Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions

We investigate the transport properties of a one-dimensional superconductor-normal metal-superconductor (S-N-S) system described within the tight-binding approximation. We compute the equilibrium dc Josephson current and the time-dependent oscillating current generated after the switch-on of a constant bias. In the first case an exact embedding procedure to calculate the Nambu-Gorkov Keldysh Green's function is employed and used to derive the continuum and bound states contributions to the dc current. A general formalism to obtain the Andreev bound states (ABS) of a normal chain connected to superconducting leads is also presented. We identify a regime in which all Josephson current is carried by the ABS and obtain an analytic formula for the current-phase relation in the limit of long chains. In the latter case the condition for perfect Andreev reflections is expressed in terms of the microscopic parameters of the model, showing a limitation of the so called wide-band-limit (WBL) approximation. When a finite bias is applied to the S-N-S junction we compute the exact time-evolution of the system by solving numerically the time-dependent Bogoliubov-deGennes equations. We provide a microscopic description of the electron dynamics not only inside the normal region but also in the superconductors, thus gaining more information with respect to WBL-based approaches. Our scheme allows us to study the ac regime as well as the transient dynamics whose characteristic time-scale is dictated by the velocity of multiple Andreev reflections

Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems

Time-dependent quantum transport: A practical scheme using density functional theory

We present a computationally tractable scheme of time-dependent transport phenomena within open-boundary time-dependent density-functional-theory. Within this approach all the response properties of a system are determined from the time-propagation of the set of ``occupied'' Kohn-Sham orbitals under the influence of the external bias. This central idea is combined with an open-boundary description of the geometry of the system that is divided into three regions: left/right leads and the device region (``real simulation region''). We have derived a general scheme to extract the set of initial states in the device region that will be propagated in time with proper transparent boundary-condition at the device/lead interface. This is possible due to a new modified Crank-Nicholson algorithm that allows an efficient time-propagation of open quantum systems. We illustrate the method in one-dimensional model systems as a first step towards a full first-principles implementation. In particular we show how a stationary current develops in the system independent of the transient-current history upon application of the bias. The present work is ideally suited to study ac transport and photon-induced charge-injection. Although the implementation has been done assuming clamped ions, we discuss how it can be extended to include dissipation due to electron-phonon coupling through the combined simulation of the electron-ion dynamics as well as electron-electron correlations.Comment: 14 pages, 9 figures, one of which consist of two separate file

The Role of Bound States in Time-Dependent Quantum Transport

Charge transport through a nanoscale junction coupled to two macroscopic electrodes is investigated for the situation when bound states are present. We provide numerical evidence that bound states give rise to persistent, non-decaying current oscillations in the junction. We also show that the amplitude of these oscillations can exhibit a strong dependence on the history of the applied potential as well as on the initial equilibrium configuration. Our simulations allow for a quantitative investigation of several transient features. We also discuss the existence of different time-scales and address their microscopic origin.Comment: 10 pages, 8 figure

Density functional calculations of nanoscale conductance

Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a Master equation.Comment: topical review, 28 pages, updated version with some revision

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum-statistical mechanics provide consistent but computational costly approaches; alternatively, use of density-dependent ballistic-transport calculations [e.g., Phys. Rev. B 52, 5335 (1995)], here denoted `DBT', provide computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest order approximation to an exact nonequilibrium thermodynamics density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that a uniqueness-of-density proof from a closely related study [Phys. Rev. B 78, 165109 (2008)] makes it possible to provide a single-particle formulation based on universal electron-density functionals. I illustrate a formal evaluation of the thermodynamics grand potential value which is closely related to the variation in scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamics forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamics forces and observes that these are suited for a nonequilibrium implementation of the Born-Oppenheimer approximation.Comment: 37 pages, 3 Figure

Exact exchange-correlation potential of a ionic Hubbard model with a free surface

We use Lanczos exact diagonalization to compute the exact exchange-correlation (xc) potential of a Hubbard chain with large binding energy ("the bulk") followed by a chain with zero binding energy ("the vacuum"). Several results of density functional theory in the continuum (sometimes controversial) are verified in the lattice. In particular we show explicitly that the fundamental gap is given by the gap in the Kohn-Sham spectrum plus a contribution due to the jump of the xc-potential when a particle is added. The presence of a staggered potential and a nearest-neighbor interaction V allows to simulate a ionic solid. We show that in the ionic regime in the small hopping amplitude limit the xc-contribution to the gap equals V, while in the Mott regime it is determined by the Hubbard U interaction. In addition we show that correlations generates a new potential barrier at the surface

Owning an overweight or underweight body: distinguishing the physical, experienced and virtual body

Our bodies are the most intimately familiar objects we encounter in our perceptual environment. Virtual reality provides a unique method to allow us to experience having a very different body from our own, thereby providing a valuable method to explore the plasticity of body representation. In this paper, we show that women can experience ownership over a whole virtual body that is considerably smaller or larger than their physical body. In order to gain a better understanding of the mechanisms underlying body ownership, we use an embodiment questionnaire, and introduce two new behavioral response measures: an affordance estimation task (indirect measure of body size) and a body size estimation task (direct measure of body size). Interestingly, after viewing the virtual body from first person perspective, both the affordance and the body size estimation tasks indicate a change in the perception of the size of the participant’s experienced body. The change is biased by the size of the virtual body (overweight or underweight). Another novel aspect of our study is that we distinguish between the physical, experienced and virtual bodies, by asking participants to provide affordance and body size estimations for each of the three bodies separately. This methodological point is important for virtual reality experiments investigating body ownership of a virtual body, because it offers a better understanding of which cues (e.g. visual, proprioceptive, memory, or a combination thereof) influence body perception, and whether the impact of these cues can vary between different setups

SARS-CoV-2 spike N-terminal domain modulates TMPRSS2-dependent viral entry and fusogenicity

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike N-terminal domain (NTD) remains poorly characterized despite enrichment of mutations in this region across variants of concern (VOCs). Here, we examine the contribution of the NTD to infection and cell-cell fusion by constructing chimeric spikes bearing B.1.617 lineage (Delta and Kappa variants) NTDs and generating spike pseudotyped lentivirus. We find that the Delta NTD on a Kappa or wild-type (WT) background increases S1/S2 cleavage efficiency and virus entry, specifically in lung cells and airway organoids, through use of TMPRSS2. Delta exhibits increased cell-cell fusogenicity that could be conferred to WT and Kappa spikes by Delta NTD transfer. However, chimeras of Omicron BA.1 and BA.2 spikes with a Delta NTD do not show more efficient TMPRSS2 use or fusogenicity. We conclude that the NTD allosterically modulates S1/S2 cleavage and spike-mediated functions in a spike context-dependent manner, and allosteric interactions may be lost when combining regions from more distantly related VOCs

Altered TMPRSS2 usage by SARS-CoV-2 Omicron impacts infectivity and fusogenicity

The SARS-CoV-2 Omicron BA.1 variant emerged in 20211 and has multiple mutations in its spike protein2. Here we show that the spike protein of Omicron has a higher affinity for ACE2 compared with Delta, and a marked change in its antigenicity increases Omicron’s evasion of therapeutic monoclonal and vaccine-elicited polyclonal neutralizing antibodies after two doses. mRNA vaccination as a third vaccine dose rescues and broadens neutralization. Importantly, the antiviral drugs remdesivir and molnupiravir retain efficacy against Omicron BA.1. Replication was similar for Omicron and Delta virus isolates in human nasal epithelial cultures. However, in lung cells and gut cells, Omicron demonstrated lower replication. Omicron spike protein was less efficiently cleaved compared with Delta. The differences in replication were mapped to the entry efficiency of the virus on the basis of spike-pseudotyped virus assays. The defect in entry of Omicron pseudotyped virus to specific cell types effectively correlated with higher cellular RNA expression of TMPRSS2, and deletion of TMPRSS2 affected Delta entry to a greater extent than Omicron. Furthermore, drug inhibitors targeting specific entry pathways3 demonstrated that the Omicron spike inefficiently uses the cellular protease TMPRSS2, which promotes cell entry through plasma membrane fusion, with greater dependency on cell entry through the endocytic pathway. Consistent with suboptimal S1/S2 cleavage and inability to use TMPRSS2, syncytium formation by the Omicron spike was substantially impaired compared with the Delta spike. The less efficient spike cleavage of Omicron at S1/S2 is associated with a shift in cellular tropism away from TMPRSS2-expressing cells, with implications for altered pathogenesis