The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example bulk-boundary correspondence. We show that the are not strictly tied to defined by non-Hermitian Bloch Hamiltonian. This breakdown conventional correspondence stems from non-Bloch-wave behavior eigenstates (non-Hermitian skin effect), which generates pronounced deviations phase diagrams theory. introduce non-Bloch faithfully predict modes. theory backed up open-boundary energy...

One of the unique features non-Hermitian Hamiltonians is skin effect, namely, that eigenstates are exponentially localized at boundary system. For open quantum systems, a short-time evolution can often be well described by effective Hamiltonians, while long-time dynamics calls for Lindblad master equations, in which Liouvillian superoperators generate time evolution. In this Letter, we find exhibit and uncover its unexpected physical consequences. It shown effect dramatically shapes...

The topology of non-Hermitian systems is drastically shaped by the skin effect, which leads to generalized bulk-boundary correspondence and non-Bloch band theory. essential part in formulations a general computable definition topological invariants. In this Letter, we introduce construction invariants based directly on real-space wave functions, provides straightforward approach for determining topology. As an illustration, apply formulation several representative models systems, efficiently...

We introduce two-dimensional topological insulators in proximity to high-temperature cuprate or iron-based superconductors as platforms of Majorana Kramers pairs zero modes. The proximity-induced pairing at the helical edge state insulator serves a Dirac mass, whose sign changes sample corner because symmetry high-${T}_{c}$ superconductors. This changing naturally creates each pair modes protected by time-reversal symmetry. Conceptually, this is topologically trivial superconductor-based...

We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in quantum dynamics. Specifically, a class of walk periodic lattices with open boundary condition, exceptionally large portion loss occurs at the system boundary. The physical origin this burst is found to be interplay between two unique phenomena: skin effect and imaginary gap closing. Furthermore, we establish universal bulk-edge scaling relation underlying burst. Our predictions are experimentally accessible various...

The parity-time ($\mathcal{PT}$) symmetry of a non-Hermitian Hamiltonian leads to real (complex) energy spectrum when the non-Hermiticity is below (above) threshold. Recently, it has been demonstrated that skin effect generates new type $\mathcal{PT}$ symmetry, dubbed non-Bloch featuring unique properties such as high sensitivity boundary condition. Despite its relevance wide range lattice systems, general theory still lacking for this generic phenomenon even in one spatial dimension. Here,...

The non-Hermitian skin effect dramatically reshapes the energy bands of systems, meaning that usual Bloch band theory is fundamentally inadequate as their characterization. non-Bloch theory, in which concept Brillouin zone generalized, has been widely applied to investigate systems one spatial dimension. However, its generalization higher dimensions challenging. Here, we develop a formulation and arbitrary dimensions, based on natural geometrical object known amoeba. Our provides general...

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments non-Hermitian systems, therefore, call for function formulas bands. This task is complicated by high sensitivity energy spectrums to boundary conditions, which invalidates straightforward generalization Hermitian formulas. Here, based on non-Bloch band theory, we obtain simple general one-dimensional Furthermore, in large-size limit, these dramatically reduce finding...

Accomplishing optical activity in achiral materials has long been a challenge. Achiral nanomaterials that crystallize point groups are generally optically inactive. Herein we report the surprising observation of several for supercrystals assembled from anisotropic metal nanoclusters with atomic precision. By analyzing multiple different molecular structures and symmetry space groups, have identified anisotropy nanocluster entities their asymmetric arrangement two key factors realization such...

Spectral functions of non-Hermitian Hamiltonians can reveal the existence topologically nontrivial line gaps and associated topological edge modes. However, computation spectral in a many-body system remains an open challenge. Here, we put forward numerical approach to compute Hamiltonian based on kernel polynomial method matrix-product state formalism. We show that local computed with our algorithm spin excitations model, faithfully reflecting gap topology model. further works presence skin...

We show that a local non-Hermitian perturbation in Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. When lies at finite distance to boundary, eigenstates are promoted exponentially localized modes, whose number is proportional distance. Furthermore, when respects parity-time $(\mathcal{PT})$ symmetry, $\mathcal{PT}$ symmetry breaking always accompanied by emergence of or exponential localization. Intriguingly, we find concise...

Laser powder bed fusion (L-PBF) has been employed to additively manufacture WE43 magnesium (Mg) alloy biodegradable implants, but L-PBF samples exhibit excessively rapid corrosion. In this work, dense were built with the relativity density reaching 99.9%. High temperature oxidation was performed on in circulating air via various heating temperatures and holding durations. The diffusion at elevated generated a gradient structure composed of an oxide layer surface, transition middle matrix....

The non-Hermitian skin effect, by which the eigenstates of Hamiltonian are predominantly localized at boundary, has revealed a strong sensitivity systems to boundary condition. Here we experimentally observe striking boundary-induced dynamical phenomenon known as edge burst, is characterized sharp accumulation loss in time evolutions. In contrast eigenstate localization, burst represents generic that occurs real time. Our experiment, based on photonic quantum walks, not only confirms...

We study the open XXZ spin chain with a PT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math> -symmetric non-Hermitian boundary field. find an interaction-induced scale-free skin effect by using coordinate Bethe Ansatz. The steady-state and ground state in broken phase are constructed, formulas of their eigen-energies thermodynamic limit obtained. differences between many-body states string explored,...

The non-Hermitian skin effect dramatically reshapes the energy bands of systems, meaning that usual Bloch band theory is fundamentally inadequate as their characterization. non-Bloch theory, in which concept Brillouin zone generalized, has been widely applied to investigate systems one spatial dimension. However, its generalization higher dimensions challenging. Here, we develop a formulation and arbitrary dimensions, based on natural geometrical object known amoeba. Our provides general...

The interplay between the non-Hermitian skin effect and imaginary gap of lossy lattices results in edge burst, a boundary-induced dynamical phenomenon which an exceptionally large portion particle loss occurs at edge. Here, we find that this intriguing can be exactly mapped into steady-state density distribution corresponding open quantum system. Consequently, bulk-edge scaling relation probability burst maps to density. Furthermore, introduce many-body open-system model two-body generates...

Nonreciprocal transmission of structured light has possible applications in high-capacity optical communication and high-dimensional signal processing. Here, we demonstrate the magnet-free cavity-free nonreciprocity an orbital-angular-momentum (OAM) beam using optical-pumping technology with assistance Doppler effect hot atoms. By pumping to induce a direction-dependent population transfer ground-state atoms, realize for laser that is carrying OAM. Interestingly, isolation ratio close 30 dB...

We show that a local non-Hermitian perturbation in Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. When lies at finite distance to boundary, eigenstates are promoted exponentially localized modes, whose number is proportional distance. Furthermore, when respects parity-time (PT) symmetry, PT symmetry breaking always accompanied by emergence of or exponential localization. Intriguingly, we find concise band-structure condition,...

Nonreciprocal optical devices are important in wide areas, ranging from telecommunications to signal processing. Here, we experimentally realize the magnet-free and cavity-free nonreciprocity based on phase-matched four-wave mixing (FWM) hot atoms. Specifically, isolation of more than 20 dB insertion loss less 1 without using any cavity can be achieved simultaneously. Our results provide general insights into a broad class parametrically modulated nonreciprocal behavior, paving way toward...

We construct a solvable Lindblad model in arbitrary dimensions, which the Liouvillian can be mapped to BCS-Hubbard featuring an imaginary Hubbard interaction. The Hilbert space of system divided into multiple sectors, each characterized by on-site invariant configuration. exhibits bistable steady states all spatial is guaranteed fermion-number parity. Notably, gap Zeno transition, below linear with respect dissipation. also uncover generic dimension-dependent behavior: In one dimension,...