.77 eVÅ b c 1 v 2 16

Giant Tunability of Intersubband Transitions and Quantum Hall Quartets in Few-Layer InSe Quantum Wells

“…It follows that from the ratio of the slopes, we can extract the ratio of the effective masses, which is estimated to be m 2 */ m 1 * ∼ 1.9; using m 1 * = 0.14 m e , as determined in prior reports , and first-principles calculations, we obtain that m 2 * ∼ 0.27 m e , which is significantly enhanced with respect to that of the first subband. This enhancement is qualitatively consistent with the first-principles calculations in this and prior works, , and should provide further constraints for fine-tuning parameters in band structure calculations of few-layer InSe.…”

“…The electronic band structures of 7-layer InSe obtained by first-principles calculations, shown in Figure e, indeed feature the presence of subbands and Rashba SOC, in harmony with previous theoretical studies. − The onset charge density for reaching the second subband, n on , is strongly thickness dependent. Figure d plots n on (left axis) for six devices of different thicknesses, and the right axis shows the energetic separation E 12 between the first two subbands, calculated from E 12 = ℏ 2 ( 2 π n o n ) 2 m 1 * , where m 1 * = 0.14 m e is the subband’s in-plane effective mass ( m e is the rest mass of the electron). , From the particle-in-a-box model, E 12 = 3 ℏ 2 π 2 2 m ⊥ false( L + 2 v false) 2 , where m ⊥ is the effective mass in the out-of-plane direction, ℏ the reduced Planck constant, and v = 1.42 is a parameter that accounts for the anharmonicity of the bands. , From the slope of the fitting, we estimate that m ⊥ = 0.09 m e , in agreement with the bulk value of 0.08 m e . We also note that the measured E 12 values are smaller by a factor of ∼2 than those from the first-principles calculations; this discrepancy may arise from the anharmonicity of the bands and/or neglecting the electronic interactions filling the first subband in our first-principles calculations.…”

“…The electronic band structures of 7-layer InSe obtained by first-principles calculations, shown in Figure e, indeed feature the presence of subbands and Rashba SOC, in harmony with previous theoretical studies. − The onset charge density for reaching the second subband, n on , is strongly thickness dependent. Figure d plots n on (left axis) for six devices of different thicknesses, and the right axis shows the energetic separation E 12 between the first two subbands, calculated from , where m 1 * = 0.14 m e is the subband’s in-plane effective mass ( m e is the rest mass of the electron). , From the particle-in-a-box model, , where m ⊥ is the effective mass in the out-of-plane direction, ℏ the reduced Planck constant, and v = 1.42 is a parameter that accounts for the anharmonicity of the bands. , From the slope of the fitting, we estimate that m ⊥ = 0.09 m e , in agreement with the bulk value of 0.08 m e . We also note that the measured E 12 values are smaller by a factor of ∼2 than those from the first-principles calculations; this discrepancy may arise from the anharmonicity of the bands and/or neglecting the electronic interactions filling the first subband in our first-principles calculations.…”

Strong Sliding Ferroelectricity and Interlayer Sliding Controllable Spintronic Effect in Two-Dimensional HgI2 Layers

“…The corresponding Rashba SOC term can be formulated as H SOC = α × (σ x k y – σ y k x ), where α is the Rashba coefficient. After examining the dependence of the α coefficient on the layer number, the Rashba effect of the considerable SOC strength can be expected in thick FE-HgI 2 multilayers (Figure S9 and Table S3 of the Supporting Information).…”