Alex Levchenko

Keldysh technique and non-linear σ-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.

Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films

We study light diffraction in the periodically modulated ultrathin metal films both analytically and numerically. Without modulation these films are almost transparent. The periodicity results in the anomalous effects, such as suppression of the transmittance accompanied by a strong enhancement of the absorptivity and specular reflectivity, due to excitation of the surface plasmon polaritons. These phenomena are opposite to the widely known enhanced transparency of periodically modulated optically thick metal films. Our theoretical analysis can be a starting point for the experimental investigation of these intriguing phenomena.

Coulomb drag in quantum circuits

We study the drag effect in a system of two electrically isolated quantum point contacts, coupled by Coulomb interactions. Drag current exhibits maxima as a function of quantum point contacts gate voltages when the latter are tuned to the transitions between quantized conductance plateaus. In the linear regime this behavior is due to enhanced electron-hole asymmetry near an opening of a new conductance channel. In the nonlinear regime the drag current is proportional to the shot noise of the driving circuit, suggesting that the Coulomb drag experiments may be a convenient way to measure the quantum shot noise. Remarkably, the transition to the nonlinear regime may occur at driving voltages substantially smaller than the temperature.

Topological Defect-Phase Soliton and the Pairing Symmetry of a Two-Band Superconductor: Role of the Proximity Effect

We suggest a mechanism which promotes the existence of a phase soliton--a topological defect formed in the relative phase of superconducting gaps of a two-band superconductor with s(+-) type of pairing. This mechanism exploits the proximity effect with a conventional s-wave superconductor which favors the alignment of the phases of the two-band superconductor which, in the case of s(+-) pairing, are π shifted in the absence of proximity. In the case of a strong proximity such an effect can be used to reduce the solitons energy below the energy of a soliton-free state, thus making the soliton thermodynamically stable. Based on this observation we consider an experimental setup, applicable for both stable and metastable solitons, which can be used to distinguish between ss(+-) and s(++) types of pairing in the iron-based multiband superconductors.

Nernst effect from fluctuating pairs in the pseudogap phase of the cuprates.

The observation of a large Nernst signal in cuprates above the superconducting transition temperature has attracted much attention. A potential explanation is that it originates from superconducting fluctuations. Although the Nernst signal is indeed consistent with Gaussian fluctuations for overdoped cuprates, Gaussian theory fails to describe the temperature dependence seen for underdoped cuprates. Here, we consider the vertex correction to Gaussian theory resulting from the pseudogap. This yields a Nernst signal in good agreement with the data.

Raman scattering as a probe of nematic correlations

We use the symmetry constrained low energy effective Hamiltonian of iron based superconductors to study the Raman scattering in the normal state of underdoped iron-based superconductors. The incoming and scattered Raman photons couple directly to orbital fluctuations and indirectly to the spin fluctuations. We computed both couplings within the same low energy model. The symmetry constrained Hamiltonian yields the coupling between the orbital and spin fluctuations of only the same symmetry type. Attraction in B2g symmetry channel was assumed for the system to develop the subleading instability towards the discrete in-plane rotational symmetry breaking, referred to as Ising nematic transition. We find that upon approaching this instability, the Raman spectral function develops a quasi-elastic peak as a function of energy transferred by photons to the crystal. We attribute this low-energy B2g scattering to the critical slow-down associated with the build up of nematic correlations.

Josephson current and density of states in proximity circuits with s+- superconductors

We study the emergent proximity effect in mesoscopic circuits that involve a conventional superconductor and an unconventional pnictide superconductor separated by a diffusive normal or ferromagnetic wire. The focus is placed on revealing signatures of the proposed s+- state of pnictides from the proximity-induced density of states and Josephson current. We find analytically a universal result for the density of states that exhibits both the Thouless gap at low energies, and peculiar features near the superconducting gap edges at higher energies. The latter may be used to discriminate between s+- and s++ symmetry scenarios in scanning tunneling spectroscopy experiments. We also calculate Josephson current-phase relationships for different junction configurations, which are found to display robust 0-\pi transitions for a wide range of parameters.

Transport implications of Fermi arcs in the pseudogap phase of the cuprates

We derive the fermionic contribution to the longitudinal and Hall conductivities within a Kubo formalism, using a phenomenological Greens function which has been previously developed to describe photoemission data in the pseudogap phase of the cuprates. We find that the in-plane electrical and thermal conductivities are metalliclike, showing a universal limit behavior characteristic of a

Topological Andreev bands in three-terminal Josephson junctions

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Keldysh approach to periodically driven systems with a fermionic bath: Nonequilibrium steady state, proximity effect, and dissipation

-wave spectrum as the scattering rate goes to zero. In contrast, the