Conserved Spin Quantity in Strained Hole Systems with Rashba and Dresselhaus Spin-Orbit Coupling Paul Wenk, Michael Kammermeier, John Schliemann, Klaus Richter, Roland Winkler SFB Workshop Bernried 30.09.2014 SFB 689
Nonballistic Spin-FET Characteristics of considered systems: Uncorrelated, weak disorder (Ioffe-Regel criterion) Spin-independent scattering of carriers Presence of spin-orbit-coupling (SOC) After every collision the carrier is effected by an other SO field e.g. Rashba SOC. Problem: In the s-band D'yakonov-Perel' Spin Relaxation or Elliot-Yafet-SR,... 2 [D yakonov, Sov.Phys.JETP (1971)] [P.W, Handbook on Nanophysics, Taylor& Francis (2010)]
Nonballistic Spin-FET Characteristics of considered systems: Uncorrelated, weak disorder (Ioffe-Regel criterion) Spin-independent scattering of carriers Presence of spin-orbit-coupling (SOC) After every collision the carrier is effected by an other SO field e.g. Rashba SOC. Problem: In the s-band D'yakonov-Perel' Spin Relaxation or Elliot-Yafet-SR,... Goal: As proposed in PRL 90,146801 (2003) by JS: Switching spin relaxation on/off on state Lin. Rashba lin. Dresselhaus in a [001] 2DEG Device operation: off state 3 [D yakonov, Sov.Phys.JETP (1971)] [P.W, Handbook on Nanophysics, Taylor& Francis (2010)]
on-state in 2DEG When linear Rashba linear Dresselhaus in a [001] 2DEG For 2DEG: Two persistent solutions for the spin-density s: 4 [P.W, Handbook on Nanophysics, Taylor& Francis (2010)]
Approach in Hole Systems Recall Starting point in our paper PRB 90.115306(2014) (with T.Dollinger) presented last year: - Luttinger Hamiltonian with Rashba+Dresselhaus SOC for a zinc blende crystal system - Inclusion of a confinement (in [001] direction) 2DHG - Loewdin perturbation effective 2x2 Hamiltonian Similar approach by Sacksteder et al., PRB 89.161307(2014) but - no Dresselhaus SOC - strain included via Bir-Pikus Hamiltonian - however: inconsistent application of Loewdin perturbation 5
Bulk Hole-Hamiltonian Luttinger's Hamiltonian for III-V semiconductors (valence band Γ8v) with Dresselhaus and Rashba SOC Luttinger parameters Ji : angular momentum matrices for j=3/2 6
Bulk Hole-Hamiltonian Luttinger's Hamiltonian for III-V semiconductors (valence band Γ8v) with Dresselhaus and Rashba SOC Luttinger parameters Contribution due to bulk-inversion asymmetry (BIA) Ji : angular momentum matrices for j=3/2 7
Bulk Hole-Hamiltonian Luttinger's Hamiltonian for III-V semiconductors (valence band Γ8v) with Dresselhaus and Rashba SOC Luttinger parameters Contribution due to structureinversion asymmetry (SIA) by applying an electric field E, Ji : angular momentum matrices for j=3/2 Here 8
Bulk Hole-Hamiltonian Luttinger's Hamiltonian for III-V semiconductors (valence band Γ8v) with Dresselhaus and Rashba SOC Luttinger parameters Assume to be small Ji : angular momentum matrices for j=3/2 9
Previous Results: 2DHG PRB 90.115306(2014) Gapless triplet mode in Cooperon spectrum Persistent spin-state if PRB 89.161307(R)(2014) Bir-Pikus strain Hamiltonian 10
Previous Results: 2DHG PRB 90.115306(2014) Gapless triplet mode in Cooperon spectrum Persistent spin-state if PRB 89.161307(R)(2014) Bir-Pikus strain Hamiltonian Useful: recast in VF In-plane strain amplitude orientation 11
Previous Results: 2DHG PRB 90.115306(2014) Gapless triplet mode in Cooperon spectrum Persistent spin-state if PRB 89.161307(R)(2014) Persistent spin-state if Bir-Pikus strain Hamiltonian Useful: recast in VF In-plane strain amplitude orientation 12
Problems PRB 90.115306(2014) Persistent spin-state if PRB 89.161307(R)(2014) Persistent spin-state if Example by Sacksteder et al., Boron doped diamond is wrong, rather ( Niels Christensen priv. communication), 13
Problems PRB 90.115306(2014) Persistent spin-state if Is it correct to use the bulk Rashba parameter when deriving the 2DHG Hamiltonian? PRB 89.161307(R)(2014) Persistent spin-state if Sacksteder et al.: electric pot. Rashba contribution in 2nd order LP? 14
A Way Out Include Rashba SOC, Dresselhaus SOC and biaxial/uniaxial in-plane strain When applying the confinement to generate 2DHG, note: Loewdin perturbation (LP) for lowest HH(LH)-like subband with Rashba bulk parameter gives not the dominant contribution due to Rashba SOC, subband gaps dominate! Rederive Rashba SOC for confined 2DHG: In contrast to Sacksteder et al.: 3Rd order LP and at least 3 subbands necessary! Search for a conserved spin quantity in an experimentally accessible part of the parameter-space. 15
Results Effective vector field due to Rashba and Dresselhaus SOC in case of a... HH-like ground state LH-like ground state 16
Results Effective vector field due to Rashba and Dresselhaus SOC in case of a... HH-like ground state LH-like ground state Rashba SOC in 3rd order LP! 17
Conserved Spin Quantity Example: InSb Here we present only the case for the HH-like ground state. Using Dresselhaus/Rashba deviation from spherical sym. Strain amplitude Quantum well width 18
Conserved Spin Quantity Example: InSb Here we present only the case for the HH-like ground state. Using Dresselhaus/Rashba deviation from spherical sym. Strain amplitude Quantum well width Uniaxial compression in [110] direction 19
Conserved Spin Quantity Example: InSb Thank you for your attention! SFB 689 Uniaxial compression in [110] direction 20
Conserved Spin Quantity Example: InSb Experimental coefficients and parameters used For the InSb example: Uniaxial compression in [110] direction 21
Reduced Luttinger Parameter Using extended Kane model (14x14) If we neglect all remote band contributions in the valence band block, [H.Mayer, U. Roessler, PRB 44.9048(1991)] 22
Shift of the ground HH and LH subband Problem: Only in-plane biaxial tensile stress 23 [Y.Sun et al., Strain Effects in Semiconductors, Springer (2010)]
Bir-Pikus Strain Hamiltonian are the three deformation potentials corresponding to strain tensors with symmetries [G.E.Pikus, G.L. Bir, Sov. Phys. Solid State 1, 1502 1517 (1960)] 24
Persistent Solutions in 2DEG When linear Rashba Spin-orbit field uniform in linear Dresselhaus in a [001] 2DEG direction Two persistent solutions for the spin-density s: 25 [P.W, Handbook on Nanophysics, Taylor& Francis (2010)]
Loewdin Perturbation Theory A B 26
Loewdin Perturbation Theory Indices m, m', m'': Block A Indices l, l', l'' : Block B 27
Expansion Coefficients: BIA 28 [R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, (2003)]
Expansion Coefficients: SIA 29 [R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, (2003)]
Suitable Compounds 30