Holonomic Quantum Computing Based on the Stark Effect

We propose a spin manipulation technique based entirely on electric fields applied to acceptor states in $p$-type semiconductors with spin-orbit coupling. While interesting in its own right, the technique can also be used to implement fault-resilient holonomic quantum computing. We explicitly compute adiabatic transformation matrix (holonomy) of the degenerate states and comment on the feasibility of the scheme as an experimental technique.Comment: 5 page

Nonlocal edge state transport in the quantum spin Hall state

We present direct experimental evidence for nonlocal transport in HgTe quantum wells in the quantum spin Hall regime, in the absence of any external magnetic field. The data conclusively show that the non-dissipative quantum transport occurs through edge channels, while the contacts lead to equilibration between the counter-propagating spin states at the edge. We show that the experimental data agree quantitatively with the theory of the quantum spin Hall effect.Comment: 13 pages, 4 figure

Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.Comment: 14 pages, contribution to the proceedings of the Group 27 conference, Yerevan, Armenia, August 13-19, 2008, published versio

Quantum Blockades and Loop Currents in Graphene with Topological Defects

We investigate the effect of topological defects on the transport properties of a narrow ballistic ribbon of graphene with zigzag edges. Our results show that the longitudinal conductance vanishes at several discrete Fermi energies where the system develops loop orbital electric currents with certain chirality. The chirality depends on the direction of the applied bias voltage and the sign of the local curvature created by the topological defects. This novel quantum blockade phenomenon provides a new way to generate a magnetic moment by an external electric field, which can prove useful in carbon electronics.Comment: 6 pages, 7 figure

Insulating behavior in ultra-thin bismuth selenide field effect transistors

Ultrathin (~3 quintuple layer) field-effect transistors (FETs) of topological insulator Bi2Se3 are prepared by mechanical exfoliation on 300nm SiO2/Si susbtrates. Temperature- and gate-voltage dependent conductance measurements show that ultrathin Bi2Se3 FETs are n-type, and have a clear OFF state at negative gate voltage, with activated temperature-dependent conductance and energy barriers up to 250 meV

The Quantum Spin Hall Effect: Theory and Experiment

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an "inverted" type at a critical thickness $d_c$. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width $d_{QW}< 6.3$ nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells ($d_{QW}> 6.3$ nm), the nominally insulating regime shows a plateau of residual conductance close to $2e^2/h$. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, $d_c= 6.3$ nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.Comment: Invited review article for special issue of JPSJ, 32 pages. For higher resolution figures see official online version when publishe

Evidence of silicene in honeycomb structures of silicon on Ag(111)

In the search for evidence of silicene, a two-dimensional honeycomb lattice of silicon, it is important to obtain a complete picture for the evolution of Si structures on Ag(111), which is believed to be the most suitable substrate for growth of silicene so far. In this work we report the finding and evolution of several monolayer superstructures of silicon on Ag(111) depending on the coverage and temperature. Combined with first-principles calculations, the detailed structures of these phases have been illuminated. These structure were found to share common building blocks of silicon rings, and they evolve from a fragment of silicene to a complete monolayer silicene and multilayer silicene. Our results elucidate how silicene formes on Ag(111) surface and provide methods to synthesize high-quality and large-scale silicene.Comment: 6 pages, 4 figure

Single valley Dirac fermions in zero-gap HgTe quantum wells

Dirac fermions have been studied intensively in condensed matter physics in recent years. Many theoretical predictions critically depend on the number of valleys where the Dirac fermions are realized. In this work, we report the discovery of a two dimensional system with a single valley Dirac cone. We study the transport properties of HgTe quantum wells grown at the critical thickness separating between the topologically trivial and the quantum spin Hall phases. At high magnetic fields, the quantized Hall plateaus demonstrate the presence of a single valley Dirac point in this system. In addition, we clearly observe the linear dispersion of the zero mode spin levels. Also the conductivity at the Dirac point and its temperature dependence can be understood from single valley Dirac fermion physics.Comment: version 2: supplementary material adde

Quantum Mechanics Model on K\"ahler conifold

We propose an exactly-solvable model of the quantum oscillator on the class of K\"ahler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.Comment: 5 pages, RevTeX format, some misprints heve been correcte

New Family of Robust 2D Topological Insulators in van der Waals Heterostructures

We predict a new family of robust two-dimensional (2D) topological insulators in van der Waals heterostructures comprising graphene and chalcogenides BiTeX (X=Cl, Br and I). The layered structures of both constituent materials produce a naturally smooth interface that is conducive to proximity induced new topological states. First principles calculations reveal intrinsic topologically nontrivial bulk energy gaps as large as 70-80 meV, which can be further enhanced up to 120 meV by compression. The strong spin-orbit coupling in BiTeX has a significant influence on the graphene Dirac states, resulting in the topologically nontrivial band structure, which is confirmed by calculated nontrivial Z2 index and an explicit demonstration of metallic edge states. Such heterostructures offer an unique Dirac transport system that combines the 2D Dirac states from graphene and 1D Dirac edge states from the topological insulator, and it offers new ideas for innovative device designs