arXiv subjects

Linhu Li

Publications and source records attributed to Linhu Li.

At least 73 records · Page 4Linked to original sources

arXiv2019

Boundary states of 4D topological matter: Emergence and full 3D-imaging of nodal Seifert surfaces

With its boundary tracing out a link or knot in 3D, the Seifert surface is a 2D surface of core importance to topological classification. We propose the first-ever experimentally realistic setup where Seifert surfaces emerge as the boundary states of 4D topological matter. Unlike ordinary real space knots that exist in polymers, biomolecules and everyday life, our knots and their Seifert surfaces exist as momentum space nodal structures, where topological linkages have profound effects on optical and transport phenomena. Realized with 4D circuit lattices, our nodal Seifert systems are freed from symmetry constraints and readily tunable due to the dimension and distance agnostic nature of circuit connections. Importantly, their Seifert surfaces manifest as very pronounced impedance peaks in their 3D-imaging via impedance measurements, and are directly related to knot invariants like the Alexander polynomial and knot Signature. This work thus unleashes the great potential of Seifert surfaces as sophisticated yet accessible mathematical tools in the study of exotic band structures.

cond-mat.mes-hall↗

arXiv2019

Geometric classification of non-Hermitian topological systems through the singularity ring

This work unveils how geometric features of two-band non-Hermitian Hamiltonians can completely classify the topology of their eigenstates and energy manifolds. Our approach generalizes the Bloch sphere visualization of Hermitian systems to a ``Bloch torus'' picture for non-Hermitian systems, where a singularity ring (SR) captures the degeneracy structure of generic exceptional points. The SR picture affords convenient visualization of various symmetry constraints and reduces their topological characterization to the classification of simple intersection or winding behavior, as detailed by our explicit study of chiral, sublattice, particle-hole and conjugated particle-hole symmetries. In 1D, the winding number about the SR corresponds to the band vorticity measurable through the Berry phase. In 2D, more complicated winding behavior leads to a variety of phases that illustrate the richness of the interplay between SR topology and geometry beyond mere Chern number classification. Through a normalization procedure that puts generic 2-band non-Hermitian Hamiltonians on equal footing, our SR approach also allows for vivid visualization of the non-Hermitian skin effect.

cond-mat.mes-hall↗

arXiv2019

Robust one-dimensionality at twin-grain-boundaries in MoSe$_{2}$

We show that 1D electron states confined at twin-grain-boundaries in MoSe$_{2}$ can be modeled by a three-orbital tight binding model including a minimum set of phenomenological hopping terms. The confined states are robust to the details of the defect hopping model, which agrees with their experimental ubiquity. Despite a valley Chern number which is finite and opposite on both sides of the defect, there is no topological protection of the confined states. This turns out to be an essential feature to have only one confined electronic band, in agreement with experiments, instead of two, as the bulk-edge correspondence would imply. Modeling the confined state as a 1D interacting electronic system allows us to unveil a mobile quantum impurity type behavior at energy scales beyond the Tomonaga-Luttinger liquid with an interaction range which extends up to the lattice spacing, in excellent agreement with ARPES measurements.

cond-mat.mes-hall↗

arXiv2018

Broken-symmetry phases of interacting nested Weyl and Dirac loops

We study interaction-induced broken symmetry phases that can arise in metallic or semimetallic band structures with two nested Weyl or Dirac loops. The odered phases can be of the charge or (pseudo)spin density wave type, or superconductivity from interloop pairing. A general analysis for two types of Weyl loops is given, according to whether a local reflection symmetry in momentum space exists or not, for Hamiltonians having a global PT symmetry. The resulting density-wave phases always have lower total energy, and can be metallic, insulating, or semimetallic (with nodal loops), depending on both the reflection symmetry of the loops and the symmetry transformation that maps one loop onto the other. We extend this study to nested $\mathbb{Z}_2$ nodal lines, for which the ordered phases include also nodal point and nodal chain semimetals, and to spinful Dirac nodal lines. Superconductivity from interloop pairing can be fully gapped only if the initial double loop system is semimetallic.

cond-mat.str-el↗

arXiv2018

Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems

Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we propose to predict different configurations of corner states from winding numbers defined for one-dimensional edges of the system. We first demonstrate the winding number characterization with a generalized two-dimensional square lattice belonging to the BDI symmetry class. In addition to the second-order topological insulating phase, the system may also be a nodal point semimetal or a weak topological insulator with topologically protected one-dimensional edge states coexisting with the corner states at zero energy. A three-dimensional cubic lattice with richer configurations of corner states is also studied. We further discuss several experimental implementations of our models with photonic lattices or electric circuits.

cond-mat.mes-hall↗

arXiv2018

Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops

Valence and conduction bands in nodal loop semimetals (NLSMs) touch along closed loops in momentum space. If such loops can proliferate and link intricately, NLSMs become exotic topological phases with unconventional topological characteristics and potentially peculiar transport properties. In conventional quantum materials or cold atom systems alike, such exotic phases necessarily require non-local hopping and are therefore intrinsically unrealistic. In this work, we show how this hurdle can be surmounted through an experimentally feasible periodic driving scheme. In particular, by tuning the period of a two-step periodic driving or some experimentally accessible parameters, we show how to generate arbitrarily many nodal loops that are linked with various levels of complexity. Furthermore, we propose to use both the Berry phase winding and the Alexander polynomial topological invariant to characterize the fascinating linkages among the nodal loops. This work thus presents a class of exotic Floquet topological phase that has hitherto not been proposed in any realistic setup.

cond-mat.mes-hall↗

arXiv2018

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems being integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number $ν$ of a non-Hermitian system is equal to half of the summation of two winding numbers $ν_1$ and $ν_2$ associated with two exceptional points respectively. The winding numbers $ν_1$ and $ν_2$ represent the times of real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of $ν_1$ and $ν_2$ is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number $ν_1$ and $ν_2$.

cond-mat.mes-hall↗

arXiv2017

Characterization of Lifshitz transitions in topological nodal line semimetals

We introduce a two-band model of three-dimensional nodal line semimetals, the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface states of the model, and find that the transitions between different configurations, namely, the Lifshitz transitions, can be identified solely by the number of gap-closing points on some high-symmetry planes in the Brillouin zone. A global phase diagram of this model is also obtained accordingly. We then investigate the effect of some extra terms analogous to a two-dimensional Rashba-type spin-orbit coupling. The introduced extra terms open a gap for the nodal line semimetals and can be useful in engineering different topological insulating phases. We demonstrate that the behavior of surface Dirac cones in the resulting insulating system has a clear correspondence with the different configurations of the original nodal lines in the absence of the gap terms.

cond-mat.mes-hall↗

arXiv2017

Dynamical topological invariant after a quantum quench

We show how to define a dynamical topological invariant for general one-dimensional topological systems after a quantum quench. Focusing on two-band topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifold $S^2$, and thus we are able to define a dynamical topological invariant on each of the sphere. We also unveil the intrinsic relation between the dynamical topological invariant and the difference of topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

cond-mat.str-el↗

arXiv2017

Engineering topological phases with a three-dimensional nodal-loop semimetal

A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D tight-binding model of a nodal-loop semimetal, we obtain a rich variety of topological phases of great interest to ongoing theoretical and experimental studies, including chiral insulator, degenerate-surface-loop insulator, second-order topological insulator, as well as Weyl semimetal with tunable Fermi arc profiles. The unique concept underlying our approach is to engineer topological surface states that inherit their dispersion relations from a gap term. The results provide one rather unified principle for the creation of novel topological phases and can guide the search for new topological materials. Two-terminal transport studies are also carried out to distinguish the engineered topological phases.

cond-mat.mes-hall↗

arXiv2017

Transition from nodal loop to nodal chain phase in a periodically modulated optical lattice

We propose to study the transition from a nodal loop to nodal chain phase in a tunable two-dimensional $π$-flux lattice with periodical modulation potential. The Hamiltonian describes a periodically modulated optical lattice system under artificial magnetic fluxes and the tunable modulation phase factor provides additionally an artificial dimension of external parameter space. We demonstrate that this lattice system is able to describe a semimetal with either nodal loop or nodal chain Fermi surface in the extended three-dimensional Brillouin zone. By changing the strength of modulation potential $V$, we realize the transformation between the nodal-loop and nodal-chain semimetal.

cond-mat.other↗

arXiv2017

$2π$-flux loop semimetals

We introduce a model of $2π$-flux loop semimetals which holds nodal loops described by a winding number $ν=2$. By adding some extra terms, this model can be transformed into a recently discovered Hopf-link semimetal, and the symmetries distinguishing these two phases are studied. We also propose a simpler physical implementation of $2π$-flux loops and of the Hopf-link semimetals which only involves nearest-neighbor hoppings, although in the presence of spin-orbit interaction. Finally, we investigate the Floquet properties of the $2π$-flux loop, and find that such a loop may be driven into two separated $π$-flux loops or four Weyl points by light with circular polarization in certain directions.

cond-mat.str-el↗

arXiv2017

Chiral topological insulating phases from three-dimensional nodal loop semimetals

We identify a topological Z index for three dimensional chiral insulators with P*T symmetry where two Hamiltonian terms define a nodal loop. Such systems may belong in the AIII or DIII symmetry class. The Z invariant is a winding number assigned to the nodal loop and has a correspondence to the geometric relation between the nodal loop and the zeroes of the gap terms. Dirac cone edge states under open boundary conditions are in correspondence with the winding numbers assigned to the nodal loops. We verify our method with the low-energy effective Hamiltonian of a three-dimensional material of topological insulators in the Bi$_2$Te$_3$ family.

cond-mat.mes-hall↗

arXiv2016

Topological insulating phases from two-dimensional nodal loop semimetals

Starting from a minimal model for a 2D nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak and strong field regimes, as well as the edge states in a ribbon geometry.

cond-mat.mes-hall↗

arXiv2016

Strain induced topological phase transition at zigzag edges of monolayer transition-metal dichalcogenides

The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal 3-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive -- in which case a small built in strain is enough to destroy the topological phase -- to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing in particular how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multi-band Berry phase, which serves as a topological invariant of this system.

cond-mat.mes-hall↗

arXiv2015

Topological invariants for phase transition points of one-dimensional $\mathbb{Z}_2$ topological systems

We study topological properties of phase transition points of two topologically non-trivial $\mathbb{Z}_2$ classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter. While the topological property of the $\mathbb{Z}_2$ system is generally characterized by a $\mathbb{Z}_2$ topological invariant, we identify that it has a correspondence to the quantized Berry phase protected by the particle-hole symmetry, and then give a proper definition of Berry phase to the phase transition point. By applying our scheme to some specific models of class D and DIII, we demonstrate that the topological phase transition can be well characterized by the Berry phase of the transition point, which reflects the change of Berry phases of topologically different phases across the phase transition point.

cond-mat.str-el↗

arXiv2015

Characterization of topological phase transitions via topological properties of transition points

We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of momentum and transition driving parameter. By applying our scheme to the Su-Schrieffer-Heeger model and Haldane model, we demonstrate that the topological phase transition can be well characterized by the defined topological invariant of the transition point, which reflects the change of topological invariants of topologically different phases across the phase transition point.

cond-mat.str-el↗

arXiv2015

Winding numbers of phase transition points for one-dimensional topological systems

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.

cond-mat.str-el↗