Negative differential Rashba effect in two-dimensional hole systems

Abstract

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...

Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system

“…Note that this condition can be satisfied when the quasi-2D system is sufficiently narrow and the density and the temperature are not too high. In this way, the effective Hamiltonian for a single heavy-hole subjected a spin-orbit interaction due to the structural inversion asymmetry, can be written as 7,22,23,24,25,26,27 …”

Spin dynamics in semiconductors

“…is the splitting between the i-th heavy-hole subband and the j-th light-hole subband. Similar to the case in the electron system, the hole Rashba spin-orbit coupling can also be tuned by gate-voltage and structure asymmetry, but now α hh is also electric field dependent [113,[211][212][213][214].…”

Superefficient electric-field–induced spin-orbit splitting in strained p -type quantum wells

“…∆k initially increases with electric field but for larger ε we find an inverse Rashba effect with ∆k decreasing with ε. This phenomenon has recently been demonstrated experimentally [21]. A qualitative explanation is that the electric field increases the energy separation between HH1 and LH1 and thereby 7 decreases the interaction between them.…”