Green's functions of quasi-one-dimensional layered systems and their application to Josephson junctions

We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic polynomials in the momentum operator with matrix-valued (multichannel) coefficients. This, in particular, allows one to study transport in heterostructures consisting of multichannel conducting, superconducting, or insulating components with band structures of arbitrary complexity. We find a general expression for the single-particle Green's function of the combined setup in terms of the bulk (translationally invariant) Green's functions of its constituents. Furthermore, we provide the expression for the global density of states of the combined system and establish the bound state equation in terms of bulk Green's functions. We apply our formalism to investigate the spectrum and current-phase relations in ordinary and topological Josephson junctions, additionally showing how to account for the effects of static disorder and local Coulomb interaction

Spin-density induced by electromagnetic wave in two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit couplings

We consider the magnetic response of a two-dimensional electron gas (2DEG) with both Rashba and Dresselhaus spin-orbit coupling to a microwave excitation. We generalize the results of [A. Shnirman and I. Martin, Europhys. Lett. 78, 27001 (2007).], where pure Rashba coupling was studied. We observe that the microwave with the in-plane electric field and the out-of-plane magnetic field creates an out-of-plane spin polarization. The effect is more prominent in clean systems with resolved spin-orbit-split subbands. Considered as response to the microwave magnetic field, the spin-orbit contribution to the magnetization far exceeds the usual Zeeman contribution in the clean limit. The effect vanishes when the Rashba and the Dresselhaus couplings have equal strength.Comment: 4 pages, 2 figure

U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Sch\"on approaches

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Sch\"on approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).Comment: Contribution for Leonid Keldysh 85 Festschrif

Quiet SDS Josephson Junctions for Quantum Computing

Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBCO single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor. The sign change in the order parameter can be exploited to construct a new type of s-wave - d-wave - s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a `quiet' qubit --- a solid state implementation of a quantum bit which remains optimally isolated from its environment.Comment: 4 pages, 2 ps-figure

Recurrent Large Sunspot Structures and 27-Day Component of Solar Activity as Proxies to Axis-Nonsymmetry

The purpose of this paper is to design tools that quantify the structure of the nonsymmetrical component of the solar magnetic field. With the Fourier transform and the machine learning identification of recurrent objects, we define the 27-day component of solar proxies and recurrent large sunspot structures (ReLaSS), respectively. These two closely related characteristics are established to represent different components of the asymmetry of the solar magnetic field. We derive that the 27-day component and ReLaSS have anticorrelated since 1970 after dozens of years of a strong correlation. The persistence of the correlation sign during few solar cycles reflects yet unknown regularities of solar activity. The contribution of both proxies to the nonsymmetry of solar activity is shown to be lower in 1990–2010 than ∼100 years earlier. This property may be the trace of the asymmetry at the scales that are longer than the centennial Gleissberg cycle

A correlation of mean period of MJO indices and 11-yr solar variation

International audienceThis paper focuses on the decadal to multi-decadal evolution of the spectral properties of the Madden-Julian Oscillation (MJO). Guided by former studies, we test whether the ∼11-yr (Schwabe) cycle of solar activity could be reflected in the spectral features of MJO indices: namely, we study the evolution of MJO mean period within different period ranges and compare these with the evolution of solar activity. We focus on solar proxies best linked to UV emission and cosmic rays: sunspot number WN, F10.7 flux, core-to-wing ratio MgII, and galactic cosmic rays (GCR). A clear solar signature in MJO spectral properties is indeed found and shown to be both statistically significant and robust. UV proxies are found to be better correlated with MJO mean period than GCR, thus supporting rather the ozone mechanism of solar impact on MJO. The overall correlation with solar activity is found to be stronger in the Indian Ocean. Long periods (e.g. 50-80 day) are better correlated with solar activity than shorter periods (e.g. 30-60 day). A marked change in the relationship between MJO mean period and solar activity takes place in the declining phase of solar cycle 23, adding to its unusual character

The 27-Day Signal in Sunspot Number Series and the Solar Dynamo

International audienceWe analyze the Wolf number daily series WN (1849 to present) as well as two other related series characterizing solar activity. Our analysis consists in computing the amplitude of a given Fourier component in a sliding time window and examining its long-term evolution. We start with the well-known 27.03- and 27.6-day periods and observe strong decadal variations of this amplitude as well as a sharp increase of the average value starting around 1905. We then consider a packet of 31 lines with periods from 25.743 to 28.453 days, which is shown to be a better representation of the synodic solar rotation. We first examine the temporal evolution of individual lines, then the energy of the packet. The energy of the packet increases sharply at the beginning of the 20th century, leading by more than two decades the well-known increase of the Wolf number. The nonaxisymmetry of sunspots increases before the total increase of activity and may be considered as a precursor. We discuss briefly and tentatively this observation in terms of solar dynamo theory

Slow and Fast Rotating Coronal Holes from Geomagnetic Indices

International audienceThe evolution of the 27-day recurrence in the series of two solar indices (Wolf number WN and 10.7 cm radio flux F) and two geomagnetic indices ( Dst and ζ, variance of the geomagnetic field recorded at a magnetic observatory) have been studied over the 1957 - 2007 time span. Spectral energies contained in two period domains (25 - 27.3 and 27.3 - 31 days), designated as E 1 and E 2, have been computed. Whereas the evolution of E 1 is the same for the four indices, that of E 2 is essentially different for WN and F on the one hand, Dst and ζ on the other hand. Some general conclusions on the dynamics of the solar outer layers are inferred from these results. First the solar activity, as measured by WN, and when averaged over a few years, evolves in the same way whatever the latitude. Second, two families of coronal holes (CHs) are identified; the rapidly and the slowly rotating CHs evolve quite differently