Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topologica...Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.展开更多
Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topolog...Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.展开更多
The free-fermion topological phases with Z_(2)invariants cover a broad range of topological states,including the time-reversal invariant topological insulators,and are defined on the equilibrium ground states.Whether ...The free-fermion topological phases with Z_(2)invariants cover a broad range of topological states,including the time-reversal invariant topological insulators,and are defined on the equilibrium ground states.Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance.Here we uncover the universal topological quench dynamics linking to these equilibrium topological phases of different dimensionality and symmetry classes in the tenfold way,with a general framework being established.We show a novel result that a generic d-dimensional topological phase represented by Dirac type Hamiltonian and with Z_(2)invariant defined on high symmetry momenta can be characterized by topology reduced to certain arbitrary discrete momenta of Brillouin zone called the highest-order bandinversion surfaces.Such dimension-reduced topology has unique correspondence to the topological pattern emerging in far-from-equilibrium quantum dynamics by quenching the system from trivial phase to the topological regime,rendering the dynamical hallmark of the equilibrium topological phase.This work completes the dynamical characterization for the full tenfold classes of topological phases,which can be partially extended to even broader topological phases protected by lattice symmetries and in non-Dirac type systems,and shall advance widely the research in theory and experiment.展开更多
There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonst...There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional(3D) spin-orbit(SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics.展开更多
The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like...The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.展开更多
基金Supported by the Major State Basic Research Development Program of China under Grant No 2016YFB0700700the National Natural Science Foundation of China(NSFC)under Grants Nos 11634003,11474273,61121491 and U1530401+1 种基金supported by the National Young 1000 Talents Plansupported by the Youth Innovation Promotion Association of CAS(2017154)
文摘Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.
基金the Singapore Ministry of Education Academic Research Fund Tier-3 Grant No.MOE2017T3-1-001(WBS.No.R-144-000-425-592)the Singapore National Research Foundation Grant No.NRF-NRFI2017-04(WBS No.R-144-000-378-281)。
文摘Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.
基金supported by the National Key Research and Development Program of China(2021YFA1400900)the National Natural Science Foundation of China(11825401 and 11921005)+1 种基金the Open Project of Shenzhen Institute of Quantum Science and Engineering(SIQSE202003)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000)。
文摘The free-fermion topological phases with Z_(2)invariants cover a broad range of topological states,including the time-reversal invariant topological insulators,and are defined on the equilibrium ground states.Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance.Here we uncover the universal topological quench dynamics linking to these equilibrium topological phases of different dimensionality and symmetry classes in the tenfold way,with a general framework being established.We show a novel result that a generic d-dimensional topological phase represented by Dirac type Hamiltonian and with Z_(2)invariant defined on high symmetry momenta can be characterized by topology reduced to certain arbitrary discrete momenta of Brillouin zone called the highest-order bandinversion surfaces.Such dimension-reduced topology has unique correspondence to the topological pattern emerging in far-from-equilibrium quantum dynamics by quenching the system from trivial phase to the topological regime,rendering the dynamical hallmark of the equilibrium topological phase.This work completes the dynamical characterization for the full tenfold classes of topological phases,which can be partially extended to even broader topological phases protected by lattice symmetries and in non-Dirac type systems,and shall advance widely the research in theory and experiment.
基金supported by the National Natural Science Foundation of China (11825401, 11761161003, and 11921005)the National Key R&D Program of China (2016YFA0301604)Strategic Priority Research Program of CAS (XDB28000000)。
文摘There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional(3D) spin-orbit(SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics.
基金funding support by the National Natural Science Foundation of China (12104519)the Guangdong Basic and Applied Basic Research Foundation (2020A1515110773)
文摘The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.
