A quantum spin liquid with a Z2 topological order has long been thought to be important for the application of quantum computing and may be related to high-temperature superconductivity [1][2][3]. While a two-dimensional kagome antiferromagnet may host such a state, strong experimental evidences are still lacking [4][5][6][7][8][9]. Here we show that the spin excitations from the kagome planes in magnetically ordered Cu4(OD)6FBr and non-magnetically ordered Cu3Zn(OD)6FBr are similarly gapped although the content of inter-kagome-layer Cu 2+ ions changes dramatically. This suggests that the spin triplet gap and continuum of the intrinsic kagome antiferromagnet are robust against the interlayer magnetic impurities. Our results show that the ground state of Cu3Zn(OD)6FBr is a gapped quantum spin liquid with Z2 topological order.

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We study new types of Josephson junctions composed of helical p-wave superconductors with and -pairing symmetries using quasi-classical Green’s functions with generalized Riccati parametrization. The junctions can host rich ground states: π phase, 0 + π phase, φ0 phase and φ phase. The phase transition can be tuned by rotating the magnetization in the ferromagnetic interface. We present the phase diagrams in the parameter space formed by the orientation of the magnetization or by the magnitude of the interfacial potentials. The selection rules for the lowest order current which are responsible for the formation of the rich phases are summarized from the current-phase relations based on the numerical calculation. We construct a Ginzburg–Landau type of free energy for the junctions with d-vectors and the magnetization, which not only reveals the interaction forms of spin-triplet superconductivity and ferromagnetism, but can also directly lead to the selection rules. In addition, the energies of the Andreev bound states and the novel symmetries in the current-phase relations are also investigated. Our results are helpful both in the prediction of novel Josephson phases and in the design of quantum circuits.

Coherently driven atomic gases inside optical cavities hold great promise for generating rich dynamics and exotic states of matter. It was shown recently that an exotic topological superradiant state exists in a two-component degenerate Fermi gas coupled to a cavity, where local order parameters coexist with global topological invariants. In this work, we characterize in detail various properties of this exotic state, focusing on the feedback interactions between the atoms and the cavity field. In particular, we demonstrate that cavity-induced interband coupling plays a crucial role in inducing the topological phase transition between the conventional and topological superradiant states. We analyze the interesting signatures in the cavity field left by the closing and reopening of the atomic bulk gap across the topological phase boundary and discuss the robustness of the topological superradiant state by investigating the steady-state phase diagram under various conditions. Furthermore, we consider the interaction effect and discuss the interplay between the pairing order in atomic ensembles and the superradiance of the cavity mode. Our work provides many valuable insights into the unique cavity-atom hybrid system under study and is helpful for future experimental exploration of the topological superradiant state.

We investigate the transport problem that a spinful matter wave is incident on a strong localized spin-orbit-coupled Bose-Einstein condensate in optical lattices, where the localization is admitted by atom interaction only existing at one particular site, and the spin-orbit coupling arouse spatial rotation of the spin texture. We find that tuning the spin orientation of the localized Bose-Einstein condensate can lead to spin-nonreciprocal/spin-reciprocal transport, meaning the transport properties are dependent on/independent of the spin orientation of incident waves. In the former case, we obtain the conditions to achieve transparency, beam-splitting, and blockade of the incident wave with a given spin orientation, and furthermore the ones to perfectly isolate incident waves of different spin orientation, while in the latter, we obtain the condition to maximize the conversion of different spin states. The result may be useful to develop a novel spinful matter wave valve that integrates spin switcher, beam-splitter, isolator, and converter. The method can also be applied to other real systems, e.g., realizing perfect isolation of spin states in magnetism, which is otherwise rather difficult.