Plausible arguments for a large elastic response of the fluxoid lattice

The non-local elastic behaviour of the Fluxoid Lattice in type-II superconductors, established rigorously elsewhere, may be deduced by plausible reasoning from well known properties of the Lattice.     

Experimental observation of lattice distortions due to a flux line lattice in niobium

A polarized neutron scattering investigation of the flux line lattice in the type-II superconductor niobium is reported. A modulation of the nuclear lattice has been detected, and the magnitude of the first Fourier component of the lattice distortion established relative to the magnitude of the magnetic scattering. This constitutes the first experimental observation of lattice distortions due to the presence of magnetic flux lines within the bulk of a type-II superconductor. Using a simple microscopic model the lattice distortion in niobium is estimated. A new mechanism is suggested for the coupling of the flux line lattice to the crystallographic lattice. The experimental technique opens up the possibility of investigating the microscopic mechanism of flux line - nuclear lattice interactions, in particular the pinning of flux lines within the bulk of a type-II superconductor. Received: 8 August 1997 / Accepted: 16 October 1997     

Total and surface density of states on the Bethe lattice

A novel approach for calculating the density of surface states in a disordered system is presented. It is shown that the node counting method for calculating the energy spectrum of a system holds for the Bethe lattice. An exact method for calculating the total density of states of a disordered Bethe system terminating on a closed surface, as well as the contribution of the bulk and surface states to it is then developed and applied to the cases of Lorentzian and Gaussian randomness. The results are discussed in connection to relevant material from the literature.     

Single-atom density of states of an optical lattice

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter kappa denoting the strength of the harmonic trap. It is shown that the kappa-->0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (kappa-->0) is qualitatively different from that of a translationally invariant lattice (kappa=0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.     

Observation of cascaded two-photon-induced transitions between fluxoid states of a SQUID

We present evidence for transitions between fluxoid wells of a SQUID due to cascaded, two-photon processes. Such transitions are evidenced by an anomalous dependence on the transition rate from the one-photon resonant level within the initial well, which cannot be explained by previously observed macroscopic resonant tunneling. These two-photon processes may be a significant source of decoherence in SQUID qubits subject to microwave radiation.     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

Structure of the Abrikosov vortex lattice in a thin superconducting film in a parallel magnetic field

The structure of a vortex lattice in thin (d<λ, where d is the film thickness and λ is the London penetration depth) superconducting films is investigated in a magnetic field parallel to the film surface. It is shown that the stable configuration has the form of discrete vortex rows whose number changes discretely with an increase in the applied magnetic field. The entry fields H _c1 ^(N) (d) for vortex rows are calculated for N=1, 2. It is shown that the structural transition in the vortex ensemble is a second-order phase transition. A simpler method (as compared to the Monte Carlo technique) is proposed for calculating the vortex lattice parameters.     

ε-expansion for the density of states of a disordered system near an Anderson transition

The density of states for the Schrödinger equation with a Gaussian random potential is calculated in a space of dimension d=4?ε in the entire energy range, including the vicinity of an Anderson transition.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Long-wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long-wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.     

Electronic density of states of the cluster-Bethe-lattice and the diamond lattice with continued fraction method

The electronic density of states of diamond lattice was evaluated with the continued fraction method, up to the third and the fourth level. The result was found to be superior to the cluster-Bethe-lattice approximation to the diamond lattice.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.