Stability of flat zero-energy states at the dirty surface of a nodal superconductor

We discuss the stability of highly degenerate zero-energy states tha appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. We show that an index defined in terms of the chiral eigenvalues of the zero-energy states can be used to measure the degree of degeneracy at zero energy in the presence of potential disorder. We also discuss the relationship between the index and the topological numbers.Comment: 12 pages, 7 figure

Large-scale imaging of brain network activity from >10,000 neocortical cells

Large-scale recording from populations of neurons is a promising strategy in the study of complex brain function. Here we introduce a simple optical technique that simultaneously probes the calcium activity of ~10,000 cells at the single cell resolution _in vitro_. We employed a combination of a low-magnification objective lens and an electron-multiplying charge-coupled device megapixel camera to achieve large-view-field and high-resolution imaging

Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface

We discuss the symmetry property of a nodal superconductor that hosts robust flat-band zero-energy states at its surface under potential disorder. Such robust zero-energy states are known to induce the anomalous proximity effect in a dirty normal metal attached to a superconductor. A recent study has shown that a topological index ${\cal N}_\mathrm{ZES}$ describes the number of zero-energy states at the dirty surface of a $p$-wave superconductor. We generalize the theory to clarify the conditions required for a superconductor that enables ${\cal N}_\mathrm{ZES}\neq 0$. Our results show that ${\cal N}_\mathrm{ZES}\neq 0$ is realized in a topological material that belongs to either the BDI or CII class. We also present two realistic Hamiltonians that result in ${\cal N}_\mathrm{ZES}\neq 0$.Comment: 9 pages, 3 figure

Tunable φ\varphi-Josephson junction with a quantum anomalous Hall insulator

We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $\theta$. The phase shift $\varphi$ appealing in the current-phase relationship $J\propto \sin(\theta-\varphi$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains the physical origin of $\varphi$. A quantum anomalous Hall insulator breaks time-reversal symmetry and mirror reflection symmetry simultaneously. However it preserves magnetic mirror reflection symmetry. Such characteristic symmetry property enable us to have a tunable $\varphi$-junction with a quantum Hall insulator.Comment: 10pages, 9figure

Quantization of Conductance Minimum and Index Theorem

We discuss the minimum value of the zero-bias differential conductance $G_{\textrm{min}}$ in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that $G_{\textrm{min}}$ is quantized at $(4e^2/h) N_{\mathrm{ZES}}$ in the limit of strong impurity scatterings in the normal metal. The integer $N_{\mathrm{ZES}}$ represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that $N_{\mathrm{ZES}}$ corresponds to the Atiyah-Singer index in mathematics.Comment: 5 pages, 1 figur

Josephson effect in two-band superconductors

We study theoretically the Josephson effect between two time-reversal two-band superconductors, where we assume the equal-time spin-singlet $s$-wave pair potential in each conduction band. %as well as the band asymmetry and the band hybridization in the normal state. The superconducting phase at the first band $\varphi_1$ and that at the second band $\varphi_2$ characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green's function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band $\delta\varphi_1$, the phase difference at the second band $\delta\varphi_2$, and the difference at the center-of-mass phase $\delta(\varphi_1+\varphi_2)/2$. A Cooper pairs generated by the band hybridization carries the last current component. In some cases, the current-phase relationship deviates from the sinusoidal function as a result of time-reversal symmetry breaking down.Comment: 6 page, 2 figure

Spontaneous Plasticity of Multineuronal Activity Patterns in Activated Hippocampal Networks

Using functional multineuron imaging with single-cell resolution, we examined how hippocampal networks by themselves change the spatiotemporal patterns of spontaneous activity during the course of emitting spontaneous activity. When extracellular ionic concentrations were changed to those that mimicked in vivo conditions, spontaneous activity was increased in active cell number and activity frequency. When ionic compositions were restored to the control conditions, the activity level returned to baseline, but the weighted spatial dispersion of active cells, as assessed by entropy-based metrics, did not. Thus, the networks can modify themselves by altering the internal structure of their correlated activity, even though they as a whole maintained the same level of activity in space and time