Simulating the time-dependent dx2-y2 Ginzburg-Landau equations using the finite-element method

The time-dependent Ginzburg-Landau equations describing a d-wave superconductor are simulated by the finite-element method. The equilibrium vortex structure in bulk samples, the nature of vortices in bulk and finite-size samples subject to various types of pinnings, and the transport behaviors are addressed. The extended finite-element method proves to be flexible to deal with various types of boundary conditions, desirable to simulate relaxation processes with very long time scales as well as the dynamics of vortices, especially in high-κ superconductors.published_or_final_versio

Internal-noise-enhanced signal transduction in neuronal systems

The ability of a neuron to detect and enhance a weak periodic flow of information within an "internal-noise" background has been studied through the mechanism of stochastic resonance. Two kinds of nonlinear synaptic input, a coherent firing of spikes from a number of coupled neurons and an irregular firing of spikes from a single neuron, are considered as the internal noise for a neuron. The output signal-to-noise ratio (SNR) is found to be finite. This nonzero SNR is able to account for the relevant experiments where the SNR is nonzero when the external noise is switched to zero.published_or_final_versio

Vortex flow in a two-component unconventional superconductor

Using a time-dependent two-component Ginzburg-Landau theory, we have studied the flow resistivity of vortices in the time-reversal-symmetry-breaking (T-breaking) phases of unconventional superconductors. The free vortex flow resistivity is found to be generally nonlinear against the magnetic field. The relevance of these results in explaining a recent experiment by Wu et al. is addressed.published_or_final_versio

Information coding via spontaneous oscillations in neural ensembles

The encoding and decoding of information via spontaneous oscillations is investigated by using an ensemble of Hodgkin-Huxley neurons. Results show that a signal can be encoded implicitly in spontaneous and highly irregular spike trains via high-order rate coding with the second-order statistics being relevant. The signal is reconstructed in the post-synaptic potential (PSP) through the spatiotemporal integration of the synapses.published_or_final_versio

Vortex state and dynamics of a d-wave superconductor: Finite-element analysis

The finite-element method is extended to simulate the d-wave time-dependent Ginzburg-Landau equations. By utilizing this method and in the context of the (s+d)-wave pairing, we discuss the nature of a single vortex, the structure of equilibrium vortex lattices in bulk samples, the nature of vortices in finite-size samples, and most importantly the transport of the vortices. In particular, the low-field free-flux-flow resistivity turns out to obey the law of corresponding states discovered in conventional superconductors, while the high-field resistivity reveals a noticeable effect of the s-wave coupling on lifting the effective upper critical field. The flux flow near and above the depinning current in the presence of a twin boundary or random impurities also assumes a conventional behavior: The current dependence of the flux-flow resistivity can be well described by an overdamped model for a particle subject to driving and pinning forces. However, our results show a noticeable difference between the flux-flow resistivities at large currents in the presence and absence of pinning.published_or_final_versio

Firing and signal transduction associated with an intrinsic oscillation in neuronal systems

We study the nonlinear firing and signal transduction of a neuron subject to both a constant stimulus and a weak periodic signal, each of which is too small to, separately, fire spikes for the neuron. The subthreshold constant stimulus, regarded as the total input to the neuron from other neurons and from the external world, is found to give rise to only an intrinsic subthreshold oscillation. This oscillation can lead to the transduction of the weak periodic signal via a mechanism similar to stochastic resonance. This may enable us to understand reported experimental results of oscillation associated signal transduction and of finite signal-to-noise ratio in the absence of external noise. In addition, the most sensitive frequency range for signal transduction is also found.published_or_final_versio

Postinhibitory rebound delay and weak synchronization in Hodgkin-Huxley neuronal networks

The postinhibitory rebound delay and weak synchronization in neuronal networks were discussed. A kind of intrinsic delay induced by the rebound was observed and was found to be important in determining the overall frequency of the network. The comparisons with the results for the excitatory coupling were also addressed.published_or_final_versio

Transverse resistivity and Hall effect of d-wave superconductors with twin boundaries: Numerical solutions of time-dependent Ginzburg-Landau equations in the presence of thermal noise

Taking into account thermal fluctuations, we solve numerically the time-dependent Ginzburg-Landau equations to study the role of twin boundaries on the transverse resistivity as well as Hall effect for a d-wave superconductor. In the presence of an external current parallel to the twin boundary, we observe that the twin boundary (TB) not only behaves as a pinning center, but also induces a negative component of transverse resistivity. A sign reversal may occur for the transverse resistivity and Hall signal, changing from negative to positive as the magnetic field increases. The increase of the strength of the TB can enhance the negative transverse resistivity, but will soon saturate at higher twin-boundary strengths. Only the antisymmetric part of the transverse resistivity is significantly affected by the normal-state off-diagonal conductivity, while the symmetric part may reflect a key role of the TB on the anisotropy.published_or_final_versio

Novel Z2 Topological Metals and Semimetals

© 2016 American Physical Society.We report two theoretical discoveries for Z2 topological metals and semimetals. It is shown first that any dimensional Z2 Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for Z Fermi points in a periodic system without any discrete symmetry, is generalized so that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all Z2 Fermi points have the same topological charge νZ2=1 or 0 for periodic systems. Moreover, we also establish all six topological types of Z2 models for realistic physical dimensions.postprin

Supercurrent determined from the Aharonov-Bohm effect in mesoscopic superconducting rings

We have solved the Bogoliubov-de Gennes equation for a clean, one-dimensional mesoscopic superconducting ring threaded by a magnetic flux Φ. We show that the superfluid velocity is driven directly by Φ while the relative motion of the pair of electrons is independent of Φ. Meanwhile, the fluxoid quantization is obtained straightforwardly. More importantly, we have also calculated the supercurrent numerically and self-consistently and find it is periodic in Φ with the period Φshc/2e for Φs≤Φd=(mvdL/ Latin small letter h with strokeπ)Φs and with the period Φ0hc/e for Φd<Φs, which arises from mesoscopic effects. © 1994 The American Physical Society.published_or_final_versio