Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization effects

We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits significant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization effects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, bothe-/2solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonice-/2fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.

Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines' chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.

Uniquely identifying topological order based on boundary-bulk duality and anyon condensation

Topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It was known that R and F matrices, which characterize the fusion-braiding properties of anyons, can be used to uniquely identify topological order. In this article, we explore an essential question: how can the R and F matrices be experimentally measured? We show that the braidings, i.e. the R matrices, can be completely determined by the half braidings of boundary excitations due to the boundary-bulk duality and the anyon condensation. The F matrices can also be measured by comparing the quantum states involving the fusion of three anyons in two different orders. Thus we provide a model-independent experimental protocol to uniquely identify topological order. By using quantum simulations based on a toric code model with boundaries encoded in three- and four-qubit systems and state-of-the-art technology, we obtain the first experimental measurement of R and F matrices by means of an NMR quantum computer at room temperature.

Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer's Principle

Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer's principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models-the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.

Detection of Topological Spin Textures via Nonlinear Magnetic Responses

Topologically nontrivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation race-track memory and unconventional computing. A major challenge for these applications and the investigation of nanoscale magnetic structures in general is the realization of suitable detection schemes. We study magnetic disclinations, dislocations, and domain walls in FeGe and reveal pronounced responses that distinguish them from the helimagnetic background. A combination of magnetic force microscopy (MFM) and micromagnetic simulations links the response to the local magnetic susceptibility, that is, characteristic changes in the spin texture driven by the MFM tip. On the basis of the findings, which we explain using nonlinear response theory, we propose a read-out scheme using superconducting microcoils, presenting an innovative approach for detecting topological spin textures and domain walls in device-relevant geometries.

Charge Density Wave Vortex Lattice Observed in Graphene-Passivated 1T-TaS2 by Ambient Scanning Tunneling Microscopy

The nearly commensurate charge density wave (CDW) excitations native to the transition-metal dichalcogenide crystal, 1T-TaS₂, under ambient conditions are revealed by scanning tunneling microscopy (STM) and spectroscopy (STS) measurements of a graphene/TaS₂ heterostructure. Surface potential measurements show that the graphene passivation layer prevents oxidation of the air-sensitive 1T-TaS₂ surface. The graphene protective layer does not however interfere with probing the native electronic properties of 1T-TaS₂ by STM/STS, which revealed that nearly commensurate CDW hosts an array of vortex-like topological defects. We find that these topological defects organize themselves to form a lattice with quasi-long-range order, analogous to the vortex Bragg glass in type-II superconductors but accessible in ambient conditions.

Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order

Fermi surface (FS) topology is a fundamental property of metals and superconductors. In electron-doped cuprate Nd_2-x Ce _x CuO₄ (NCCO), an unexpected FS reconstruction has been observed in optimal- and overdoped regime (x = 0.15-0.17) by quantum oscillation measurements (QOM). This is all the more puzzling because neutron scattering suggests that the antiferromagnetic (AFM) long-range order, which is believed to reconstruct the FS, vanishes before x = 0.14. To reconcile the conflict, a widely discussed external magnetic-field-induced AFM long-range order in QOM explains the FS reconstruction as an extrinsic property. Here, we report angle-resolved photoemission (ARPES) evidence of FS reconstruction in optimal- and overdoped NCCO. The observed FSs are in quantitative agreement with QOM, suggesting an intrinsic FS reconstruction without field. This reconstructed FS, despite its importance as a basis to understand electron-doped cuprates, cannot be explained under the traditional scheme. Furthermore, the energy gap of the reconstruction decreases rapidly near x = 0.17 like an order parameter, echoing the quantum critical doping in transport. The totality of the data points to a mysterious order between x = 0.14 and 0.17, whose appearance favors the FS reconstruction and disappearance defines the quantum critical doping. A recent topological proposal provides an ansatz for its origin.

Hidden Order and Haldane-Like Phase in Molecular Chains Assembled from Conformation-Switchable Molecules

Topological properties of matters have attracted tremendous interest in the past years due to the scientific and technological importance. It is of great interest to discover the analogs of topological phases in molecular architectures, if the key constituents of the phases are properly mimicked. Using scanning tunneling microscopy, we demonstrate that quasi-1D molecular chains assembled from conformation-switchable dibenzo[ g, p]chrysene molecules show hidden antiparallel order analogous to the hidden antiferromagnetic order in the Haldane phase, a known topological phase of quantum spin-1 chains. This is realized by mimicking the spin degree of freedom with the intramolecular helicene chiral switches and by emulating the interspin antiferromagnetic coupling with intermolecular homochiral coupling. The discovery of the molecular analog of topological matters may inspire the search of molecular architectures with nontrivial topological properties.

Topological order in the pseudogap metal

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

The establishment of peripheral sensory arbors in the leech: in vivo time-lapse studies reveal a highly dynamic process

Pressure-sensitive (P) neurons located in the leech CNS form elaborate terminal arbors in the body wall of the animal during mid-embryogenesis. In the experiments discussed here, arbor development in the target region was studied in intact, unanesthetized leech embryos using time-lapse video microscopy of individual, fluorescently stained P neurons. Analysis of time-lapse recordings made over a period of several days revealed that arbor formation is a very dynamic process. At any particular time, most high-order terminal branches were either extending or retracting, in approximately equal numbers and at very similar rates. Many branches underwent several rounds of extension and retraction every hour. Net arbor growth occurred at a much lower rate than the extension and retraction rates of individual branches. Process retraction sometimes resulted in an apparent change in the topological order of processes. Significantly, the initiation of new branches was restricted to a few locations along the parent process, which were termed "hot spots." Moreover, the capacity to generate high-order branches correlated with parent process stability. The target region of the growing P cell arbor in the body wall was subsequently examined using confocal microscopy in fixed preparations. The arbor expanded between the longitudinal and circular muscle layers, a region occupied by small unidentified cells. Simultaneous imaging of the dye-labeled terminal arbor and the surrounding tissue at two different wavelengths suggested that the high-order processes were navigating around these cells, which sometimes forced the growing processes to assume a bent form. These observations suggest that the formation of the P cell arbor can be best described as a "dynamically unstable" process that is constrained by interactions with its environment.