arXiv subjects

L. B. Shao

Publications and source records attributed to L. B. Shao.

17 recordsLinked to original sources

arXiv2022

Spinless Mirror Chern Insulator from Projective Symmetry Algebra

It was commonly believed that a mirror Chern insulator (MCI) must require spin-orbital coupling, since time-reversal symmetry for spinless systems contradicts with the mirror Chern number. So MCI cannot be realized in spinless systems which include the large field of topological artificial crystals. Here, we disprove this common belief. The first point to clarify is that the fundamental constraint is not from spin-orbital coupling but the symmetry algebra of time reversal and mirror operations. Then, our theory is based on the conceptual transformation that the symmetry algebras will be projectively modified under gauge fields. Particularly, we show that the symmetry algebra of mirror reflection and time-reversal required for MCI can be achieved projectively in spinless systems with lattice $\mathbb{Z}_2$ gauge fields, i.e., by allowing real hopping amplitudes to take $\pm$ signs. Moreover, we propose the basic structure, the twisted $π$-flux blocks, to fulfill the projective symmetry algebra, and develop a general approach to construct spinless MCIs based on these building blocks. Two concrete spinless MCI models are presented, which can be readily realized in artificial systems such as acoustic crystals.

cond-mat.other↗

arXiv2022

Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers

Recent advances in topological artificial systems open the door to realizing topological states in dimensions higher than the usual three-dimensional space. Here, we present a "tensor product" theory, which offers a method to construct Chern insulators with arbitrarily high dimensions and Chern numbers. Particularly, we show that the tensor product of a $d_A$D Chern insulator $\langle \mathcal{H}_A^{(κ_{A})}, C_A\rangle$ with a $d_B$D Chern insulator $\langle \mathcal{H}_B^{(κ_B)}, C_B\rangle$ leads to a $(d_A+d_B)$D Chern insulator $\langle \mathcal{H}_{A B}^{(κ_A\star κ_B)},-2C_AC_B\rangle $, where in the brackets, $\mathcal{H}^{(κ)}$ is the $d$D Hamiltonian with $d$ even, $C$ is the corresponding $(d/2)$th Chern number, and $κ$ labels the five non-chiral Altland-Zirnbauer symmetry classes A, AI, D, AII and C. The four real classes AI, D, AII and C form a Klein four-group under the multiplication `$\star$' with class AI the identity, and class A is the zero element. Our theory leads to novel higher-dimensional topological physics. (i) The construction can generate large higher-order Chern numbers, e.g., for some cases the resultant classification is $8\mathbb{Z}$. (ii) Fascinatingly, the boundary states feature flat nodal hypersurfaces with nontrivial Chern charges. For the constructed $(d_A+d_B)$D Chern insulator, a boundary perpendicular to a direction of $\mathcal{H}_A$ generically hosts $|C_A|$ $d_B$D nodal hypersurfaces, each of which has topological charge $\pm 2C_B$. Under perturbations, each nodal hypersurface bursts into stable unit nodal points, with the total Chern charge conserved. Examples are given to demonstrate our theory, which can be experimentally realized in artificial systems such as acoustic crystals, electric circuit arrays, ultracold atoms, or mechanical networks.

cond-mat.mes-hall↗

arXiv2021

The gauge-field extended $k\cdot p$ method and novel topological phases

Although topological artificial systems, like acoustic/photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable $\mathbb{Z}_2$ gauge fields. Hence, it is fundamentally important to explore new topological phases based on their unique features. Here, we point out that the $\mathbb{Z}_2$ gauge field leads to two fundamental modifications of the conventional $k\cdot p$ method: (i) The little co-group must include the translations with nontrivial algebraic relations; (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular $π$-flux model exhibiting graphene-like semimetal phases, and a graphite model with interlayer $π$ flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to artificial systems and establishes the approach to analyze these phases.

cond-mat.other↗

arXiv2020

Unified Theory of Quantum Crystalline Symmetries

Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two complementary aspects. First, we provide a decomposition form for the space-group factor systems to characterize all quantum space groups. It consists of three factors, the factor system for the translation subgroup $L$, an in-homogeneous factor system for the point group $P$, and a factor connecting $L$ and $P$. The three factors satisfy three consistency equations, which are exactly solvable and can completely exhaust all factor systems for space groups. Second, since factors systems are classified by the second cohomology group, we show the (co)homology groups for space groups can be derived from Borel's equivariant (co)homology theory, which leads to an algorithm that can compute all (co)homology groups for space groups. To demonstrate the general theory, we explicitly present quantum wallpaper groups with the $\mathbb{Z}_2$ gauge group. Furthermore, as a primitive application, we find the time-reversal invariant quantum space groups with inversion symmetry can lead to a novel clifford band theory, where each band is fourfold degenerate to represent certain real Clifford algebras with topologically nontrivial pinor structures over the Brillouin zone. Our work serves as a foundation for exploring quantum mechanical space groups, and can find applications in spin liquids, unconventional superconductors, and artificial lattice systems, including cold atoms, photonic and phononic crystals, and even LC electric circuit networks.

math-ph↗

arXiv2020

Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals

For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present $PT$-invariant $2$D topological insulators and $3$D topological semimetals that go beyond this bulk-boundary correspondence framework. With unchanged bulk topological invariant, their first-order boundaries undergo transitions separating different phases with second-order-boundary zero-modes. For the $2$D topological insulator, the helical edge modes appear at the transition point for two second-order topological insulator phases with diagonal and off-diagonal corner zero-modes, respectively. Accordingly, for the $3$D topological semimetal, the criticality corresponds to surface helical Fermi arcs of a Dirac semimetal phase. Interestingly, we find that the $3$D system generically belongs to a novel second-order nodal-line semimetal phase, possessing gapped surfaces but a pair of diagonal or off-diagonal hinge Fermi arcs.

cond-mat.mes-hall↗

arXiv2020

Detecting non-Abelian statistics of topological states on a chain of superconducting circuits

In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state materials, experimental realization of non-Abelian statistics is lacking. The superconducting quantum circuit system is scalable and controllable, and thus is a promising platform for quantum simulation. Here we propose a scheme to demonstrate non-Abelian statistics of topologically protected zero-energy edge modes on a chain of superconducting circuits. Specifically, we can realize topological phase transition by varying the hopping strength and magnetic field in the chain, and the realized non-Abelian operation can be used in topological quantum computation. Considering the advantages of the superconducting quantum circuits, our protocol may shed light on quantum computation via topologically protected states.

quant-ph↗

arXiv2019

Engineering chiral edge states in 2D topological insulator/ferromagnetic insulator heterostructures

Chiral edge state (CES) at zero magnetic field has already been realized in the magnetically doped topological insulator (TI). However, this scheme strongly relies on material breakthroughs, and in fact, most of the TIs cannot be driven into a Chern insulator in this way. Here, we propose to achieve the CESs in 2D TI/ferromagnetic insulator/TI sandwiched structures through spin-selective coupling between the helical edge states of the two TIs. Due to this coupling, the edge states of one spin channel are gapped and those of the other spin channel remain almost gapless, so that the helical edge states of each isolated TI are changed into the CESs. Such CESs can be hopefully achieved in all TI materials, which are immune to magnetic-disorder-induced backscattering. We propose to implement our scheme in the van der Waals heterostructures between monolayer 1T'-WTe$_2$ and bilayer CrI$_3$. The electrical control of magnetism in bilayer CrI$_3$ switches the transport direction of the CESs, which can realize a low-consumption transistor.

cond-mat.str-el↗

arXiv2018

Effective Long-Range Pairing and Hopping in Topological Nanowires Weakly Coupled to $ s $-Wave Superconductors

In this Letter, we first formulate an effective theory, which generally captures long-range proximity effects of a surface system weakly coupled to an s-wave superconductor. The long-range proximity effects include both the emergent long-range pairing and hopping interactions in the surface system. We then model the Rashba spin-orbit-coupled nanowire in proximity with an s-wave superconductor by taking into account the emergent nonlocal effects in the weak-coupling limit. In this limit the induced superconducting pair potential is found much smaller than that of the host superconductor, which is in good agreement with recent experiments. Compared with the previously considered strong coupling limit with local proximity effects, the long-range interactions can significantly modify the topological phase diagram, and considerably lower the threshold magnetic field for the emergence of Majorana zero modes.

cond-mat.supr-con↗

arXiv2018

Four-Dimensional Topological Insulators with Nodal-Line Boundary States

Conventional topological insulators and superconductors have topologically protected nodal points on their boundaries, and the recent interests in nodal-line semimetals only concerned bulk band structures. Here, we present a novel four-dimensional topological insulator protected by an anti-unitary reflection symmetry, whose boundary band has a single $PT$-symmetric nodal line with double topological charges. Inspired by the recent experimental realization of the four-dimensional quantum Hall effect, we also propose a cold-atom system which realizes the novel topological insulator with tunable parameters as extra dimensions.

cond-mat.mes-hall↗

arXiv2016

Electron Interaction Effects in Periodically Driven Kitaev Model: Topology Breaking and Enhancement of Quantum Chaos

The effect of electron-electron interaction on Floquet topological superconducting chains is investigated numerically through full diagonalization and time evolution. The preservation of topology in the weak interacting regime is represented by a many-body form of the Majorana survival probability, and the emergence of chaos is characterized using the level statistics. In the presence of weak interaction, there appear a multitude of avoided crossings in quasi-energy spectra, and the resulting chaos is not full but can coexist with the topology. Strong interaction will lead the system into a topologically trivial and fully chaotic phase.

cond-mat.str-el↗

arXiv2013

Tunable interfaces for realizing universal quantum computation with topological qubits

We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits, which can realize arbitrary single-qubit gate on the topological qubit. When two qubits are involved, the interface between the topological qubits and a microwave cavity can induce a nontrivial two-qubit gate, which can not be constructed based on braiding operations. The two interfaces, being tunable via an external magnetic flux, may serve as the building blocks towards universal quantum computation with topological qubits.

quant-ph↗

arXiv2013

Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic (FM) region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the FM region, and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes", the QSH effect becomes robust against symmetry-breaking perturbations.

cond-mat.mes-hall↗

arXiv2013

Controlling Fusion of Majorana Fermions in one-dimensional systems by Zeeman Field

We propose to realize Majorana fermions (MFs) on an edge of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs localized at two junctions and that a reverse in direction of h can lead to permutation of two MFs. With decreasing h, the MF states can either be fused or form one Dirac fermion on the π-junctions, exhibiting a topological phase transition. This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions localized on the π-junction. A condition of decoupling two MFs is also given.

cond-mat.mes-hall↗

arXiv2011

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing order parameter has always the $p+ip$-wave symmetry regardless of the strength of pairing interaction, justifying an important conclusion obtained by the mean field theory. Analytical results are derived for two simple systems with respectively spin-orbit interactions and Zeeman coupling.

cond-mat.supr-con↗

arXiv2011

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.

cond-mat.quant-gas↗

arXiv2009

Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms

We design an ingenious scheme to realize the Haldane's quantum Hall model without Landau level by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on-site energies in two sublattices required in the Haldane's model can be implemented through tuning the phase of one of the laser beams. The staggered magnetic field is generated from the Berry phase associated with the atom moving in a region with other three standing-wave laser beams. Moreover, we establish a relation between the Hall conductivity and the equilibrium atomic density upon turning on a stimulated uniform magnetic field, which enables us to detect the topological Chern number with the density profile measurement technique that is typically used in ultracold atoms experiments.

cond-mat.mes-hall↗

arXiv2006

Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators

We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are the same (or {\it mod} $2π$) while the corresponding geometric phases are nontrivial. We illustrate how this strategy to work in a simple but typical NMR-type qubit system.

quant-ph↗