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Epitaxial semiconductor nanowires with charge carrier holes can exhibit an infinite mass of holes and spin-locking due to chiral spectrum linear in momentum and spin. The criterion for emergence of topological superconductivity and Majorana fermions in these wires coupled to an s-type superconductors is the same as in topological insulators, and opposite to the criterion of onset of Majorana modes in quantum wires with parabolic spectrum in the presence of spin-orbit interactions., Comment: 5 pages, 3 figures

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one, in which impurity disorder strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and the other, where Majorana fermions are protected by disorder-robust superconductor gap. In this work we predict a third class of topological superconductivity and Majorana modes, in which they appear exclusively in the presence of impurity disorder. Observation and control of Majorana fermions and other non-Abelions often requires a symmetry leading to a gap in a single-particle spectra. Disorder introduces states into the gap and enables conductance and proximity-induced superconductivity via the in-gap states. We show that disorder-enabled topological superconductivity can be realized in a quantum Hall ferromagnet, when helical domain walls are coupled to an s-wave superconductor. Solving a general quantum mechanical problem of impurity bound states in a system of spin-orbit coupled Landau levels, we show that disorder-induced Majorana modes emerge in a setting of the quantum Hall ferromagnetic transition in a CdMnTe quantum wells at a filling factor $\nu=2$. Recent experiments on transport through electrostatically controlled single domain wall in this system indicated the vital role of disorder in conductance, but left an unresolved question whether this could intrinsically preclude generation of Majorana fermions. The proposed resolution of the problem, demonstrating emergence of Majorana fermions exclusively due to impurity disorder, opens a path forward. We show that electrostatic control of domain walls in an integer quantum Hall ferromagnet allows manipulation of Majorana modes. Similar physics can emerge for ferromagnetic transitions in the fractional quantum Hall regime leading to the formation and control of higher order non-Abelian excitations., Comment: Connection to existing experiment discussed in more detail. 27 preprint pages, 11 figures, Supplemental material: 7 pages, 1 figure. Submitted to Physical Review X

The reentrant integer quantum Hall effects (RIQHE) are due to formation of electronic crystals. We show analytically and numerically that topological textures in the charge density distribution in these crystals in the vicinity of charged defects strongly reduce energy required for current-carrying excitations. The theory quantitatively explains sharp insulator-metal transitions experimentally observed in RIQHE states. The insulator to metal transition in RIQHE emerges as a thermodynamic unbinding transition of topological charged defects., Comment: 13 pages + Supplemental materials

At each of the boundaries of the two-dimensional (2D) rectangular conductor parallel to the electric current there arises a stripe with an electric field transverse to the current and a 100% electron spin polarization. The two stripes have opposite spin orientations and opposite directions of electric fields. The magnitudes of the fields, directly related to the spin current if the spin relaxation is negligible, are the same. The periphery stripes 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 center-line and reaches +1 or -1 at the boundaries between the central and periphery stripes. Weak relaxation of the z-component of spin normal to the 2D plane modifies the magnitudes of the spin polarization and fields, with +1 (-1) spin polarization persisting at the edges of the sample. Favorable experimental settings, in which the electron spin relaxation of the z-component of spin is suppressed but the spin current is not, are discussed.

We propose a novel scheme of solid state realization of a quantum computer based on single spin "enhancement mode" quantum dots as building blocks. In the enhancement quantum dots, just one electron can be brought into initially empty dot, in contrast to depletion mode dots based on expelling of electrons from multi-electron dots by gates. The quantum computer architectures based on depletion dots are confronted by several challenges making scalability difficult. These challenges can be successfully met by the approach based on ehnancement mode, capable of producing square array of dots with versatile functionalities. These functionalities allow transportation of qubits, including teleportation, and error correction based on straightforward one- and two-qubit operations. We describe physical properties and demonstrate experimental characteristics of enhancement quantum dots and single-electron transistors based on InAs/GaSb composite quantum wells. We discuss the materials aspects of quantum dot quantum computing, including the materials with large spin splitting such as InAs, as well as perspectives of enhancement mode approach in materials such as Si., 38 pages, 7 figures

Using singly connected rings with a collimating contact to current leads, we have observed the spin quantum beating in the Aharonov-Bohm conductance oscillations. We demonstrate that the beating is a result of the superposition of two independent interference patterns associated with two orthogonal spin chiral states arising from intrinsic spin-orbit interactions. Our work provides the conclusive evidence of the spin Berry's phase in the conductance of quantum rings., pdf-file, 4 figures attached, submitted to Physical Review Letters