Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fermions at a half-quantum vortex

The spectrum of the fermion zero modes in the vicinity of a vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2-vortex in high-temperature superconductors made by [J.R. Kirtley, C.C. Tsuei, M. Rupp et al., Phys. Rev. Lett. 76, 1336 (1996)]. The fractional value of the winding number leads to a frac-tional value of the invariant which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the “half-crossing:” the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of fermion condensation is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 729–734 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Defects in a TGBA phase: A theoretical approach

Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the χ-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of λ-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the leastcurvaturemodel, that requires the introduction of a third type of defects: the densitiesofedgedislocations of the smectic layers. Received 20 February 2002     

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the experimental verification of the Landau-Pomeranchuk-Migdal effect

A theoretical explanation is given for the “unexpected” behavior recently observed in the radiation spectrum of ultrarelativistic electrons in a thin layer of matter in an experimental investigation of the Landau-Pomeranchuk-Migdal effect at SLAC [S. R. Klein et al., Preprint SLAC-6378, Stanford (1993); P. L. Anthony et al., Phys. Rev. Lett. 75, 1949 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 837–840 (10 June 1996)     

Influence of heterogeneous chemical reactions on the slip velocity of an inhomogeneous multicomponent gaseous mixture

In constructing a theory of thermal diffusiophoresis of volatile aerosol particles it is necessary to have boundary conditions for the tangential velocity component which allow for the presence of heterogeneous chemical reactions. Conditions of this sort have been obtained by a number of authors [R. N. Gupta et al., Technical Papers, AIAA 22nd Aerospace Science Meeting, AIAA 19th Thermophysics Conference, New York (1985), pp. 465–490; D. V. Kul’ginov, Tech. Phys. 63, 940 (1993); A. V. Bogdanov et al., Preprint No. 1051, Fiz-Tekh. Inst. Akad. Nauk. SSSR, Leningrad (1986)]. The results of Gupta et al. are in the form of analytical expressions, but their computations actually used Maxwell’s method, which is of low accuracy. Kul’ginov et al. and Bogdanov et al. used the method of matched asymptotic expansions, which did not permit them to get simple analytical expressions. In the present paper the slip velocity is calculated by the Loyalka method. Analytical expressions are obtained for the slip coefficients, and the results of numerical calculations are presented. It is shown that in the presence of concentration gradients of the components of the gaseous mixture along the surface of an aerosol particle, the slip velocity can acquire new terms due to the change in the sticking coefficient along the catalytic surface. Expressions in final form are given for these terms. Zh. Tekh. Fiz. 67, 29–33 (May 1997)     

Flat bands in topological media

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion—the fiat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines [A. P. Schnyder and S. Ryu, Phys. Rev. B 84, 060504(R) (2011); T. T. Heikkil G. E. Volovik, JETP Lett. 93, 59 (2011)] and in the vortex core in systems with topologically protected Fermi points (Weyl points) [G. E. Volovik, JETP Lett. 93, 66 (2011)]. Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.     

A correction to the Hamiltonian of the QCD string with quarks due to the rigidity term

The correction to the Hamiltonian of a quark-antiquark system due to the rigidity term in the action of the gluodynamics string is found using the action obtained by D. V. Antonov et al., Mod. Phys. Lett. A 11, 1905 (1996) with the Hamiltonian obtained by A. Yu. Dubin et al., Phys. At. Nucl. 56, 1745 (1993); Phys. Lett. B 323, 41 (1994) and E. L. Gubankova and A. Yu. Dubin, Phys. Lett. B 334, 180 (1994); preprint ITEP 62-94. This correction contains additional contributions to the orbital momentum of the system and several higher derivative operators. The resulting Hamiltonian is used to evaluate the rigid-string-induced term in the Hamiltonian of the relativistic quark model for the case of large masses of the quark and antiquark. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 673–678 (10 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quantum dot version of topological phase: Half-integer orbital angular momenta

We show that there exists a topological phase equal to π for circular quantum dots with an odd number of electrons. The non-zero value of the topological phase is explained by axial symmetry and two-dimensionality of the system. Its particular value (π) is fixed by the Pauli exclusion principle and leads to half-integer values for the eigenvalues of the orbital angular momentum. Our conclusions agree with the experimental results of T. Schmidt et al., Phys. Rev. B 51, 5570 (1995), which can be considered as the first experimental evidence for the existence of the new topological phase and half-integer quantization of the orbital angular momentum in a system of an odd number of electrons in circular quantum dots. The article is published in the original.     

Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s-wave superconductor: E=(n+1/2)ω₀, with integral n. In class II the corresponding spectrum is E=nω₀ and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period ΔE=2ω₀ and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 9, 601–606 (10 November 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform, and a second-order phase transition to a broken-symmetry phase occurs by propagation of a temperature front. Two parameters, the cooling rate τ _Q and the transition front velocity ν _T determine the nucleation of topological defects. Depending on the relation of these parameters, two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow-propagation regime vortex formation is suppressed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 96–101 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Poisson bracket scheme for vortex dynamics in superfluids and superconductors and the effect of the band structure of the crystal

Poisson brackets for the Hamiltonian dynamics of vortices are discussed for 3 regimes, in which the dissipation can be neglected and the vortex dynamics is reversible: (i) The superclean regime, in which the spectral flow is suppressed. (ii) The regime in which the fermions are pinned by the crystal lattice. This includes the regime of extreme spectral flow of fermions in the vortex core: these fermions are effectively pinned by the normal component. (iii) The case when the vortices are strongly pinned by the normal component. All these limits are described by the single parameter C ₀, the physical meaning of which is discussed for superconductors containing several bands of electrons and holes. The effect of the topology of the Fermi surface on the vortex dynamics is also discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 794–800 (10 December 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Efficient nonlinear-optical frequency conversion in periodic media in the presence of diffraction of the pump and harmonic fields

It has been predicted by Shelton and Shen [Phys. Rev. A 5, 1867 (1972)] and observed by Kajikawa et al. [Jpn. J. Appl. Phys. Lett. 31, L679 (1992)] and Yamada et al. [Appl. Phys. B 60, 485 (1995)] that the efficiency of nonlinear-optical frequency conversion increases significantly in a nonlinear periodic medium and, accordingly, the intensity of the generated harmonic increases as the fourth power of the sample thickness, as opposed to the square law observed in homogeneous media. In this paper it is shown that the same enhancement of the efficiency of nonlinear-optical frequency conversion in a nonlinear periodic medium can be achieved using an ordinary pump wave in the form of a plane wave when both the pump wave and the harmonics are diffracted by the periodic structure of the nonlinear medium. The phenomenon is analyzed quantitatively in the example of second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 793–799 (25 December 1999)     

Expansion of matter heated by an ultrashort laser pulse

Recent experiments have utilizied high-power subpicosecond laser pulses to effect the ultrafast heating of a condensed material to temperatures far above the critical temperature. Using optical diagnostics it was established that a complicated density profile with sharp gradients, differing substantially from an ordinary rarefaction wave, forms in the expanding heated matter. The present letter is devoted to the analysis of the expansion of matter under the conditions of the experiments reported by D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Science 109/110, 1 (1996); K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri et al., Proc. Soc. Photo-Opt. Instum. Eng. 3343, 46 (1998); and, K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri et al., Phys. Rev. Lett. 81, 224 (1998). It is shown that if the unloading adiabat passes through the two-phase region, a thin liquid shell filled with low-density two-phase matter forms in the expanding material. The shell moves with a constant velocity. The velocity in the two-phase material is a linear function of the coordinate (flow with uniform deformation), and the density is independent of the coordinate and decreases with time as t ⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 4, 284–289 (25 February 1999)     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Anomalous burn-through of thin foils by high-intensity laser radiation

The paper presents results of experiments performed on the Pico facility in which foils were heated by laser radiation, and anomalously fast burn-through of foils by a structured laser beam was detected. Comparison with two-dimensional calculations has allowed us to suggest a tentative mechanism for the effect under investigation. The targets in the experiments were thin aluminum foils of thickness 3 to 40 μm. The flux density of laser radiation on the target surface varied between 10¹³ and 10¹⁴ W/cm². We detected a strong dependence of the transmitted energy on the foil thickness and the shortening of the transmitted laser pulse. Penetration of laser radiation through foils with thicknesses considerably larger than 3 μm has been observed, although it was stated in earlier publications [V. V. Ivanov, A. K. Knyazev, A. V. Kutsenko, et al., Kratk. Soobshch. Fiz. FIAN No. 7–8, 37 (1997)]; A. é. Bugrov, I. N. Burdonskii, V. V. Gol’tsov et al., Zh. éksp. Teor. Fiz. 111, 903 (1997) [JETP 84, 903 (1997)] that, at the laser radiation parameters used in our experiment, the evaporated layer of the foil could not be thicker than 2 μm. Two-dimensional calculations have allowed us to interpret this effect in terms of local “piercing” of the target at spots on the target surface where the radiation intensity has its peaks. The possibility of reducing these peaks by using a symmetrizing prepulse is discussed in the paper. Zh. éksp. Teor. Fiz. 116, 1287–1299 (October 1999)     

The magnetic field and energy of an Abrikosov vortex in an anisotropic London superconductor

The behavior of a straight Abrikosov vortex in an anisotropic uniaxial London superconductor is studied. Analytical expressions are derived that approximately describe the magnetic field in three regions: the asymptotic region, where the distance r from the vortex line is greater than λΓ (λ is the London length and Γ is the anisotropy constant), the intermediate region λ<r<λΓ, and the region r<λ. It is found that in the intermediate region with high anisotropy the component of the magnetic field along the vortex line changes sign for a certain interval of angles between the vortex line and the anisotropy axis. Because of this the interaction of parallel vortices whose plane is parallel to the anisotropy axis has a minimum and a maximum. This means that numerous metastable vortex lattices can exist. Additional terms in the vortex self-energy are obtained, and although they are smaller than the leading logarithmic term, they display a different dependence on the angle between the vortex line and the anisotropy axis. Zh. éksp. Teor. Fiz. 111, 954–963 (March 1997)     

Cherenkov radiation from an Abrikosov-Josephson vortex

The Cherenkov radiation of generalized Swihart waves is investigated in connection with the slow motion of an Abrikosov-Josephson vortex, which corresponds to a 2 π kink in the phase difference of Cooper pairs on opposite sides of a tunnel junction. The radiative friction force acting on such a vortex is determined. An evaluation is made of the steady-state vortex velocity when the accelerating influence of an electric current through the Josephson junction is compensated by radiative slowing of the vortex due to Cherenkov radiation from the Abrikosov-Josephson vortex. Fiz. Tverd. Tela (St. Petersburg) 39, 444–448 (March 1997)     

Nonradiative decay of the low-lying nuclear isomer 229m Th(3.5 eV) in a metal

A new nonradiative decay channel for the anomalously low-lying isomeric level 3/2⁺ (3.5±1.0 eV) of the ²²⁹Th nucleus in a metal via the conduction electrons is examined. The lifetime of the isomer in a metal is calculated. An explanation is given for the experimental results of S. B. Utter et al., Phys. Rev. Lett. 82, 505 (1999), where the optical radiation spectrum of the indicated isomer was investigated. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 367–370 (25 September 1999)