arXiv subjects
Publications and source records attributed to D. A. Ivanov.
Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov-de-Gennes equations in the vortex core we derive the non-abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.
In the presence of strong disorder, the statistics of quasiparticle levels in the core of a vortex in a two-dimensional p-wave superconductor belongs to the universality class B corresponding to the ensemble of orthogonal matrices in odd dimensions. This novel universality class appears as a consequence of the O(2) spin symmetry of p-wave pairing. It is preserved in the presence of random disorder, of electromagnetic vector potential, and of an admixture of the pairing of opposite chirality in the vortex core, but may be destroyed by spin-orbit coupling and by Zeeman splitting.
We report staggered vorticity correlations of current in the d-wave variational wave function for the lightly-doped t-J model. Such correlations are explained from the SU(2) symmetry relating d-wave and staggered-flux mean-field phases. The correlation functions computed by the variational Monte Carlo method suggest that pairs are formed of holes circulating in opposite directions.
Superconducting quantum point contacts are known to possess two subgap states per each propagating mode. In this note we compute the low-temperature relaxation rate of the upper subgap state into the lower one with the emission of an acoustic phonon. If the reflection in the contact is small, the relaxation time may become much longer than the characteristic lifetime of a bulk quasiparticle.
In a superconducting quantum point contact, dynamics of the superconducting phase is coupled to the transitions between the subgap states. We compute this coupling and derive the two-level Hamiltonian of the contact.
We study the nuclear spin-lattice relaxation rate $1/T_1$ in the two-leg antiferromagnetic spin-1/2 Heisenberg ladder. More specifically, we consider the contribution to $1/T_1$ from the processes with momentum transfer $(π,π)$. In the limit of weak coupling between the two chains, this contribution is of activation type with gap $2Δ$ at low temperatures ($Δ$ is the spin gap), but crosses over to a slowly-decaying temperature dependence at the crossover temperature $T\approxΔ$. This crossover possibly explains the recent high-temperature NMR results on ladder-containing cuprates by T. Imai et al.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy $E_C \ll Δ$. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to $π$, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge $Q_x=C V_g$ with period $2e$.
We study counting statistics of electric current pumped by pulses of an external field. The fluctuations depend on the pulse shape, and can be minimized by choosing the pulse shape properly. For an optimal pulse shape, the fluctuations are reduced to the {\it dc} level, i.e., they do not depend on the duty cycle of the signal. We develop an approach that allows to calculate all counting statistics for various driving fields, optimal and non-optimal. The statistics depend in an interesting way on the analytic structure of the field time dependence, and display an analogy with coherent states and instantons.