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We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted., Comment: 5 pages, 4 figures, supp. mat

We report transport studies on a three dimensional, 70 nm thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semi-metallic HgTe, which thus becomes a three dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states., Comment: 7 pages, 6 figures

Bi2Te3 compound has been theoretically predicted (1) to be a topological insulator, and its topologically non-trivial surface state with a single Dirac cone has been observed in photoemission experiments (2). Here we report that superconductivity (Tc^~3K) can be induced in Bi2Te3 as-grown single crystal (with hole-carriers) via pressure. The first-principles calculations show that the electronic structure under pressure remains to be topologically nontrivial, and the Dirac-type surface states can be well distinguished from bulk states at corresponding Fermi level. The proximity effect between superconducting bulk states and Dirac-type surface state could generate Majorana fermions on the surface. We also discuss the possibility that the bulk state could be a topological superconductor., Comment: Published ahead of print December 20, 2010, doi:10.1073/pnas.1014085108

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 added

Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare earth element Ln which can realize additional properties ranging from superconductivity (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors., Comment: 20 pages, 5 figures

Using $\vec{k}$$\cdot$$\vec{p}$ theory, we derive an effective four band model describing the physics of the typical two-dimensional topological insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in z-direction inversion breaking and in-plane confining potentials. We find that up to third order in perturbation theory, only the inversion breaking potential generates new elements to the four band Hamiltonian that are off-diagonal in spin space. When this new effective Hamiltonian is folded into an effective two band model for the conduction (electron) or valence (heavy hole) bands, two competing terms appear: (1) a Rashba spin-orbit interaction originating from inversion breaking potential in z-direction and (2) an in-plane Pauli term as a consequence of the in-plane confining potential. Spin transport in the conduction band is further analysed within the Landauer-B\"uttiker formalism. We find that for asymmetrically doped HgTe quantum wells, the behaviour of the spin-Hall conductance is dominated by the Rashba term., Comment: 23 pages, 4 figures, submitted to special NJP issue "Focus on topological insulators"

The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin Hall effect have been discovered in recent years. However, the quantized anomalous Hall (QAH) effect has not yet been realized experimentally. In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically non-trivial electronic structure, leading to the quantized Hall effect without any external magnetic field. In this work, based on state-of-art first principles calculations, we predict that the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$ form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor where free carriers are necessary to mediate the magnetic coupling. Magnetic order in two-dimensional thin films gives rise to a topological electronic structure characterized by a finite Chern number, with quantized Hall conductance $e^{2}/h$. Experimental realization of the long sought-after QAH insulator state could enable robust dissipationless charge transport at room temperature., Comment: 19 pages, 5 figures

We investigate the surface state of Bi$_2$Te$_3$ using angle resolved photoemission spectroscopy (ARPES) and transport measurements. By scanning over the entire Brillouin zone (BZ), we demonstrate that the surface state consists of a single non-degenerate Dirac cone centered at the $\Gamma$ point. Furthermore, with appropriate hole (Sn) doping to counteract intrinsic n-type doping from vacancy and anti-site defects, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states, consistent with a carrier sign change near this doping in transport properties. Our experimental results establish for the first time that Bi$_2$Te$_3$ is a three dimensional topological insulator with a single Dirac cone on the surface, as predicted by a recent theory., Comment: Submitted for publication on March 03, 2009

Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the intrinsic spin Hall effect from the extrinsic one., Comment: 4 pages, 4 figures

By combining experimental measurements of the quasiparticle and dynamical magnetic properties of optimally electron-doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$ with theoretical calculations we demonstrate that the conventional fermiology approach cannot possibly account for the magnetic fluctuations in these materials. In particular, we perform tunneling experiments on the very same sample for which a dynamical magnetic resonance has been reported recently and use photoemission data by others on a similar sample to characterize the fermionic quasiparticle excitations in great detail. We subsequently use this information to calculate the magnetic response within the conventional fermiology framework as applied in a large body of work for the hole-doped superconductors to find a profound disagreement between the theoretical expectations and the measurements: this approach predicts a step-like feature rather than a sharp resonance peak, it underestimates the intensity of the resonance by an order of magnitude, it suggests an unreasonable temperature dependence of the resonance, and most severely, it predicts that most of the spectral weight resides in incommensurate wings which are a key feature of the hole-doped cuprates but have never been observed in the electron-doped counterparts. Our findings strongly suggest that the magnetic fluctuations reflect the quantum-mechanical competition between antiferromagnetic and superconducting orders., Comment: 10 pages, 9 figures, 1 table

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice., Comment: 4 pages; The published version

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 pages

We construct a generalization of the quantum Hall effect where particles move in an eight dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the octonions. Two fundamentally different liquids with distinct configurations spaces can be constructed, depending on whether the particles carry spinor or vector SO(8) quantum numbers. One of the liquids lives on a 20 dimensional manifold of with an internal component of SO(7) holonomy, whereas the second liquid lives on a 14 dimensional manifold with an internal component of $G_2$ holonomy., Comment: 5 pages

We present numerical studies of a quantum ``projected'' SO(5) model which aims at a unifying description of antiferromagnetism and superconductivity in the high-T$_c$ cuprates, while properly taking into account the Mott insulating gap. Our numerical results, obtained by the Quantum Monte Carlo technique of Stochastic Series Expansion, show that this model can give a realistic description of the global phase diagram of the high-$T_c$ superconductors and accounts for many of their physical properties. Moreover, we address the question of dynamic restoring of the SO(5) symmetry at the critical point., Comment: Final version. Accepted for publication in Phys. Rev. Lett

The zero-temperature dynamical spin-spin correlation functions are calculated for the spin-1/2 two-leg Heisenberg ladder in a magnetic field above the lower critical field Hc1. The dynamical structure factors are calculated which exhibit both massless and massive excitations. These modes appear in different sectors characterized by the parity in the rung direction and by the momentum in the direction of the chains. The structure factors have power-law singularities at the lower edges of their support. The results are also applicable to spin-1 Heisenberg chain. The implications are briefly discussed for various correlation functions and the pi-resonance in the SO(5) symmetric ladder model., Comment: 15 pages, 6 figures, added references; final version to appear in Phys. Rev. B

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping., Comment: Revtex file, 7 pages and 7 eps-figures

A recent theory of the resonant neutron scattering peaks in YBCO superconductors predicts the existence of a sharp spin triplet two particle collective mode (the ``\pi resonance") in the normal state. In this paper, we propose an experiment in which the \pi resonance could be probed directly in a two particle tunneling measurement., Comment: 10 pages, LATEX , 3 ps figures

We show that the RMS fluctuation of the antisymmetric part of the Hall conductance of a planar mesoscopic metal in a random magnetic field with zero average is universal, of the order of $e^2/h$, independent of the amplitude of the random magnetic field and the diffusion coefficient even in the weak field limit. This quantity is exactly zero in the case of ordinary scalar disorder. We propose an experiment to measure this surprising effect, and also discuss its implications on the localization physics of this system. Our result applies to some other systems with broken time-reversal ({\bf T}) symmetry., Comment: 4 pages, Revtex 3.0; added the paragraph regarding applicability to other systems with broken T-invariance, misc. minor changes

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the localization length $\xi$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $\xi(E)\propto |E-E_c|^{-\nu}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($\nu\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed., Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request), #phd11