Session T14: Focus Session: Spins in Semiconductors - Spins and Edge States

Controlled coupling of spin-resolved quantum Hall edge states

Spin resolved edge states in quantum Hall systems at filling fraction $\nu $ = 2 posses large coherence [1] and relaxation [2] lengths. They are ideal candidates for the implementation of dual-rail quantum computation architectures [3] by encoding the qubit in the spin degree of freedom of the co-propagating spin resolved edge states. An important element for realization of such architectures is a coherent beam splitter that controllably mixes the two co-propagating spin-resolved edge channels to create any superposition of the two logic states. In this talk we demonstrate a new method to controllably couple spin resolved edge states and induce inter-edge charge transfer associated to spin-flip scattering events [4]. The process exploits the coupling of the electron spin with a spatially-dependent periodic in-plane magnetic field that is created by an array of Cobalt nano-magnets placed at the boundary of the GaAs/AlGaAs modulation doped heterostructure. The maximum charge/spin transfer of 28 $\pm $ 1 {\%} is achieved at 250 mK by fine tuning the perpendicular magnetic field. These results are key steps towards the realization of a scalable quantum interferometric device currently under investigation in our group. \\[4pt] [1] Y. Ji et al. Nature 422 (2003) 415.\\[0pt] [2] G. Muller et al. Phy. Rev. B 45 (1992) 3932.\\[0pt] [3] V. Giovannetti et al., \textit{Phys. Rev. B} 77 (2008) 155320.\\[0pt] [4] B. Karmakar et al., (accepted in PRL).   

Theory of Temperature-dependent Spin Dynamics with Electron-Phonon Interaction

We develop a theory of temperature-dependent spin dynamics in spin-orbit coupled semiconductors that includes the effects of electron-phonon interaction. A set of coupled kinetic equations for the spin density matrix are derived starting from the quantum Liouville equation. The spin-conserving and spin-flipping scattering terms due to electron-phonon interaction in the presence of spin-orbit coupling are derived explicitly using an effective low-energy Hamiltonian for the conduction and valence bands. From the solution of the kinetic equations, we extract the temperature dependence of spin transport and relaxation in various parameter regimes. In particular, we discuss the effect of electron-phonon interaction on the persistent spin helix lifetime.   

Absence of intrinsic spin splitting in 1D quantum wires of tetrahedral semiconductors

The energy bands of 3D, 2D, and 1D structures are generally split at certain wavevector values into spin-components, a spin splitting that occurs even without external magnetic field and reflects the effect of spin-orbit interaction on certain symmetries. We show via atomistic theory that 1D quantum-wires made of conventional zincblende semiconductors have unexpected zero SS for all electron and hole bands if the wire is oriented along (001) (belonging to D2d symmetry), and for some of bands if the wire is oriented along (111) (belonging to C3v symmetry). We find that the predicted absence of Dresselhaus SS in both (001)-oriented and (111)-oriented 1D wires is immune to perturbations lowering their original $D_{2d}$ and $C_{3v}$ structural symmetries, such as alloying of the matrix around the wire or application of an external electric field. Indeed, such perturbations induce only Rashba SS. We find that the scaling of the SS with wavevector is dominated by a linear term plus a minor cubic term.\\[4pt]J.W. Luo, L. Zhang, and A. Zunger, Phys. Rev. B 84, 121303(R) (2011).   

chiral magnon edge mode in a magnonic crystal

A bosonic system with a periodically crystalline potential has a Chern integer associated with its magnetic Bloch wavefunction. As in its fermionic counterpart like integer quantum Hall states, the Chern number thus introduced is defined for each bosonic energy band which is energetically separated from the others. When two bosonic systems having different Chern integers are connected, or when a bosonic system with non-zero Chern integer is terminated with the vaccum, chiral bosonic edge modes appear in their boundaries. We argue that a simple magnonic crystal can realize such magnonic chiral edge modes. Based on this example, we show how to design spin-wave guides in a magnonic crystal and how to channelize, spit and manipulate them.   

Anomalous Hall and Nernst effects in electron and hole-doped semiconductors

Recently it has been proposed that Majorana fermions may exist in a thin film semiconductor with proximity induced s-wave superconductivity. We compute anomalous Hall and anomalous Nernst coefficients for both electron and hole-doped semiconducting systems in the presence of an in-plane magnetic field and Rashba and Dresselhaus spin-orbit coupling. The anomalous Nernst coefficient vanishes and has plateaus as a function of the chemical potential corresponding to carrier densities which realize the topological state.   

The Origin of Dirac Cones for Classical Waves in Periodic Systems

By using a perturbation method, we propose a general theory to understand the origin of Dirac cone dispersions for classical waves in periodic structures. A selection rule for the existence of Dirac cones is established under the group theory analysis, which reveals the relation between the unusual linear dispersions and the symmetry of the degenerate Bloch states at the Dirac point. The theory is capable of accurately predicting the linear slopes at various symmetry points in the Brilliouin zone, independent of frequency and lattice structure. Furthermore, it can be also used to construct the Hamiltonian, which is in consistent with the Berry phase calculations.   

Exactly Solvable Topological Chiral Spin Liquid with Random Exchange

We extend the Yao-Kivelson decorated honeycomb lattice Kitaev model [Phys. Rev. Lett.99, 247203 (2007)] of an exactly solvable chiral spin liquid by including disordered exchange couplings. We have determined the phase diagram of this system and found that disorder enlarges the region of the topological non-Abelian phase with finite Chern number. We study the energy level statistics as a function of disorder and other parameters in the Hamiltonian, and show that the phase transition between the non-Abelian and Abelian phases of the model at large disorder can be associated with pair annihilation of extended states at zero energy. Analogies to integer quantum Hall systems, topological Anderson insulators, and disordered topological Chern insulators are discussed.   

Lie algebras for time-dependent Rashba-Dresselhaus materials

We study the spin dynamics of Rashba and Dresselhaus interactions in systems with unconfined and confined geometries. We show how Lie algebra factorization of the evolution can be used to describe systems with arbitrary time-dependence in the parameters.   

Quantum Spin Holography with Surface State Electrons

Recently Moon et~al. have shown that information can be stored in a fermionic state of a two-dimensional electron gas and have dubbed the proposed concept quantum holographic encoding. They have constructed molecular holograms of CO molecules on a Cu(111) surface, hosting a surface state (SS) [2]. Interference of electron waves scattered at the molecules leads to formation of an electron density pattern representing an information page [1]. This page has then been read out with an STM. It has been also shown that using the innate energy dispersion of SS electrons one can project the hologram not only in two spatial degrees of freedom but also in the energy dimension. In our contribution we expand the concept and show that the spin of the electron can also act as a new dimension for information storage. If the molecules or atoms used for a hologram are magnetic then the scattering of surface state electrons becomes spin-dependent, allowing one to store different information pages in different spin channels. As an example we demonstrate the possibility of simultaneous encoding two different information pages with electrons of the same energy but opposite spins. \\[4pt] [1] C.R. Moon et al., Nature Nano. 4, 167 (2009)\\[0pt] [2] W. Shockley, Phys. Rev. 56, 317 (1939)