Alexei Vagov

Extended Ginzburg-Landau formalism : Systematic expansion in small deviation from the critical temperature

Based on the Gor’kov formalism for a clean s-wave superconductor, we develop an extended version of the single-band Ginzburg-Landau (GL) theory by means of a systematic expansion in the deviation from the critical temperature Tc, i.e., τ = 1 − T/T c. We calculate different contributions to the order parameter and the magnetic field: the leading contributions (∝ τ 1/2 in the order parameter and ∝ τ in the magnetic field) are controlled by the standard GL theory, while the next-to-leading terms (∝ τ 3/2 in the gap and ∝ τ 2 in the magnetic field) constitute the extended GL (EGL) approach. We derive the free-energy functional for the extended formalism and the corresponding expression for the current density. To illustrate the usefulness of our formalism, we calculate, in a semianalytical form, the temperature-dependent correction to the GL parameter at which the surface energy becomes zero, and analytically, the temperature dependence of the thermodynamic critical field. We demonstrate that the EGL formalism is not just a mathematical extension to the theory: variations of both the gap and the thermodynamic critical field with temperature calculated within the EGL theory are found in very good agreement with the full BCS results down to low temperatures, which dramatically improves the applicability of the formalism compared to its standard predecessor.

Atypical BCS-BEC crossover induced by quantum-size effects

Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow the size-dependent changes in the single-particle density of states. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size effects, overlooked previously. The many-body physics is revealed in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. Quantized perpendicular spectrum results in the formation of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both the BCS and BEC-like components.

Ultrafast terahertz-field-induced dynamics of superconducting bulk and quasi-1D samples

Within a density-matrix formalism based on the Bardeen–Cooper–Schrieffer (BCS) model and the Bogoliubov–de Gennes equations we provide a description of the dynamics of the non-equilibrium superconducting pairing induced by a terahertz (THz) laser pulse in bulk and quasi-one-dimensional (1D) samples of conventional (BCS-type) superconductors. A cross-over from an adiabatic to a non-adiabatic regime takes place for short and intense THz pulses. In the non-adiabatic regime, the order parameter performs a damped oscillation. We discuss how the parameters of the THz pulse influence the amplitude and the mean value of the oscillation in bulk samples. It is demonstrated that for high intensities the non-adiabatic regime can be reached even for pulses longer than the oscillation period. For the 1D samples we find that the oscillation may attenuate with a different power law. This is analysed by comparing the THz-induced dynamics with the dynamics induced by a sudden switching of the pairing strength, which exhibits essentially the same behaviour. The numerical calculations show that the exponent of the power law depends critically on the density of states in the Debye window and therefore changes in an oscillatory way with the confinement strength. Irregularities in the decay of the oscillation are predicted when the 1D quantum wire is cut short to an elongated zero-dimensional quantum dot structure.

Nanofilms as quantum-engineered multiband superconductors: The Ginzburg-Landau theory

Recently fabricated single-crystalline atomically flat metallic nanofilms are in fact quantum-engineered multiband superconductors. Here the multiband structure is dictated by the nanofilm thickness through the size quantization of the electron motion perpendicular to the nanofilm. This opens the unique possibility to explore superconductivity in well-controlled multi-band systems. However, a serious obstacle is the absence of a convenient and manageable theoretical tool to access new physical phenomena in such quasi–two-dimensional systems, including interplay of quantum confinement and fluctuations. Here we cover this gap and construct the appropriate multiband Ginzburg-Landau functional for nano-thin superconductors.

Asymptotic-boundary-layer method for unstable trajectories: semiclassical expansions for individual scar wave functions.

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

Atomically flat superconducting nanofilms: multiband properties and mean-field theory

Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D–2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin–Wagner–Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri–Perot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg–Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems

We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.

Nonlinear cavity feeding and unconventional photon statistics in solid-state cavity QED revealed by many-level real-time path-integral calculations

The generation of photons in a microcavity coupled to a laser-driven quantum dot interacting with longitudinal acoustic (LA) phonons is studied in the regime of simultaneously strong driving and strong dot-cavity coupling. The stationary cavity photon number is found to depend in a non-trivial way on the detuning between the laser and the exciton transition in the dot. In particular, the maximal efficiency of the cavity feeding is obtained for detunings corresponding to transition energies between cavity-dressed states with excitation numbers larger than one. Phonons significantly enhance the cavity feeding at large detunings. In the strong-driving, strong-coupling limit, the photon statistics is highly non-Poissonian. While without phonons a double-peaked structure in the photon distribution is predicted, phonons make the photon statistics thermal-like with very high effective temperatures

Phonon limited superconducting correlations in metallic nanograins.

\sim 10^5

Competition between pure dephasing and photon losses in the dynamics of a dot-cavity system

K, even for low phonon temperatures