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...

Dual‐ion batteries (DIBs) inherently suffer from limited energy density. Proposed here is a strategy to effectively tackle this issue by employing locally ordered graphitized carbon (LOGC) cathodes. Quantum mechanical modeling suggests that strong anion–anion repulsions and severe expansion at the deep‐charging stage raise the anion intercalation voltage, therefore only part of the theoretical anion storage sites in graphite is accessible. The LOGC interconnected with disordered carbon is predicted to weaken the interlaminar van der Waals interactions, while disordered carbons not only interconnect the dispersed nanographite but also partially buffer severe anion–anion repulsion and offer extra capacitive anion storage sites. As a proof‐of‐concept, ketjen black (KB) with LOGC was used as a model cathode for a potassium‐based DIB (KDIB). The KDIB delivers an unprecedentedly high specific capacity of 232 mAh g−1 at 50 mA g−1, a good rate capability of 110 mAh g−1 at 2000 mA g−1, and excellent cycling stability of 1000 cycles without obvious capacity fading.