Session J14: Focus Session: Spins in Semiconductors - Spin-Orbit Coupled Electrons and Holes in Semiconductors

Spin-dependent transport of spin-orbit coupled holes in GaAs nanostructures

In undergraduate physics, we are often taught that holes in the valence band are just positively charged heavy electrons. But valence band holes are spin-3/2 particles, and this gives them very different properties to spin-1/2 electrons, particularly when confined to low dimensions. These differences show up as highly anisotropic spin properties, which can be directly probed with conventional transport measurements. We have fabricated high quality hole quantum wires that show clean and stable quantized conductance plateaus [1]. In contrast to 1D electron quantum systems, the spin-splitting in these hole wires is highly anisotropic [2], and depends only on the orientation of the in-plane magnetic field relative to the quantum wire [3]. However the orientation and $k$-dependence of the spin-splitting cannot be reconciled with existing theories, suggesting that more theoretical work is needed before we understand the physics of spin-3/2 holes, even on ``simple'' (100) surfaces. We have also studied spin-3/2 holes in quantum dots, which show characteristic signatures of Kondo physics. A clear zero-bias peak is observed in the differential conductance, which splits with an applied in-plane magnetic field. The splitting is twice as large as the splitting for the lowest one-dimensional subband, consistent with Kondo physics. Unlike electrons this splitting is highly anisotropic with magnetic field, due to the strong spin-orbit coupling [4]. \\[4pt] [1] O. Klochan \textit{et al.}, Appl. Phys. Lett. \textbf{89}, 092105 (2006).\\[0pt] [2] R. Danneau \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 026403 (2006).\\[0pt] [3] J C H Chen \textit{et al,} New Journal of Physics \textbf{12}, 033043 (2010).\\[0pt] [4] O. Klochan \textit{et al}, Phys. Rev. Lett. \textbf{107}, 076805 (2011).   

Quantum-confined holes: More spin for your buck!

The physical properties of charge carriers in crystalline solids are dictated largely by the material's band structure. Typically, band electrons from the (lowest) conduction band behave very similarly to free electrons in vacuum, only with parameters such as their mass and $g$-factor adjusted. In contrast, holes from the (upper-most) valence band show a much richer behavior owing to their intrinsic spin-$3/2$ degree of freedom and this spin{'}s strong coupling to the crystal momentum of holes. In a two-dimensional (2D) quantum well, size quantisation induces an energy splitting between heavy-hole (HH) and light-hole (LH) subbands. The existence of this HH-LH \emph{splitting\/} makes it tempting to consider HH and LH degrees of freedom separately, in particular in situations where only the highest (generally HH-like) 2D hole subband is occupied. In my talk, I will focus on how such an approach overlooks intriguing differences in the mesoscopic and many-particle properties exhibited by quantum-confined holes as compared with their conduction-electron counterparts. Recent results on the density response [1] and spin susceptibility of 2D holes will be presented to illustrate the ramifications of ubiquitous HH-LH \emph{mixing\/}. I will also discuss how the temporal modulation of Rashba spin splitting in hole nanostructures generates larger-magnitude spin currents than in corresponding band-electron systems [2]. Finally, Andreev reflection of holes in a p-type-semiconductor~--~superconductor hybrid system will be considered [3], which also exhibits novel behavior due to band mixing. \\[4pt] [1] T. Kernreiter, M. Governale, and U. Zulicke, New J. Phys. \textbf{12}, 093002 (2010).\\[0pt] [2] T. Kernreiter, M. Governale, A. R. Hamilton, and U. Zulicke, Appl. Phys. Lett. \textbf{98}, 152101 (2011).\\[0pt] [3] D. Futterer, M. Governale, U. Zulicke, and J. Konig, Phys. Rev. B \textbf{84}, 104526 (2011).   

Spin-electric stripes: electric voltage generated by spin current

At the boundaries of the two-dimensional conductor, stripes arise with an electric field transverse to the flowing electric current, and with 100\% electron spin polarization perpendicular to the 2D plane. In these boundary stripes, the magnitudes of spin polarizations are the same, the magnitudes of transverse electric fields are the same, but the directions of electric fields and orientations of spins are opposite. If the spin relaxation is negligible, the magnitudes of the electric fields are directly related to the spin current. The stripes at boundaries are separated by a center-stripe, in which the magnitude and direction of the electric field depend on the ratio of the skew scattering and side jump spin currents. The spin polarization is zero on the centerline and reaches +1 or -1 at the boundaries between the central and periphery stripes if spin relaxation of the z-component of spin normal to the 2D plane is absent. Weak spin relaxation modifies the magnitudes of the spin polarization and electric fields, with +1 or -1 spin polarization persisting at the edges of the sample. Favorable experimental settings, in which electron or hole spin relaxation of the z-component of spin is suppressed but the spin current is not, are discussed.   

Spin-orbit or Aharonov-Casher edge states in semiconductor two-dimensional systems

In semiconductors with spin-orbit interaction we experimentally search for edge states induced by the Aharonov-Casher vector potential or Rashba-type spin-orbit interaction. The Aharonov-Casher effect is electromagnetically dual to the Aharonov-Bohm effect and is predicted to lead to a possibly helical edge state structure at two-dimensional sample edges. We use InGaAs/InAlAs heterostructures patterned into mesoscopic side-gated channel structures, where the edge states can be induced, and where backscattering between edge states can be experimentally measured in the resistance. Sweeping side-gate voltage, low temperature resistances are measured across such mesoscopic closed-path structures at either low applied magnetic field, in-plane or normal to the plane, or at fixed magnetic filling factors of 5, 6, 7, and 8 to obtain states of defined spin. Resistance oscillations are observed at low magnetic fields and around filling factor 6 as function of side-gate voltage, and we analyze the oscillations in the light of the search for the edge states (DOE DE-FG02-08ER46532, NSF DMR-0520550).   

Spin orbit coupling induced splitting in excitations of high mobility 2DESs

Spin orbit interaction (SOI) induces a splitting of the conduction bands in two-dimensional electron systems (2DES) in GaAs. We study the impact of zero-field spin-splitting on excitations of ultra high mobility 2DESs by resonant inelastic light scattering experiments. To distinguish between splitting caused by bulk inversion asymmetry (Dresselhaus) and structure inversion asymmetry (Rashba), we studied symmetric (two-side modulation doped) and asymmetric (single-side modulation doped) quantum wells grown along (001) and (110) crystallographic directions. We probe the excitation modes as a function of transferred momentum for different crystallographic directions in the plane of the QW. At large wave vectors we find a complex splitting of the single-particle intersubband excitation mode that is strongly dependent on the combination of Dresselhaus and Rashba SOI. The observed mode splitting is a result of effective SOI fields in both, ground and first excited subband. Suitable choices of crystallographic orientations yield Dresselhaus and Rashba terms.   

Current-induced spin polarization along spin orbit fields in strained InGaAs

Current-induced spin polarization is a phenomenon in which electron spins undergo a momentum-dependent net spin polarization \footnote{Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett. {\bf93}, 176601 (2004)}, but the mechanism and how material parameters govern the magnitude of this effect remains an open question. Conductive channels are etched into strained n-doped InGaAs samples along the [110], [1$\overline{1}$0], [100] and [010] crystal axes with ohmic contacts at either end to allow control of electrical current. While the spin polarization direction is found to align along the direction of the measured spin-orbit effective magnetic fields \footnote{B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, Phys. Rev. B. {\bf82}, 081304(R) (2010)}, the magnitude of the spin polarization is not proportional to the magnitude of the spin-orbit fields. Surprisingly, crystal axes with the smallest spin-orbit fields appear to have the largest net spin polarization. Our measurements suggest that the longer spin dephasing time for smaller spin-orbit interactions may play a significant role.   

Thermodynamic compressibility and spin-splitting in one-dimensional quantum wires

We study spin-splitting and the much-debated $0.7$ structure in GaAs quantum wires using compressibility measurements that directly probe the thermodynamic density of states. Two quantum wires are simultaneously defined in the upper and lower well of a GaAs/AlGaAs double quantum well heterostructure, using midline-gated split-gate devices [1]. The lower wire probes the ability of the upper wire to screen the electric field from a biased surface gate. The technique is sensitive enough to resolve spin splitting of the 1D subbands in the presence of an in-plane magnetic field. The compressibility response of the $0.7$ structure is measured, and its evolution with increasing temperature and magnetic field is studied [2]. Despite the sensitivity of our measurements we see no evidence of the formation of the quasibound state predicted by the Kondo model of the $0.7$ structure. Instead our data are more consistent with theories which predict that the $0.7$ structure arises as a result of spontaneous spin polarization. \\[4pt] [1] I.M. Castleton \emph{et al}, Physica B 249, 157 (1998).\\[0pt] [2] L.W. Smith \emph{et al}, Phys. Rev. Lett. 107, 126801 (2011)   

Spin-orbit effects in two-dimensional hole systems on hydrogen-terminated silicon (111) surfaces

We have studied spin-orbit effects in two-dimensional hole systems (2DHSs) on hydrogen-terminated Si(111) surfaces using Shubnikov-de Haas (SdH) oscillations. The device has a vacuum field-effect transistor structure [1], and the 2DHS is induced on the H-Si(111) surface. Hole concentrations up to $8\times 10^{11}$ cm$^{-2}$ are obtained, and the peak hole mobility is about 15,000 cm$^{2}$/Vs at T = 1.5 K. SdH oscillations show that the heavy hole subband is spin split due to spin-orbit effects. Both frequencies and beating node locations of the SdH oscillations are used to characterize the spin-orbit effects. The spin-splitting energy is measured as a function of the hole concentration, and the underlying physics will be discussed. Heavy-hole effective mass is determined by the temperature dependence of the SdH oscillations, and the relationship between the effective mass and the hole concentration will be presented. [1] K. Eng, R. N. McFarland, and B. E. Kane, Appl. Phys. Lett. \textbf{87}, 052106 (2005)   

Quasiparticle velocities in 2D electron/hole liquids with spin-orbit coupling

We study the influence of spin-orbit interactions on quasiparticle dispersions in two-dimensional electron and heavy-hole liquids in III-V semiconductors. To obtain closed-form analytical results, we work within the screened Hartree-Fock approximation, valid in the high-density limit. For electrons having a linear-in momentum spin-orbit interaction, we confirm known results based on the random-phase approximation and we extend those results to higher order in the spin-orbit coupling. For hole systems, with a leading nonlinear-in-momentum spin-orbit interaction, we find two important distinctions. First, the group velocities associated with the two hole-spin branches acquire a significant difference in the presence of spin-orbit interactions, allowing for the creation of spin-polarized wavepackets in zero magnetic field. Second, we find that the interplay of Coulomb and spin-orbit interactions is significantly more important for holes than for electrons and can be probed through the quasiparticle group velocities. These effects should be directly observable in magnetotransport, Raman scattering, and femtosecond-resolved Faraday rotation measurements.   

Spin Coulomb drag and optical excitations in low dimensional systems

Within the remit of new quantum technologies, an intense effort is devoted to improving our understanding of spin dynamics, with the aim of building novel spintronics devices. In this context the theory of spin Coulomb drag (SCD) was recently developed. It shows that Coulomb interactions are an intrinsic decay mechanism for spin currents. As confirmed by experiments, SCD can be substantial in semiconductors, and it is bound to become one of the most serious issues in spin polarized transport, since, due to its intrinsic nature, it cannot be avoided even in the purest material. More recently the influence of SCD on optical spin-injection and spin-resolved optical experiments has been considered. Here we report on SCD effects on intersubband optical spin excitations in III-V quantum wells, where SCD may contribute substantially to the linewidth of spin plasmons. By going beyond the usual local density functional approximation and properly including the effects due to the inhomogeneity of the system in the growth direction, we show that the quantization of states in the growth direction may strongly reduce the intrinsic plasmon linewidth.   

Theory of Helical Fermi liquids

We extend the Landau Fermi Liquid (FL) theory to include spin-orbit coupling (SOC). In particular, the Rashba SOC is chosen as an example. It is shown that although ``charge-part'' quantities, such as the charge susceptibility and effective mass, are determined solely by the quasi-particles, ``spin-part'' quantities, such as the spin susceptibility, have contributions from the damped states in between the two Fermi surfaces induced by the SOC. However, contributions to the lowest order in the SOC can still be extracted from the theory. The nature of the instabilities of such spin-orbit coupled FL is discussed.