Anomalous Rashba spin splitting in two-dimensional hole systems

Winkler, Roland; Noh, Hwayong; Tutuc, Emanuel; Shayegan, M.

doi:10.1103/physrevb.65.155303

Cited by 133 publications

(171 citation statements)

References 17 publications

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“…Recently, it has also been proposed 7 that hole-doped nanowires, because of the possibly stronger spin-orbit coupling 22,23 and larger effective mass of holes, might be a better candidate for creating topological superconductors and Majorana fermions. The hole-bands of a group III-V semiconductor such as InAs or GaAs are composed of p-orbitals, which have orbital angular momentum L = 1.…”

Section: B Hole-doped Semiconductorsmentioning

confidence: 99%

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

2012

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In proximity to an s-wave superconductor, a one-or two-dimensional, electron-or hole-doped semiconductor with a sizable spin-orbit coupling and a Zeeman splitting can support a topological superconducting (TS) state. The semiconductor TS state has Majorana fermions as localized zeroenergy excitations at order parameter defects such as vortices and sample edges. Here we examine the effects of quenched disorder from the semiconductor surface on the stability of the TS state in both electron-and hole-doped semiconductors. By considering the interplay of broken time reversal symmetry (due to Zeeman splitting) and disorder we derive an expression for the disorder suppression of the superconducting quasiparticle gap in the TS state. We conclude that the effects of disorder can be minimized by increasing the ratio of the spin-orbit energy with the Zeeman splitting. By giving explicit numbers we show that a stable TS state is possible in both electron-and holedoped semiconductors for experimentally realistic values of parameters. We discuss possible suitable semiconductor materials which should be the leading candidates for the Majorana search in solid state systems.

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Section: B Hole-doped Semiconductorsmentioning

confidence: 99%

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

2012

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“…We obtained α 3 ¼ 2.26 × 10 5 e Å 4 . The coefficient α 3 is about 1 order smaller than for the 2DHG in the GaAs/AlGaAs single heterostructure [21], which is a nearly lattice matched system. The smaller α 3 value is due to the large HH-LH separation in Ge=Si 0.5 Ge 0.5 compared to that of the GaAs/AlGaAs structure; the large HH-LH separation decreases the coefficient α 3 .…”

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confidence: 99%

“…For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19]. Recently, the cubic-Rashba SOI has been reported in a two-dimensional hole gas (2DHG) in inversion asymmetric semiconductors InGaAs and GaAs [20,21], and a twodimensional electron gas formed at a surface of the inversion symmetric oxide SrTiO 3 [15]. However in the former case, the InGaAs and GaAs possess both BIA and SIA; thus, they are always influenced by both Dresselhaus and Rashba SOI contributions [22].…”

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Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGeQuantum Well

et al. 2014

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The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge=SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum m j ¼ AE3=2 nature of the HH wave function. DOI: 10.1103/PhysRevLett.113.086601 PACS numbers: 72.25.Dc, 73.20.Fz, 73.21.-b The spin-orbit interaction (SOI) in a two-dimensional system is a subject of considerable interest because the SOI induces spin splitting at a zero magnetic field, which is important in both fundamental research and electronic device applications [1]. Recent developments of SOI-induced phenomena in the solid state demonstrate many possibilities utilizing spin current and the emergence of new physics such as the spin interferometer [2,3], persistent spin helix [4,5], spin Hall effect [6][7][8], and quantum spin Hall effect [9,10]. Up to now, there have been two well-known SOIs existing in solids: the Dresselhaus SOI [11] due to bulk inversion asymmetry (BIA) in the crystal structure and the Rashba SOI [12,13] due to spatial inversion asymmetry (SIA).In low-dimensional systems, the Rashba SOI becomes more important because it is stronger at the heterointerface and can be controlled by an external electric field. Many of the pioneering studies on the SOI-induced phenomena mentioned above were performed in two-dimensional electron systems, where the Rashba SOI is described by the k-linear Rashba term. In the Hamiltonian, the k-linear Rashba term can be written aswhere σ AE ¼ 1=2ðσ x AE iσ y Þ denote combinations of Pauli spin matrices, k AE ¼ k x AE ik y , and k x , k y are the components of the in-plane wave vector k ∥ . The effective magnetic field Ω 1 ðk ∥ Þ acting on the transport carrier due to the k-linear Rashba term is illustrated in Fig. 1(a).Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed asand the effective magnetic field Ω 3 ðk ∥ Þ in k space is illustrated in Fig. 1(b) [15]. There is a significant difference in the effective field symmetry between the k-linear and the k-cubic Rashba SOI with one and three rotations in k space, respectively. The k 3 symmetry of the SOI is an interesting subject because it influences all of the SOI-induced phenomena as opposed to the k-linear Rashba term. For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19].

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“…In a previous study [20] this surprising behavior of β h 1 E ⊥ was shown as a function of density. By lowering the density, spin splitting and E ⊥ both decrease but the term β h 1 E ⊥ increases.…”

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confidence: 99%

Negative differential Rashba effect in two-dimensional hole systems

Habib

Tutuc

Melinte

et al. 2004

Applied Physics Letters

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We demonstrate experimentally and theoretically that two-dimensional (2D) heavy hole systems in single heterostructures exhibit a decrease in spin-orbit interaction-induced spin splitting with an increase in perpendicular electric field. Using front and back gates, we measure the spin splitting as a function of applied electric field while keeping the density constant. Our results are in contrast to the more familiar case of 2D electrons where spin splitting increases with electric field.In a solid that lacks inversion symmetry, the spin-orbit interaction leads to a lifting of the spin degeneracy of the energy bands, even in the absence of an applied magnetic field, B. In such a solid, the energy bands at finite wave vectors are split into two spin subbands with different energy surfaces, populations, and effective masses. The problem of inversion asymmetry-induced spin splitting in two-dimensional (2D) carrier systems in semiconductor heterojunctions and quantum wells [1,2,3,4] has become of renewed interest recently [5] because of their possible use in realizing spintronic devices such as a spin field-effect transistor [6,7], and for studying fundamental phenomena such as the spin Berry phase [8,9].In 2D carrier systems confined to GaAs/AlGaAs heterostructures, the bulk inversion asymmetry (BIA) of the zinc blende structure and the structure inversion asymmetry (SIA) of the confining potential contribute to the B = 0 spin splitting [4,5]. While BIA is fixed, the so called Rashba spin splitting [10] due to SIA can be tuned by means of external gates that change the perpendicular electric field (E ⊥ ) in the sample. For many years it has been assumed that the Rashba spin splitting in 2D carrier systems is proportional to E ⊥ that characterizes the inversion asymmetry of the confining potential [4]. 2D holes contained in a GaAs square quantum well provide an example [11]. On the contrary, in the present work we show both experimentally and theoretically that for heavy holes confined to a triangular well at the GaAs/AlGaAs interface, spin splitting decreases with an increase in E ⊥ . We demonstrate this negative differential Rashba effect by analyzing the Shubnikov-de Haas oscillations in this system at a constant density. We note that hole systems have recently gained great attention for spintronics applications [12] because ferromagnetic (III,Mn)V compounds are intrinsically p type. A detailed understanding of the B = 0 spin splitting in hole systems is thus of great importance.The sample used in our study was grown on a GaAs (001) substrate by molecular beam epitaxy and contains a modulation-doped 2D hole system confined to a GaAs/AlGaAs heterostructure [ Fig. 1(a)]. The Al 0.3 Ga 0.7 As/GaAs interface is separated from a 16 nm thick Be-doped Al 0.3 Ga 0.7 As layer (Be concentration of 3.5 × 10 18 cm −3 ) by a 25 nm Al 0.3 Ga 0.7 As spacer layer. We fabricated Hall bar samples via lithography and used In/Zn alloyed at 440 • C for the ohmic contacts. Metal gates were deposited on the sample's front and back to c...

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Anomalous Rashba spin splitting in two-dimensional hole systems

Cited by 133 publications

References 17 publications

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGeQuantum Well

Negative differential Rashba effect in two-dimensional hole systems

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