# Publications

We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties: ferromagnetic, half-metallic, or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realizes a φ0 junction with sample-specific φ0 and critical current. Cooper pair splitting between the two arms plays a major role and leads to 2Φ0 periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

The two-point correlation tensor of small-scale fluctuations of magnetic field B in a two-dimensional chaotic flow is studied. The analytic approach is developed in the framework of the Kraichnan–Kazantsev model. It is shown that the growth of the field fluctuations takes place in an essentially resistive regime and stops at large times in accordance with the so-called anti-dynamo theorems. The value of B2 is enhanced in the course of the evolution by the magnetic Prandtl number.

The low-frequency dynamical response of an Anderson insulator is dominated by so-called Mott resonances: hybridization of pairs of states close in energy but separated spatially. We study the effect of interaction on Mott resonances in the model of spinful fermions (electrons) with local attraction. This model is known to exhibit a so-called pseudogap: a suppression of the low-energy, single-particle excitations. Correspondingly, the low-energy dynamical response is also reduced. However, this reduction has mostly quantitative character. In particular, the Mott formula for frequency-dependent conductivity preserves its functional asymptotic behavior at low frequencies, but with a small numerical prefactor. This result can be explained in terms of Mott resonances for electron pairs instead of single electrons.

A method is proposed for the creation of an entangled metastable (subradiance) excited state in a system of two closely spaced identical atoms. The system of unexcited atoms is first placed in a magnetic field that is directed at a magic angle of α0=arccos(1/3–√)≈54.7∘α0=arccos(1/3)≈54.7∘ to the line connecting the atoms and has a transverse gradient. The gradient of the field results in the detuning of frequencies of an optical transition of the atoms. Then, the resonant laser excitation of an atom with a higher transition frequency is performed with the subsequent adiabatic switching-off of the gradient of the magnetic field. It is shown that the excited atomic system in this case transits with overwhelming probability to an entangled subradiance state. Requirements on the spectroscopic parameters of the transitions and on the rate of varying the gradient of the magnetic field necessary for the implementation of this effect are analyzed.

Original Russian Text © A.A. Makarov, V.I. Yudson, 2017, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 105, No. 3, pp. 193–197.

We discuss the emergence of p-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wave functions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a p-wave Feshbach resonance. This opens possibilities to obtain the topological px+ipy superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.

The correlation tensors of magnetic field in a two-dimensional chaotic flow of conducting fluid are studied. It is shown that there is a stage of resistive evolution where the field correlators grow exponentially with time. The two-and four-point field correlation tensors are computed explicitly in this stage in the framework of Batchelor–Kraichnan–Kazantsev model. They demonstrate strong temporal intermittency of the field fluctuations and high level of non-Gaussianity in spatial field distribution

We consider a problem of persistent magnetization precession in a single-domain ferromagnetic nanoparticle under the driving by the spin-transfer torque. We find that the adjustment of the electronic distribution function in the particle renders this state unstable. Instead, abrupt switching of the spin orientation is predicted upon increase of the spin-transfer torque current. On the technical level, we derive an effective action of the type of Ambegaokar-Eckern-Schön action for the coupled dynamics of magnetization [gauge group SU(2)] and voltage [gauge group U(1)].

We develop the two-instanton approximation to the current-voltage characteristic of a single electron transistor within the Ambegaokar-Eckern-Schön model. We determine the temperature and gate voltage dependence of the Coulomb blockade oscillations of the conductance and the effective charge. We find that a small (in comparison with the charging energy) bias voltage leads to significant suppression of the Coulomb blockade oscillations and to appearance of the bias-dependent phase shift.

We report on an electron spin resonance (ESR) study of a nearly one-dimensional (1D) spin-12 chain antiferromagnet, Sr2CuO3, with extremely weak magnetic ordering. The ESR spectra at T>TN, in the disordered Luttinger-spin-liquid phase, reveal nearly ideal Heisenberg-chain behavior with only a very small, field-independent linewidth, ∼1/T. In the ordered state, below TN, we identify field-dependent antiferromagnetic resonance modes, which are well described by pseudo-Goldstone magnons in the model of a collinear biaxial antiferromagnet. Additionally, we observe a major resonant mode with unusual and strongly anisotropic properties, which is not anticipated by the conventional theory of Goldstone spin waves. We propose that this unexpected magnetic excitation can be attributed to a field-independent magnon mode renormalized due to its interaction with the high-energy amplitude (Higgs) mode in the regime of weak spontaneous symmetry breaking.

Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [Phys. Rev. Lett.116,054501(2016)]. Here we study how a thin (monomolecular) film presented on the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case of liquid with a free surface, and the parameter is the quality factor of surface waves up to numerical factor. We also discuss the PIV experimental scheme intended to observe the generated vorticity and find that Stokes drift influences the measured velocity field. Explicit expression for the vertical vorticity was obtained.

An important role of the morphology of a superconducting layer in the superconducting spin-valve effect has been established. The triplet pairing induced by the superconductor/ferromagnet proximity effect has been experimentally investigated for samples CoO x /Py1/Cu/Py2/Cu/Pb (where Py = Ni 0.81 Fe 0.19 ) with a smooth superconducting layer. The optimization of the parameters of this structure has demonstrated a complete switching between the normal and superconducting states with a change in the relative orientation of magnetizations of the ferromagnetic layers from the antiparallel to orthogonal orientation. A pure triplet contribution has been observed for the sample with a permalloy layer thickness at which the superconducting spin-valve effect vanishes. A direct comparison of the experimental data with the theoretical calculation of the temperature of the transition to the superconducting state has been performed for the first time.

It is established that cyclotron resonance (CR) in a high-quality GaAs/AlGaAs two-dimensional electron system (2DES) originates as a *pure* resonance that does not hybridize with dimensional magnetoplasma excitations. The magnetoplasma resonances form a fine structure of the CR. The observed fine structure of the CR results from the interplay between coherent radiative and incoherent collisional mechanisms of two-dimensional plasma relaxation. We show that the range of 2DES filling factors from which the phenomenon arises is intimately connected to the fundamental fine-structure constant.

Electron spin resonance experiment reveals that non-magnetic bond doping of the spin-gap magnet (C4H12N2)Cu2Cl6 (abbreviated PHCC) results in the formation of S = 1 paramagnetic centers that dominate low-temperature ESR response. We have followed evolution of this signal with doping impurity content and have found that the concentraion of these centers is quadratic over the impurity content. We also observe coexistence of the ESR responses from these local centers and from delocalized triplet excitations over a certain temperature range.

We study indirect exchange interaction between magnetic impurities in the (001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and the case of the chemical potential placed in the energy gap of the two-dimensional quasiparticle spectrum. We find that the indirect exchange interaction is suppressed exponentially with the distance between magnetic impurities. The presence of inversion asymmetry results in oscillations of the indirect exchange interaction with the distance and generates additional terms which are noninvariant under rotations in the (001) plane. The indirect exchange interaction matrix has complicated structure with some terms proportional to the sign of the energy gap.

We explore the inelastic electron-scattering cross section off a metallic quantum dot close to the Stoner instability. We focus on the regime of strong Coulomb blockade in which the scattering cross section is dominated by the cotunneling processes. For large enough exchange interaction, the quantum dot acquires a finite total spin in the ground state. In this so-called mesoscopic Stoner instability regime, we find that at low enough temperatures, the inelastic scattering cross section (including the contribution due to an elastic electron spin flip) for an electron with an energy close to the chemical potential is different from the case of a magnetic impurity with the same spin. This difference stems from (i) the presence of low-lying many-body states of a quantum dot and (ii) the correlations of the tunneling amplitudes. Our results provide a possible explanation for the absence of the dephasing rate saturation at low temperatures in a recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012)] in which the existence of local spin droplets in disordered electron liquid has been unraveled.

We explore the inelastic electron-scattering cross section off a metallic quantum dot close to the Stoner instability. We focus on the regime of strong Coulomb blockade in which the scattering cross section is dominated by the cotunneling processes. For large enough exchange interaction, the quantum dot acquires a finite total spin in the ground state. In this so-called mesoscopic Stoner instability regime, we find that at low enough temperatures, the inelastic scattering cross section (including the contribution due to an elastic electron spin flip) for an electron with an energy close to the chemical potential is different from the case of a magnetic impurity with the same spin. This difference stems from (i) the presence of low-lying many-body states of a quantum dot and (ii) the correlations of the tunneling amplitudes. Our results provide a possible explanation for the absence of the dephasing rate saturation at low temperatures in a recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012)] in which the existence of local spin droplets in disordered electron liquid has been unraveled.

We have studied the proximity-induced superconducting triplet pairing in CoO_x/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni_{0.81}Fe_{0.19}). By optimizing the parameters of this structure we found a triplet channel assisted full switching between the normal and superconducting states. To observe an "isolated" triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect ΔTc in the dependence of the Py2-layer thickness dPy2. We determined the value of dPy2 at which ΔTc caused by the ordinary spin-valve effect (the difference in the superconducting transition temperature Tc between the antiparallel and parallel mutual orientation of magnetizations of the Py1 and Py2 layers) is suppressed. For such a sample a "pure" triplet spin-valve effect which causes the minimum in Tc at the orthogonal configuration of magnetizations has been observed.

We study the stationary Josephson current in a junction between a topological and an ordinary (topologically trivial) superconductor. Such an S-TS junction hosts a Majorana zero mode that significantly influences the current-phase relation. The presence of the Majorana state is intimately related with the breaking of the time-reversal symmetry in the system. We derive a general expression for the supercurrent for a class of short topological junctions in terms of the normal-state scattering matrix. The result is strongly asymmetric with respect to the superconducting gaps in the ordinary (Δ0) and topological (Δtop) leads. We apply the general result to a simple model of a nanowire setup with strong spin-orbit coupling in an external magnetic field and proximity-induced superconductivity. The system shows parametrically strong suppression of the critical current Ic∝Δtop/RN2 in the tunneling limit (RN is the normal-state resistance). This is in strong contrast with the Ambegaokar-Baratoff relation applicable to junctions with preserved time-reversal symmetry. We also consider the case of a generic junction with a random scattering matrix and obtain a more conventional scaling law Ic∝Δtop/RN.

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the nonlinear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore two-dimensional systems that would be Anderson insulators in the absence of interaction and two- or three-dimensional systems that undergo an Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions, especially, in the regime when transition temperature is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approach the SIT.

T

) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions, especially, in the regime when

T

c is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approach the SIT.