Higher-order phases are characterized by corner or hinge modes that arise due to the interesting interplay of localization mechanisms along two or more dimensions. In this work, we introduce and construct a novel class of "hybrid" higher-order skin-topological boundary modes in non-reciprocal systems with two or more open boundaries. Their existence crucially relies on non-reciprocal pumping in addition to topological localization. Unlike usual non-Hermitian "skin" modes, they can exist in lattices with vanishing net reciprocity due to the selective nature of non-reciprocal pumping: While the bulk modes remain extended due to the cancellation of non-reciprocity within each unit cell, boundary modes experience a curious spontaneous breaking of reciprocity in the presence of topological localization, thereby experiencing the non-Hermitian skin effect. The number of possible hybridization channels increases rapidly with dimensionality, leading to a proliferation of distinct phases. In addition, skin modes or hybrid skin-topological modes can restore unitarity and are hence stable, allowing for experimental observations and manipulations in non-Hermitian photonic and electrical metamaterials.

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

Zigzag SnO2 nanobelts have been synthesized by evaporating tin grain in air. XRD, SEM, and TEM were employed to characterize the prepared samples. SEM images showed large amounts of zigzag nanobelts with periodic morphology. XRD result showed a pure tetragonal SnO2 phase. HRTEM and SAED revealed a single crystal structure with [010] zone axis on the whole zigzag zone. The zigzag structure is deduced to be formed by shifting the growth direction from [101] to [10] or vice versa. Growing nanobelts along different equivalent directions opens a new avenue for the preparation of novel nanostructured materials.

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Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a novel type of DQPTs, termed "Floquet DQPTs", as intrinsic features of systems with periodic time modulation. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.DQPTs are often associated with quantum quenches, a protocol in which parameters of a Hamiltonian are suddenly changed [1,2]. A quantum quench across an equilibrium quantum critical point may induce a DQPT. If pre-quench and post-quench systems are in topologically distinct phases, DQPTs may also be characterized by dynamical topological invariants [3][4][5]. As a promising approach to classify quantum states of matter in nonequilibrium situations, DQPTs have been theoretically explored in both closed and open quantum systems at different physical dimensions [2,7,8]. Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features. However, DQPTs under more general nonequilibrium manipulations are still largely unexplored [17][18][19]. In particular, because the dynamics of systems under time-periodic modulations has led to fascinating discoveries like Floquet topological states [20-24] and discrete time crystals [25][26][27], it is urgent to investigate how DQPTs may occur in such Floquet systems. Along this avenue, there have been scattered studies, but still with the notion that DQPTs are best aroused by a quench to some system parameters [28,29]. Here we introduce a novel class of DQPTs, termed Floquet DQPTs, which can be regarded as intrinsic features of systems with time-periodic modulations. As schematically shown in Floquet DQPT Time Time Rate function Rate function H i H f (a) H(t) (b) Conventional DQPT T T Quench T FIG. 1. Comparison between (a) DQPTs following a quantum quench, and (b) Floquet DQPTs without any quenches.Here Hi and H f denote the Hamiltonians before and after the quench, H(t) denotes a periodically and continuously modulated Hamiltonian. Fig. 1, the Floquet DQPTs we discovered occur within each period of a continuous driving field, without the need for any...

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance of periodic driving to the generation of unconventional topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1/2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading 87 Rb condensates into a periodically pulsed optical lattice. Under the on-resonance condition, the spin-1/2 double kicked rotor admits fruitful topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected 0 and π-quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked 87 Rb condensates, and suggest to detect its topological invariants by measuring the mean chiral displacement in momentum space.

Topological states of matter in non-Hermitian systems have attracted a lot of attention due to their intriguing dynamical and transport properties. In this study, we propose a periodically driven non-Hermitian lattice model in one-dimension, which features rich Floquet topological phases. The topological phase diagram of the model is derived analytically. Each of its non-Hermitian Floquet topological phases is characterized by a pair of integer winding numbers, counting the number of real 0-and π-quasienergy edge states at the boundaries of the lattice. Non-Hermiticity induced Floquet topological phases with unlimited winding numbers are found, which allow arbitrarily many real 0-and π-quasienergy edge states to appear in the complex quasienergy bulk gaps in a wellcontrolled manner. We further suggest to probe the topological winding numbers of the system by dynamically imaging the stroboscopic spin textures of its bulk states.