In the presence of non-Hermitian skin effect, non-Hermitian lattices generally have complex-valued eigenenergies under periodic boundary condition, but they can have non-Bloch PT symmetry and therefore completely real eigenenergies under open boundary condition. This novel PT symmetry and its breaking have been experimentally observed in one dimension. Here, we find that non-Bloch PT symmetry in two and higher dimensions exhibits drastically different behaviors compared to its one-dimensional counterpart. Whereas Bloch PT breaking and one-dimensional non-Bloch PT breaking generally have nonzero thresholds in the large-size limit, the threshold of two and higher-dimensional non-Bloch PT breaking universally approaches zero as the system size increases. A product measure, namely the product of bare non-Hermiticity and system size, is introduced to quantify the PT breaking tendency. This product being small is required for the perturbation theory to be valid, thus its growth with system size causes the breakdown of perturbation theory, which underlies the universal threshold. That the universal behaviors emerge only in two and higher dimensions indicates an unexpected interplay among PT symmetry, non-Hermitian skin effect, and spatial dimensionality. Our predictions can be confirmed on experimentally accessible platforms.
A hallmark of topological band theory in periodic media is that bulk properties are not affected by boundary conditions. Remarkably, in certain non-Hermitian lattices the bulk properties are largely affected by boundaries, leading to such major effects as the non-Hermitian skin effect and violation of the bulk-boundary correspondence. Here we unveil that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time ($\mathcal{PT}$) symmetry breaking phase transitions, and suggest a bulk probing method to detect such boundary-d…
The 212 species of structural phase transitions which break macroscopic symmetry are analyzed with respect to the occurrence of time-reversal invariant vector and bidirector order parameters. The possibility of discerning the orientational domain states of the low-symmetry phase by these `vectorlike' physical properties has been derived using a computer algorithm exploiting the concept of polar, axial, chiral and neutral dipoles. It is argued that for species 32 > 3, 422 > 4 and 622 > 6, Bogdanov-Yablonskii phenomenological theory for a ferromagnetic Bloch Skyrmions applies also to the ferroel…
Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional model of macroscopic T-symmetry breaking is a ferromagnetic order of itinerant Bloch electrons with an isotropic spin interaction in momentum space. Anisotropic electron interactions, on the other hand, have been a domain of correlated quantum phases, such as the T-invariant nematics or unconventional superconductors. Here we report discovery of a brok…
The phonon dispersion unfolding method is useful for obtaining hidden Bloch symmetries and comparing theoretical results with experiment spectrums (e.g., inelastic neutron scattering, inelastic X-ray scattering, Raman). In this paper, we propose a method to unfold phonon dispersions. The main advantage of this method is the ability to handle systems with heavy breaking of spatial translational symmetry. Its validity is tested by pure diamond, diamond with Si substitution, and diamond with C vacancies.
Moiré exciton features tunable Dirac dispersion and spatially dependent optical selection rules. With the long lifetime due to its interlayer nature, it is promising to realize a Bose-Einstein condensation of moiré excitons. Here we study the properties of moiré exciton condensate within the mean-field theory, with special focus on exciton-exciton interaction effect on the nonlinear Bloch band and Bloch waves of exciton condensate in moiré potential. We find the nonlinear dispersion of the moiré exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlin…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the topological invariants - giving a symmetry classification table. Here we consider various topological phases protected by different symmetries, and examine how the corresponding topological invariants evolve once the protecting symmetry is spontaneously lost. To our surprise, we find that the topological invariants and edge states can sometimes be robust to symmetry b…
Inversion symmetry breaking allows contrasted circular dichroism in different k-space regions, which takes the extreme form of optical selection rules for interband transitions at high symmetry points. In materials where band-edges occur at noncentral valleys, this enables valley dependent interplay of electrons with light of different circular polarizations, in analogy to spin dependent optical activities in semiconductors. This discovery is in perfect harmony with the previous finding of valley contrasted Bloch band features of orbital magnetic moment and Berry curvatures from inversion symm…
Non-Hermitian materials can not only exhibit exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is not clear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functio…
Three symmetries prevent a twisted bilayer of graphene from developing an in-plane spontaneous magnetization in the absence of a magnetic field - time reversal symmetry, $C_2$ symmetry to $π$ rotation and $C_3$ symmetry to $2π/3$ rotation. In contrast, there are experimental and theoretical indications that, at certain electron densities, time reversal and $C_2$ symmetries are broken spontaneously, while the $C_3$ symmetry is often broken due to strain. We show that in-plane orbital magnetization is a very sensitive probe to the simultaneous breaking of these three symmetries, exhibiting surpr…
We experimentally simulate in a photonic setting non-Hermitian (NH) metals characterized by the topological properties of their nodal band structures. Implementing nonunitary time evolution in reciprocal space followed by interferometric measurements, we probe the complex eigenenergies of the corresponding NH Bloch Hamiltonians, and study in detail the topology of their exceptional lines (ELs), the NH counterpart of nodal lines in Hermitian systems. We focus on two distinct types of NH metals: two-dimensional systems with symmetry-protected ELs, and three-dimensional systems possessing symmetr…
Intrinsic longitudinal spin-conductivity from ferroaxial spin-symmetry breaking
University of Wisconsin–Milwaukee（威斯康星大学密尔沃基分校）；University of Minnesota（明尼苏达大学）；The University of Tokyo（东京大学）；Hokkaido University（北海道大学）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
Chiral superconductors are a novel class of unconventional superconductors that host topologically protected chiral Majorana fermions at interfaces and domain walls, elusive quasiparticles that could serve as a platform for topological quantum computing. Here we show that, in analogy to a qubit, the out-of-equilibrium superconducting state in such materials can be described by a Bloch vector and controlled on ultrafast time scales. The all-optical control mechanism is universal, permitting arbitrary rotations of the order parameter, and can induce a dynamical change of handedness of the conden…
Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its impact is particularly illustrating in non-Hermitian quasicrystals where the interplay between non-Hermiticity and quasiperiodicity results in the concurrence of the delocalization-localization transition, the parity-time (PT)-symmetry breaking, and the onset of the non-Hermitian skin effects. Here we experimentally simulate non-Hermitian quasicrystals using …
Recently (PRL 113, 050403 (2014)) the concept of local symmetries in one-dimensional stationary wave propagation has been shown to lead to a class of invariant two-point currents that allow to generalize the parity and Bloch theorem. In the present work we establish the theoretical framework of local symmetries for higher-dimensional interacting many-body systems. Based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy we derive the equations of motion of local symmetry correlators which are off-diagonal elements of the reduced one-body density matrix at symmetry related positions. …
