arXiv subjects

Ming-Jian Gao

Publications and source records attributed to Ming-Jian Gao.

10 recordsLinked to original sources

arXiv2026

Converting $PT$-Symmetric Topological Classes by Floquet Engineering

Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, $PT$ symmetric topological phases are classified by $(PT)^2=1$ or $-1$. The interconversion between the two $PT$-symmetric topological classes is generally difficult due to the constraint of $(PT)^2$. Here, we propose a scheme to control and interconvert the $PT$-symmetric topological classes by Floquet engineering. We find that it is the breakdown of the $\mathbb{Z}_2$ gauge, induced by the $π$ phase difference between different hopping rates, by the periodic driving that leads to such an interconversion. Relaxing the system from the constraint of $(PT)^2$, rich exotic topological phases, e.g., the coexisting $PT$-symmetric first-order real Chern insulator and second-order topological insulators not only in different quasienergy gaps, but also in one single gap, are generated. In contrast to conventional Floquet topological phases, our result provides a way to realize exotic topological phases without changing symmetries. It enriches the family of topological phases and gives an insightful guidance for the development of multifunctional quantum devices.

cond-mat.mes-hall↗

arXiv2026

Hybrid-order nonlinear topological phases

The bulk-boundary correspondence (BBC), which relates topological invariants to boundary modes, is well understood for linear systems but remains an open question in the presence of nonlinearity, where multigap topologies make the BBC obscure and the topological description troublesome. We address this by developing an auxiliary-system formalism that enables topological classification of nonlinear-eigenvalue systems. In the two-dimension (2D) case, we show that two fixed eigenvalues can harbor first-order gapless boundary modes and second-order corner modes. Stacking this 2D system along the third dimension (3D) reveals distinct hybrid-order realizations. Under uniform stacking, the corner states in the $xy$ plane transform into hinge states along the $z$ axis, yielding a 3D second-order phase, while the gapless boundary states become side-surface states, yielding a 3D first-order phase. For dimerized stacking, these states are further confined to the two ends of the $z$ axis, yielding a 3D third-order phase, and localized at the hinges, yielding a 3D second-order phase. Our results establish a multiband bulk-boundary correspondence and identify stacking engineering as a versatile platform for exploring hybrid-order topological phases in nonlinear systems.

cond-mat.mes-hall↗

arXiv2026

Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems

The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of boundary states with nonzero topological invariants in the bulk. Widespread attention has been paid to extending topological phases to nonlinear and non-Hermitian systems. However, the BBC and topological invariants of non-Hermitian nonlinear systems remain largely unexplored. Here, we establish a complete BBC and topological characterization of the topological phases in a class of non-Hermitian nonlinear-eigenvalue systems by introducing an auxiliary system. We restore the BBC broken by non-Hermiticity via employing the generalized Brillouin zone on the auxiliary system. Remarkably, we discover that the interplay between non-Hermiticity and nonlinearity creates an exotic complex-band topological phase that coexists with the real-band topological phase. Our results enrich the family of nonlinear topological phases and lay a foundation for exploring novel topological physics in metamaterial systems.

cond-mat.other↗

arXiv2026

Breakdown of the symmetry constraint in a Floquet topological insulator

A topological insulator is regarded as an ideal candidate for information storage and high-speed lossless electrical transmission devices due to robust topological protected boundary modes. Previous studies revealed that symmetry exerts an unbreakable constraint on the existence, classes, and orders of its boundary modes. It severely limits the controllability and application of a topological insulator. Here, we propose a Floquet-engineering method to break this symmetry-imposed constraint on a topological insulator. By applying periodic driving on a system belonging to a symmetry class that prohibits the existence of first-order topological phases, we find that rich first-order boundary modes are created. Interestingly, exotic hybrid-order topological insulators with coexisting first-order helical boundary modes and second-order corner modes not only in two different quasienergy gaps but also in one single gap are generated easily by periodic driving. Refreshing the prevailing understanding of symmetry constraint on topological phases, our result opens an avenue for the creation of exotic topological insulators without altering symmetries. It greatly expands the scope of the fabricated materials that host topological insulators.

cond-mat.mes-hall↗

arXiv2025

Multiple topological corner states in the continuum of extended kagome lattice

The kagome lattice is renowned for its exotic electronic properties, such as flat bands, Dirac points, and Van Hove singularities. These features have provided a fertile ground for exploring exotic quantum phenomena. Here, we discover that a breathing kagome lattice with long-range hoppings can host multiple zero-energy corner states, which emerge as topologically protected bound states in the continuum (BICs). This result demonstrates that additional hopping control can induce further non-trivial physics of the kagome lattice. Since the zero-energy corner states in the continuum are intertwined with a substantial number of zero-energy bulk states, we also develop a momentum-space topological characterization theory to precisely quantify the number of corner states, revealing a general bulk-corner correspondence. Furthermore, we uncover three distinct types of topological phase transitions (TPTs) for the BICs driven by shifts in the spatial localization of zero-energy bulk and/or edge states. These TPTs are exactly captured by our characterization theory. This work provides deep insights into the topological physics of the kagome lattice and broadens the understanding of its electronic properties

cond-mat.mes-hall↗

arXiv2025

Topological semimetal with coexisting nodal points and nodal lines

Featuring exotic quantum transport and surface states, topological semimetals can be classified into nodal-point, nodal-line, and nodal-surface semimetals according to the degeneracy and dimensionality of their nodes. However, a topological semimetal that possesses both nodal points and nodal lines is rarely reported. Here, we propose a scheme to construct this type of topological semimetal, which simultaneously exhibits hinge Fermi arcs and drumhead surface states. Then, by applying periodic driving on the system, we find a hybrid-order topological semimetal with nodal points and rich nodal-line structures and its conversion into a first-order topological semimetal, which are absent in a static system. Our results enrich the family of topological semimetals, and establish a foundation for further exploration of their potential applications.

cond-mat.mes-hall↗

arXiv2024

Unveiling Higher-Order Topology via Polarized Topological Charges

Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization for the HOTPs, which is not conducive to revealing the essential properties of these topological states and also restricts their detection in quantum simulation systems. Here, we propose a concept of polarized topological charges to characterize chiral-symmetric HOTPs in momentum space, which further facilitates a feasible experimental scheme to detect the HOTPs in $^{87}$Rb cold atomic system. Remarkably, our characterization theory not only shows that the second-order (third-order) topological phases are determined by a quarter (negative eighth) of the total polarized topological charges, but also reveals that the higher-order topological phase transitions are identified by the creation or annihilation of polarized topological charges. Particularly, these polarized topological charges can be measured by pseudospin structures of the systems. Due to theoretical simplicity and observational intuitiveness, this work shall advance the broad studies of the HOTPs in both theory and experiment.

cond-mat.mes-hall↗

arXiv2024

Majorana modes in trapped-ion system and their Floquet engineering

Obeying non-Abelian statistics, Majorana fermions holds a promise to implement fault-tolerant quantum computing. It was found that Majorana fermions can be simulated by the zero-energy excitation in a nanowire with strong spin-orbit coupling interacting with an $s$-wave superconductor under a magnetic field. However, the signal of Majorana fermion in that system is obscured by the disorder in the nanowire and the confinement potential at the wire end. Thus, more controllable platforms are desired to simulate Majorana fermions. We here propose an alternative scheme to simulate the Majorana fermions in a trapped-ion system. Our dimerized-ion configuration permits us to generate the Majorana modes not only at zero energy but also at the nonzero ones, which enlarge the family of Majorana modes and supply another qubit carrier for quantum computing. We also investigate the controllability of the Majorana modes by Floquet engineering. It is found that a widely tunable number of Majorana modes are created on demand by applying a periodic driving on the trapped-ion system. Enriching the platforms for simulating Majorana fermions, our result would open another avenue for realizing fault-tolerant quantum computing.

quant-ph↗

arXiv2023

Engineering rich two-dimensional higher-order topological phases by flux and periodic driving

Nodal-line semimetals are commonly believed to exist in $\mathcal{PT}$ symmetric or mirror-rotation symmetric systems. Here, we find a flux-induced parameter-dimensional second-order nodal-line semimetal (SONLS) in a two-dimensional system without $\mathcal{PT}$ and mirror-rotation symmetries. It has coexisting hinge Fermi arcs and drumhead surface states. Meanwhile, we discover a flux-induced second-order topological insulator (SOTI). We then propose a Floquet engineering scheme to create exotic parameter-dimensional hybrid-order nodal-line semimetals with abundant nodal-line structures and widely tunable numbers of corner states in a SONLS and SOTI, respectively. Our results break the perception of SONLSs and supply a convenient way to artificially synthesize exotic topological phases by periodic driving.

cond-mat.mes-hall↗

arXiv2023

Engineering second-order nodal-line semimetals by breaking $\mathcal{PT}$ symmetry and periodic driving

Hosting unique drumhead surface states enclosed by nodal lines, topological nodal-line semimetals exhibit novel transport phenomena. Thus, the exploration of topological semimetals with different nodal-line structures has attracted much attention. In this paper, we first find a second-order nodal line semimetal (SONLS), which has coexisting hinge Fermi arcs and drumhead surface states, in a $\mathcal{PT}$-symmetry broken system. Then, without changing the intrinsic parameters, we artificially create exotic hybrid-order nodal-line semimetals hosted by different quasienergy gaps and rich nodal-line structures including nodal chains, crossing ring nodal nets, crossing line nodes, and nodal nets by applying a periodic driving on our SONLS. Enriching the classification of topological semimetals, such Floquet engineered high tunability of the orders and nodal-line structures of the SONLS sets up a foundation for exploring its further applications.

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