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Titus Neupert

Publications and source records attributed to Titus Neupert.

At least 181 records · Page 10Linked to original sources
arXiv2016

Boson Condensation in Topologically Ordered Quantum Liquids

Boson condensation in topological quantum field theories (TQFT) has been previously investigated through the formalism of Frobenius algebras and the use of vertex lifting coefficients. While general, this formalism is physically opaque and computationally arduous: analyses of TQFT condensation are practically performed on a case by case basis and for very simple theories only, mostly not using the Frobenius algebra formalism. In this paper we provide a new way of treating boson condensation that is computationally efficient. With a minimal set of physical assumptions, such as commutativity of lifting and the definition of confined particles, we can prove a number of theorems linking Boson condensation in TQFT with chiral algebra extensions, and with the factorization of completely positive matrices over the nonnegative integers. We present numerically efficient ways of obtaining a condensed theory fusion algebra and S matrices; and we then use our formalism to prove several theorems for the S and T matrices of simple current condensation and of theories which upon condensation result in a low number of confined particles. We also show that our formalism easily reproduces results existent in the mathematical literature such as the noncondensability of 5 and 10 layers of the Fibonacci TQFT.

cond-mat.str-el↗
arXiv2016

Wire deconstructionism of two-dimensional topological phases

A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in a periodic array. Which inter-wire couplings are allowed is dictated by symmetry and the compatibility criterion that they can simultaneously acquire a finite expectation value, opening a spectral gap between the ground state(s) and all excited states in the bulk. First, with these criteria at hand, we reproduce the tenfold classification table of integer topological insulators, where their stability against interactions becomes immediately transparent in the Luttinger liquid description. Second, we construct an example of a strongly interacting fermionic topological phase of matter with short-range entanglement that lies outside of the tenfold classification. Third, we expand the table to long-range entangled topological phases with intrinsic topological order and fractional excitations.

cond-mat.str-el↗
arXiv2015

Shiba chains of scalar impurities on unconventional superconductors

We show that a chain of nonmagnetic impurities deposited on a fully gapped two- or three-dimensional superconductor can become a topological one-dimensional superconductor with protected Majorana bound states at its end. A prerequisite is that the pairing potential of the underlying superconductor breaks the spin-rotation symmetry, as it is generically the case in systems with strong spin-orbit coupling. We illustrate this mechanism for a spinless triplet-superconductor p+ip and a time-reversal symmetric Rashba superconductor with a mixture of singlet and triplet pairing. For the latter, we show that the impurity chain can be topologically nontrivial even if the underlying superconductor is topologically trivial.

cond-mat.supr-con↗
arXiv2015

Experimental discovery of a topological Weyl semimetal state in TaP

Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of TaAs, TaP, NbAs and NbP was predicted as Weyl semimetal candidates. Here, we experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk and the Fermi arcs on the surface. Moreover, we find that the surface states show an unexpectedly rich structure, including both topological Fermi arcs and several topologically-trivial closed contours in the vicinity of the Weyl points, which provides a promising platform to study the interplay between topological and trivial surface states on a Weyl semimetal's surface. We directly demonstrate the bulk-boundary correspondence and hence establish the topologically nontrivial nature of the Weyl semimetal state in TaP, by resolving the net number of chiral edge modes on a closed path that encloses the Weyl node. This also provides, for the first time, an experimentally practical approach to demonstrating a bulk Weyl fermion from a surface state dispersion measured in photoemission.

cond-mat.mes-hall↗
arXiv2015

Atomic Scale Visualization of Quantum Interference on a Weyl Semimetal Surface by Scanning Tunneling Microscopy/Spectroscopy

Weyl semimetals may open a new era in condensed matter physics, materials science and nanotech after graphene and topological insulators. We report the first atomic scale view of the surface states of a Weyl semimetal (NbP) using scanning tunneling microscopy/spectroscopy. We observe coherent quantum interference patterns that arise from the scattering of quasiparticles near point defects on the surface. The measurements reveal the surface electronic structure both below and above the chemical potential in both real and reciprocal spaces. Moreover, the interference maps uncover the scattering processes of NbP's exotic surface states. Through comparison between experimental data and theoretical calculations, we further discover that the scattering channels are largely restricted by the orbital and/or spin texture of the surface band. The visualization of the scattering processes can help design novel transport effects and electronics on the topological surface of a Weyl semimetal.

cond-mat.mtrl-sci↗
arXiv2015

Spin polarization and texture of the Fermi arcs in the Weyl Fermion semimetal TaAs

A Weyl semimetal is a new state of matter that host Weyl fermions as quasiparticle excitations. The Weyl fermions at zero energy correspond to points of bulk band degeneracy, Weyl nodes, which are separated in momentum space and are connected only through the crystal's boundary by an exotic Fermi arc surface state. We experimentally measure the spin polarization of the Fermi arcs in the first experimentally discovered Weyl semimetal TaAs. Our spin data, for the first time, reveal that the Fermi arcs' spin polarization magnitude is as large as 80% and possesses a spin texture that is completely in-plane. Moreover, we demonstrate that the chirality of the Weyl nodes in TaAs cannot be inferred by the spin texture of the Fermi arcs. The observed non-degenerate property of the Fermi arcs is important for the establishment of its exact topological nature, which reveal that spins on the arc form a novel type of 2D matter. Additionally, the nearly full spin polarization we observed (~80%) may be useful in spintronic applications.

cond-mat.mtrl-sci↗
arXiv2015

Topological Superconductors and Category Theory

We give a pedagogical introduction to topologically ordered states of matter, with the aim of familiarizing the reader with their axiomatic topological quantum field theory description. We introduce basic noninteracting topological phases of matter protected by symmetries, including the Su-Schrieffer-Heeger model and the one-dimensional p-wave superconductor. The defining properties of topologically ordered states are illustrated explicitly using the toric code and - on a more abstract level - Kitaev's 16-fold classification of two-dimensional topological superconductors. Subsequently, we present a short review of category theory as an axiomatic description of topological order in two-dimensions. Equipped with this structure, we revisit Kitaev's 16-fold way.

cond-mat.str-el↗
arXiv2015

Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2

A topological nodal-line semimetal is a new condensed matter state with one-dimensional bulk nodal lines and two-dimensional drumhead surface bands. Based on first-principles calculations and our effective k . p model, we propose the existence of topological nodal-line fermions in the ternary transition- metal chalcogenide TlTaSe2. The noncentrosymmetric structure and strong spin-orbit coupling give rise to spinful nodal-line bulk states which are protected by a mirror reflection symmetry of this compound. This is remarkably distinguished from other proposed nodal-line semimetals such as Cu3NPb(Zn) in which nodal lines exist only in the limit of vanishing spin-orbit coupling. We show that the drumhead surface states in TlTaSe2, which are associated with the topological nodal lines, exhibit an unconventional chiral spin texture and an exotic Lifshitz transition as a consequence of the linkage among multiple drumhead surface-state pockets.

cond-mat.mes-hall↗
arXiv2015

Coupled wire construction of chiral spin liquids

We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.

cond-mat.mes-hall↗
arXiv2015

Occupation of topological Floquet bands in open systems

Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the possibility of selectively populating one of these effective bands, thereby maximizing the system's resemblance to a static topological insulator. We study such Floquet systems coupled to a zero-temperature thermal reservoir that provides dissipation. We find that the resulting electronic steady states are generically characterized by a finite density of excitations above the effective ground state, even when the driving has a small amplitude and/or large frequency. We discuss the role of reservoir engineering in mitigating this problem.

cond-mat.mes-hall↗
arXiv2015

Projective construction of the $\mathbb{Z}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.

cond-mat.str-el↗
arXiv2015

Reply to "Comment on `Floquet Fractional Chern Insulators'"

We respond to the comments expressed by L. D'Alessio in arXiv:1412.3481 on our work "Floquet Fractional Chern Insulators" [Phys. Rev. Lett. 112, 156801 (2014)]. We confirm the central result that the ground state of the effective Hamiltonian is an interacting fractional Chern insulator.

cond-mat.str-el↗
arXiv2015

Ultraquantum magnetoresistance in single-crystalline $β$-Ag$_2$Se

In the history of condensed matter physics, reinvestigation of a well-studied material with enhanced quality sometimes led to important scientific discoveries. A well-known example is the discovery of fractional quantum Hall effect in high quality GaAs/AlGaAs heterojunctions. Here we report the first single crystal growth and magnetoresistance (MR) measurements of the silver chalcogenide $β$-Ag$_2$Se (Naumannite), a compound has been known for the unusual, linear-field-dependent MR in its polycrystalline form for over a decade. With the quantum limit (QL) as low as 3 Tesla, a moderate field produced by a superconductor magnet available in many laboratories can easily drive the electrons in Ag$_2$Se to an unprecedented state. We observed significant negative longitudinal MR beyond the QL, which was understood as a `charge-pumping' effect between the novel fermions with opposite chiralities. Characterization of the single-crystalline Ag$_2$Se and the fabrication of electric devices working above the QL, will represent a new direction for the study of these exotic electrons.

cond-mat.str-el↗
arXiv2015

Topological BF theory of the quantum hydrodynamics of incompressible polar fluids

We analyze a hydrodynamical model of a polar fluid in (3+1)-dimensional spacetime. We explore a spacetime symmetry -- volume preserving diffeomorphisms -- to construct an effective description of this fluid in terms of a topological BF theory. The two degrees of freedom of the BF theory are associated to the mass (charge) flows of the fluid and its polarization vorticities. We discuss the quantization of this hydrodynamic theory, which generically allows for fractionalized excitations. We propose an extension of the Girvin-MacDonald-Platzman algebra to (3+1)-dimensional spacetime by the inclusion of the vortex-density operator in addition to the usual charge density operator and show that the same algebra is obeyed by massive Dirac fermions that represent the bulk of $\mathbb{Z}^{\,}_{2}$ topological insulators in three-dimensional space.

cond-mat.mes-hall↗
arXiv2015

A novel platform for two-dimensional chiral topological superconductivity

We show that the surface of an $s$-wave superconductor decorated with a two-dimensional lattice of magnetic impurities can exhibit chiral topological superconductivity. If impurities order ferromagnetically and the superconducting surface supports a sufficiently strong Rashba-type spin-orbit coupling, Shiba sub-gap states at impurity locations can hybridize into Bogoliubov bands with non-vanishing, sometimes large, Chern number $C$. This topological superconductor supports $C$ chiral Majorana edge modes. We construct phase diagrams for model two-dimensional superconductors, accessing the dilute and dense magnetic impurity limits analytically and the intermediate regime numerically. To address potential experimental systems, we identify stable configurations of ferromagnetic iron atoms on the Pb (111) surface and conclude that ferromagnetic adatoms on Pb surfaces can provide a versatile platform for two-dimensional topological superconductivity.

cond-mat.mes-hall↗