Towards searching for Majorana fermions in topological insulator nanowires

Developing a gate-tunable, scalable, and topologically-protectable supercurrent qubit and integrating it into a quantum circuit are crucial for applications in the fields of quantum information technology and topological phenomena. Here we propose that the nano-hybrid supercurrent transistors, a superconducting quantum analogue of a transistor, made of topological insulator nanowire would be a promising platform for unprecedented control of both the supercurrent magnitude and the current-phase relation by applying a voltage on a gate electrode. We believe that our experimental design will help probing Majorana state in topological insulator nanowire and establishing a solid-state platform for topological supercurrent qubit.Comment: 11 pages, 2 figure

Dilute magnetic topological semiconductors: What's new beyond the physics of dilute magnetic semiconductors?

Role of localized magnetic moments in metal-insulator transitions lies at the heart of modern condensed matter physics, for example, the mechanism of high T$_{c}$ superconductivity, the nature of non-Fermi liquid physics near heavy fermion quantum criticality, the problem of metal-insulator transitions in doped semiconductors, and etc. Dilute magnetic semiconductors have been studied for more than twenty years, achieving spin polarized electric currents in spite of low Curie temperatures. Replacing semiconductors with topological insulators, we propose the problem of dilute magnetic topological semiconductors. Increasing disorder strength which corresponds to the size distribution of ferromagnetic clusters, we suggest a novel disordered metallic state, where Weyl metallic islands appear to form inhomogeneous mixtures with topological insulating phases. Performing the renormalization group analysis combined with experimental results, we propose a phase diagram in $(\lambda_{so},\Gamma,T)$, where the spin-orbit coupling $\lambda_{so}$ controls a topological phase transition from a topological semiconductor to a semiconductor with temperature $T$ and the distribution for ferromagnetic clusters $\Gamma$ gives rise to a novel insulator-metal transition from either a topological insulating or band insulating phase to an inhomogeneously distributed Weyl metallic state with such insulating islands. Since electromagnetic properties in Weyl metal are described by axion electrodynamics, the role of random axion electrodynamics in transport phenomena casts an interesting problem beyond the physics of percolation in conventional disorder-driven metal-insulator transitions. We also discuss how to verify such inhomogeneous mixtures based on atomic force microscopy

Controlling transport properties of graphene nanoribbons by codoping-induced edge distortions

One notable manifestation of the peculiar edge-localized states in zigzag graphene nanoribbons (zGNRs) is the p-type (n-type) characteristics of nitrogen (boron) edge-doped GNRs, and such behavior was so far considered to be exclusive for zGNRs. Carrying out first-principles electronic structure and quantum transport calculations, we herein show that the donor-acceptor transition behavior can also arise in the B/N edge-doped armchair GNRs (aGNRs) by introducing a bipolar P codopant atom into the energetically most favorable nearest neighbor edge sites. The n-type (p-type) transport properties of B,P (N,P) co-doped aGNRs are also shown to be superior to those of reference single N (B) doped aGNRs in that the valence (conduction) band edge conductance spectra are better preserved. Disentangling the chemical doping and structural distortion effects, we will demonstrate that the latter plays an important role in determining the transport type and explains the donor-acceptor transition feature as well as the bipolar character of P-doped aGNRs. We thus propose the systematic modification of GNR edge atomic structures via co-doping as a novel approach to control charge transport characteristics of aGNRs.Comment: 11 pages, 5 figures, 1 tabl

Conductance recovery and spin polarization in boron and nitrogen codoped graphene nanoribbons

We present an ab initio study of the structural, electronic, and quantum transport properties of B-N-complex edge-doped graphene nanoribbons (GNRs). We find that the B-N edge codop-ing is energetically a very favorable process and furthermore can achieve novel doping effects that are absent for the single B or N doping. The compensation effect between B and N is predicted to generally recover the excellent electronic transport properties of pristine GNRs. For the zigzag GNRs, however, the spatially localized B-N defect states selectively destroy the doped-side spin-polarized GNR edge currents at the valence and conduction band edges. We show that the energetically and spatially spin-polarized currents survive even in the fully ferromagnetic metallic state and heterojunction configurations. This suggests a simple yet ef-ficient scheme to achieve effectively smooth GNR edges and graphene-based spintronic de-vices.Comment: 17 pages, 5 figure

A topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking

Introducing both Berry curvature and chiral anomaly into Landau's Fermi-liquid theory, we construct a topological Fermi-liquid theory, applicable to interacting Weyl metals in the absence of time reversal symmetry. Following the Landau's Fermi-liquid theory, we obtain an effective free-energy functional in terms of the density field of chiral fermions. The density field of chiral fermions is determined by a self-consistent equation, minimizing the effective free-energy functional with respect to the order-parameter field. Beyond these thermodynamic properties, we construct Boltzmann transport theory to encode both the Berry curvature and the chiral anomaly in the presence of forward scattering of a Fermi-liquid state, essential for understanding dynamic correlations in interacting Weyl metals. This generalizes the Boltzmann transport theory for the Landau's Fermi-liquid state in the respect of incorporating the topological structure and extends that for noninteracting Weyl metals in the sense of introducing the forward scattering. Finally, we justify this topological Fermi-liquid theory, generalizing the first-quantization description for noninteracting Weyl metals into the second-quantization representation for interacting Weyl metals. First, we derive a topological Fermi-gas theory, integrating over high-energy electronic degrees of freedom deep inside a pair of chiral Fermi surfaces. As a result, we reproduce a topological Drude model with both the Berry curvature and the chiral anomaly. Second, we take into account interactions between such low-energy chiral fermions on the pair of chiral Fermi surfaces. We perform the renormalization group analysis, and find that only forward scattering turns out to be marginal above possible superconducting transition temperatures, justifying the topological Fermi-liquid theory of interacting Weyl metals with time reversal symmetry breaking

Representation theory of symmetric groups and the strong Lefschetz property

We investigate the structure and properties of an Artinian monomial complete intersection quotient $A(n,d)=\mathbf{k} [x_{1}, \ldots, x_{n}] \big / (x_{1}^{d}, \ldots, x_{n}^d)$. We construct explicit homogeneous bases of $A(n,d)$ that are compatible with the $S_{n}$-module structure for $n=3$, all exponents $d \ge 3$ and all homogeneous degrees $j \ge 0$. Moreover, we derive the multiplicity formulas, both in recursive form and in closed form, for each irreducible component appearing in the $S_{3}$-module decomposition of homogeneous subspaces. 4, 5$

Spin-liquid Mott quantum criticality in two dimensions: Destabilization of a spinon Fermi surface and emergence of one-dimensional spin dynamics

Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2 k_{F}$ transfer momentum, where $k_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.Comment: Sign mistakes in previous RG equations were corrected. Physical aspects were rewritte

Temperature dependences of the surface resistance and the diamagnetic shielding susceptibility at T_c-T<<T_c for high-T_c superconductors

At T_c-T<<T_c(i.e., near T_c), in order to demonstrate the condudction mechanism and temperature dependencies of the diamagnetic-shielding susceptibility and the penetration depth, we fabricated Ba_1_xBiO_3(BKBO) thin films and measured the energy gap by tunnel effect and shielding susceptibilities which are compared with those measureed for BKBO and YBCO single crystals. The shielding susceptibilities for BKBO and YBCO single crystals well-fit \chi(T)/\chi(0)=1-exp(-2\triangle(T)/k_BT), while that for the BKBO film follows \chi(T)/\chi(0)=1-T/T_c) which may not be intrinsic. The exponential decrease of the susceptibilities near T_c indicates that the conduction mechanism is hopping. The energy gaps are observed as 2\triangle(0)=(3.5+-0.1)k_BT_c for the BKBO film by the tunnel effect, 2\triangle(0)=(3.9+-0.1)k_BT_c for the BKBO single crystal, and 2\triangle(0)=(8+-0.2)k_BT_c for the YBCO single crystal. Furthermore, for microwave device applications of superconductors, at T_c-T<<T_c, the surface resistance R_s(T) is derived from the surface impedance at \omega\tau_(tr)<<1, where \sigma_s(0) and \sigma_n are the conductivities of the superconducting state and the normal state, respectively, and f(T)=\chi(T)/\chi(0)=1-exp(-2\tringle(T)/k_BT).Comment: RevTex, 5 pages, 5 eps figure

Macroscopic Quantum Tunneling in Superconducting Junctions of \beta-Ag2_{2}Se Topological Insulator Nanowire

We report on the fabrication and electrical transport properties of superconducting junctions made of \beta-Ag$_{2}$Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to T = 0.8 K. Our observations indicate that the TI nanowire-based Josephson junctions can be a promising building block for the development of nanohybrid superconducting quantum bits.Comment: 27 pages, 8 figure

An ultrahigh-Q microsphere laser based on the evanescent-wave-coupled gain

We have demonstrated an ultrahigh-Q whispering-gallery-mode (WGM) microsphere laser based on the evanescent-wave-coupled gain. Dye molecules outside the sphere near the equator were excited, resulting in WGM lasing in the lowest radial mode order. The loaded quality factor of the lasing WGM was 8(2)\times 10^9, the highest ever achieved in the microlaser.Comment: 4 pages, 5 figure