Browsing by Author "Shapiro, I."

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3D DIRAC SEMI-METAL IN THE TRIPLET SUPERCONDUCTING STATE
(2015-01-01)
Rosenstein, B.
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Shapiro, B. Ya.
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Shapiro, I.
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交大名義發表
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National Chiao Tung University
It was recently shown that conventional phonon-electron interactions may induce a triplet pairing state in time-reversal invariant 3D Dirac semi - metals. Starting from the microscopic model of the isotropic Dirac semi-metal, the Ginzburg-Landau equations for the vector order parameter is derived using the Gorkov technique. The time dependent Ginzburg - Landau model in the presence of external fields is used to investigate some optical and magnetic properties of such superconductors. The AC conductivity of a clean sample depends on the orientation of the order parameter. It is demonstrated that the difference between the penetration depths results in rotation of the polarization vector of microwave passing a slab made of this material. The upper critical magnetic field H-c2 was found. It turns out that at fields close to H-c2 the order parameter orients itself perpendicular to the field direction. In certain range of parameters the triplet superconducting phase persists at arbitrarily high magnetic field like in some p wave superconductors.
Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator
(2015-06-01)
Li, Dingping
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Rosenstein, Baruch
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Shapiro, B. Ya.
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Shapiro, I.
;
電子物理學系
New two-dimensional systems such as the surfaces of topological insulators (TIs) and graphene offer the possibility of experimentally investigating situations considered exotic just a decade ago. These situations include the quantum phase transition of the chiral type in electronic systems with a relativistic spectrum. Phonon-mediated (conventional) pairing in the Dirac semimetal appearing on the surface of a TI causes a transition into a chiral superconducting state, and exciton condensation in these gapless systems has long been envisioned in the physics of narrow-band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the Bardeen-Cooper-Schrieffer type of Gaussian approximation is developed in the framework of functional integrals. It is shown that owing to an ultrarelativistic dispersion relation, there is a quantum critical point governing the zero-temperature transition to a superconducting state or the exciton condensed state. Quantum transitions having critical exponents differ greatly from conventional ones and belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in TIs and estimate the feasibility of phonon pairing.
Collective modes, ac response, and magnetic properties of the three-dimensional Dirac semimetal in the triplet superconducting state
(2015-08-03)
Rosenstein, B.
;
Shapiro, B. Ya.
;
Shapiro, I.
;
電子物理學系
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Department of Electrophysics
It was recently shown that conventional phonon-electron interactions may induce a triplet pairing state in time-reversal invariant three-dimensional Dirac semimetals. Starting from the microscopic model of the isotropic Dirac semimetal, the Ginzburg-Landau equations for the vector order parameter is derived using the Gor'kov technique. The collective modes including gapless Goldstone modes and gapped Higgs modes of various polarizations are identified. They are somewhat analogous to the modes in the B phase of He-3, although in the present case quantitatively there is a pronounced difference between longitudinal and transverse components. The difference is caused by the vector nature of the order parameter leading to two different coherence lengths or penetration depths. The system is predicted to be highly dissipative due to the Goldstone modes. The time-dependent Ginzburg-Landau model in the presence of external fields is used to investigate some optical and magnetic properties of such superconductors. The ac conductivity of a clean sample depends on the orientation of the order parameter. It is demonstrated that the difference between the penetration depths results in rotation of the polarization vector of microwave passing a slab made of this material. The upper critical magnetic field H-c2 was found. It turns out that at fields close to H-c2 the order parameter orients itself perpendicular to the field direction. In certain range of parameters the triplet superconducting phase persists at arbitrarily high magnetic field like in some p-wave superconductors.
Current carrying vortex crystals
(2012)
Rosenstein, B.
;
Shapiro, I.
;
Berco, D.
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Shapiro, B. Ya
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電子物理學系
Abrikosov vortices in a type-II superconducting film subjected to strong magnetic field B with periodic array of nanoholes of the density n(pin) form sometimes a vortex crystal, even when they are driven by a transport current. It is shown numerically that the crystal melting and transition to the resistive state occurs as a coherent depinning of the single vortex dislocations. For a system with interstitial vortices, f = B/Phi(0)n(pin) > 1, the mechanism of depinning depends on the current direction with respect to the pinning array. It was found that slightly above the critical current trajectories of moving vortices are not straight, but rather acquire a snake - like shape enveloping the system of pins. In contrast to the matching field case, f = 1, the transition to a resistive state is not coherent and is developing through formation of the "snake - like" vortex trajectories. It is pointed out that the depinning is closely associated with the appearance of a strongly varying electric field. We calculated the electric fields accompanying vortex crystal melting and found the voltage-current characteristics. When the pinning array is made random, the critical current is reduced.
Effect of nanoholes on the vortex core fermion spectrum and heat transport in p-wave superconductors
(2013-02-20)
Rosenstein, B.
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Shapiro, I.
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Shapiro, B. Ya
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電子物理學系
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Department of Electrophysics
The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole of the size of the coherence length is considered. While the neutral zero energy Majorana core state remains intact due to its topological origin, the energy of charged excitations is significantly enhanced compared to that in the unpinned vortex. As a consequence of the pinning the minigap separating the Majorana state from the charged levels increases from Delta(2)/E-F (E-F is the Fermi energy and Delta is the bulk p-wave superconducting gap) to a significant fraction of Delta. Suppression of the thermodynamic and kinetic effects of the charged excitations allows us to isolate the Majorana state so it can be used for quantum computation. It is proposed that thermal conductivity along the vortex cores is a sensitive method to demonstrate the minigap. Using the Butticker-Landauer-Kopnin formula, we calculate the thermal conductance beyond the linear response as a function of the hole radius.
Effect of the type-I to type-II Weyl semimetal topological transition on superconductivity
(2017-03-21)
Li, Dingping
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Rosenstein, Baruch
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Shapiro, B. Ya.
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Shapiro, I.
;
電子物理學系
The influence of recently discovered topological transition between type-I and type-II Weyl semimetals on superconductivity is considered. A set of Gorkov equations for weak superconductivity inWeyl semimetal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spikes in the transition point as functions of the tilt parameter of the Dirac cone determined, in turn, by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: The sharp cone pinnacle is characteristic for type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition to demonstrate the different weights of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.
Exchange Interaction Makes Superconductivity in 3D Dirac Semi-metal Triplet
(2015-04-01)
Rosenstein, B.
;
Shapiro, B. Ya
;
Li, Dingping
;
Shapiro, I.
;
電子物理學系
Conventional electron-phonon coupling induces either odd (triplet) or even (singlet) pairing states in a time reversal and inversion invariant Dirac semi-metal. In a certain range of the chemical potential and parameters characterizing the pairing attraction (effective electron-electron coupling constant and the Debye energy ) the energy of the singlet although always lower, prevails by a very slim margin over the triplet. This means that interactions that are small but discriminate between the spin singlet and the spin triplet determine the nature of the superconducting order there. It is shown that in materials close enough to the Dirac point ( ) a moderate exchange constant (below Stoner instability to ferromagnetism) stabilizes the odd pairing superconducting state. The 3D quantum critical point at of transition to the triplet superconductivity governs the physics of the superconductor.
Experimental Presentation of Microwave Absorption due to Shaking of JV by AC Magnetic Field in Bi2212 and Bi2223
(2009-05-01)
Shaltiel, D.
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von Nidda, H. -A. Krug
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Shapiro, B. Y.
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Rosenstein, B.
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Loidl, A.
The Josephson Vortex dynamics in high anisotropy superconductors Bi2212 and Bi2223 induced by AC magnetic field collinear to DC magnetic field and parallel to the layers is studied via their interaction with microwave field. Experimental results as function of DC magnetic field, AC magnetic field and temperature are presented. The AC induced microwave dissipation is larger than dissipation without AC field. The results are explained by the theoretical interpretation reported recently due to shaking by the AC field that depins the JV (Shaltiel et al., Phys. Rev. B 77, 014508, 2008). Similar behavior in these two compounds as a function of the variables involved discloses that the shaking effect should be observed in any high anisotropy superconductors. It shows that the AC field interacting with JV has an active and not the usual passive modulating role of the DC field in EPR dissipation experiments. The technique can be used to investigate JV dynamics and JV phase diagram.
Extended object tunneling: Current-carrying states of Abrikosov vortices in a superconductor with artificial nanobarriers
(2012-02-24)
Rosenstein, B.
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Shapiro, I.
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Shapiro, B. Ya.
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Li, Dingping
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Frydman, A.
We consider the structure and dynamics of two-dimensional fluxons created by a magnetic field in a type-II superconductor film with critical temperature T-1 in the presence of nanostripes of material with a higher critical temperature T-2. The width of the stripes is of the order of the coherence length xi. Such a stripe plays the role of a potential barrier for vortices. When subjected to the current J parallel to the stripe, vortices move toward the barrier. Below the critical current J(c), the flux flow is effectively halted by the barrier, while above J(c), flux penetrates the stripe and passes the barrier. The mechanism of the barrier penetration ("soliton tunneling" occurs even at zero temperature) is rather unusual: the vortices adjust their shape, and upon passing the barrier, they shrink their cores. The critical current and the I-V curves are calculated numerically and analytically using variational approach.
Field cooling memory effect in Bi2212 and Bi2223 single crystals
(2010-07-01)
Shaltiel, D.
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von Nidda, H-A Krug
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Rosenstein, B.
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Shapiro, B. Ya
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Golosovsky, M.
A memory effect in the Josephson vortex system created by a magnetic field in the highly anisotropic superconductors Bi2212 and Bi2223 is demonstrated using microwave power absorption. This surprising effect appears despite a very low viscosity of Josephson vortices compared to Abrikosov vortices. The superconductor is field-cooled in a DC magnetic field H(m) oriented parallel to the CuO planes through the critical temperature T(c) down to 4 K, with subsequent reduction of the field to zero and again above H(m). A large microwave power absorption signal is observed at a magnetic field just above the cooling field, clearly indicating a memory effect. The dependence of the signal on a deviation of the magnetic field from H(m) is the same for a wide range of H(m) from 1500 to 17 000 G.
Influence of quenched disorder on the square-to-rhombohedral structural transformation of the vortex lattice of type-II superconductors
(2006-11-01)
Li, D. P.
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Lin, P. -J.
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Rosenstein, B.
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Shapiro, B. Ya.
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Shapiro, I.
A theory of structural transformations of the vortex lattice in a disordered fourfold symmetric type-II superconductor is constructed using two complementary descriptions of the vortex matter. At low temperatures we use a nonlocal London approach, while near H-c2(T) the lowest Landau level Ginzburg-Landau model with an asymmetric high derivative term is utilized. The quenched disorder influences the location of the square-to-rhombohedral structural transition line, the simplest transformation of that kind. In the clean case the slope of the line in the T-B plane is generally negative, as thermal fluctuations favor a more symmetric square lattice. We calculated the transition line in the presence of pinning and find that the disorder, which plays an important role in low-T-c materials, makes the slope positive, as has been observed in recent experiments.
Interaction between Josephson and pancake vortices investigated by the induced microwave dissipation by ac magnetic field technique
(2008-06-01)
Shaltiel, D.
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von Nidda, H. -A. Krug
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Shapiro, B. Ya.
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Rosenstein, B.
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Loidl, A.
In the "induced microwave dissipation by ac magnetic field" (IMDACMF) technique, only the motion of Josephson vortices (JV) but not of pancake vortices (PV) induces microwave dissipation. This unique property is used to investigate the interaction between JV and PV in the high anisotropy superconductor Bi2212 as a function of magnetic field and tilting angle away from the a-b plane. In general, pinning of JV by PV inhibits the motion of the JV and, thus, reduces the microwave dissipation. Almost no pinning of JV is obtained at low dc magnetic fields even at high-tilting angles. Strong pinning of JV due to their interaction with PV is observed at higher magnetic fields and at tilting angles between 50 degrees and 90 degrees. The technique enables to observe transitions from the JV state to the crossing lattice state, without and with interaction between JV and PV, and to the one-dimensional vortex chains. The results obtained by the present technique are compared to results of surface imaging techniques, which investigate the interaction between PV and JV probing the PV.
Interaction of AC magnetic field with Josephson vortices in high anisotropy superconductors Bi2212 and Bi2223
(2007-09-01)
Shaltiel, D.
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von Nidda, H.-A. Krug
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Shapiro, B. Ya.
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Shapiro, I.
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Loidl, A.
We show that in both high anisotropy superconductors Bi2212 (T-c = 90 K), and Bi2223 (T-c = 110 K), an AC magnetic field applied collinear to the DC field and parallel to the Cu layers induces strong microwave dissipation. It is theoretically predicted that the Josephson solitons are responsible for this absorption. Good qualitative agreement of experimental data with theoretical predictions is found. Differences observed in the experimental results between these two compounds are discussed. (c) 2007 Elsevier B.V. All rights reserved.
Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet
(2015-03-01)
Rosenstein, Baruch
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Shapiro, B. Ya.
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Li, Dingping
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Shapiro, I.
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電子物理學系
Conventional electron-phonon coupling induces either odd (triplet) or even (singlet) pairing states in a time reversal and inversion invariant Dirac semi-metal. It was shown that the energy of the singlet channel, always lower, prevails over the triplet. The role of both magnetic and non-magnetic spatial disorder was discovered. It is predicted that the magnetic part of scattering establishes a triplet ground state suppressing the singlet phase. On the other hand, the nonmagnetic impurities slightly affecting the singlet phase may significantly suppress the triplet state. Copyright (C) EPLA, 2015
Magnetic properties of type-I and type-II Weyl semimetals in the superconducting state
(2018-04-12)
Rosenstein, Baruch
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Shapiro, B. Ya.
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Li, Dingping
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Shapiro, I.
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電子物理學系
Superconductivity was observed in certain range of pressure and chemical composition in Weyl semimetals of both type I and type II (when the Dirac cone tilt parameter kappa > 1). Magnetic properties of these superconductors are studied on the basis of microscopic phonon-mediated pairing model. The Ginzburg-Landau effective theory for the order parameter is derived using the Gorkov approach and used to determine anisotropic coherence length, the penetration depth determining the Abrikosov parameter for a layered material and applied to recent extensive experiments on MoTe2. It is found that superconductivity is of second kind near the topological transition at kappa = 1. For a larger tilt parameter, superconductivity becomes first kind. For kappa < 1, the Abrikosov parameter also tends to be reduced, often crossing over to the first kind kappa For the superconductors of the second kind, the dependence of critical fields H-c2 and H-c1 on the tilt parameter. (governed by pressure) is compared with the experiments. Strength of thermal fluctuations is estimated and it is found that they are strong enough to cause Abrikosov vortex lattice melting near H-c2. The melting line is calculated and is consistent with experiments provided the fluctuations are three dimensional in the type-I phase (large pressure) and two dimensional in the type-II phase (small pressure).
Majorana states in a p-wave superconducting ring
(2013-06-01)
Rosenstein, B.
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Shapiro, I.
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Shapiro, B. Ya.
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電子物理學系
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Department of Electrophysics
The spectrum of excitations of the chiral superconducting ring with internal and external radii R-i, R-e (comparable with coherence length xi) trapping a unit flux Phi(0) is calculated. We find within the Bogoliubov-de Gennes approach that there exists a pair of precisely zero-energy states when 2k(perpendicular to)(R-e - R-i)/pi is integer (here k(perpendicular to) is the momentum component in the disk plane while k(perpendicular to) xi > 1). They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon. Copyright (C) EPLA, 2013
Maximal persistent current in a type-II superconductor with an artificial pinning array at the matching magnetic field
(2010-02-01)
Rosenstein, B.
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Shapiro, I.
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Shapiro, B. Ya.
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電子物理學系
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Department of Electrophysics
The current carrying steady state of the pinned flux line lattice created by magnetic field is described. We calculate analytically the critical current for the case of the matching field (when the number of vortices is equal to that of the pinning centers) using a simple variational method in the framework of Ginzburg-Landau equations. The vortex cores are deformed and displaced in the current carrying state. Displacement of the centers of the vortices with respect to pinning centers and structure of these states are determined.
Microwave absorption in the cores of Abrikosov vortices pinned by artificial insulator inclusion
(2011-10-17)
Rosenstein, B.
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Shapiro, I.
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Deutch, E.
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Shapiro, B. Ya.
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電子物理學系
The spectrum of core excitations of the Abrikosov vortex pinned by a dielectric inclusion or nanoholes the size of the coherence length is considered using the Bogoliubov-deGennes equations beyond the semiclassical approximation. While the lowest excitation, minigap, in the unpinned (or pinned by a metallic defect) vortex is of the order of Delta(2)/E(F), it becomes of the order of the superconducting gap Delta (E(F) is Fermi energy). The reconstruction of the quasiparticle excitations' spectrum has a significant impact on optical properties and on the tunneling density of states. We calculate the absorption amplitude and point out that, while in scanning tunneling microscopy the energy gap Lambda(DOS) is between a quasiparticle state with angular momentum mu(e) = mu(0) > 1/2 and quasihole with mu(h) = -mu(0), the microwave absorption gap, Delta(dir), is between the states with mu(e) = mu(h) +/- 1. It is shown that Delta(dir) > Delta(DOS). The large minigap might play a role in magneto-transport phenomena broadly associated with the "superconductor-insulator" transition in quasi-two-dimensional systems in which small insulating inclusions are generally present.
Microwave absorption in the cores of the Abrikosov vortices pinned by artificial insulator inclusion
(2012-09-01)
Rosenstein, B.
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Shapiro, I.
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Shapiro, B. Ya.
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Deutch, E.
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電子物理學系
The spectrum of core excitations of the Abrikosov vortex pinned by a dielectric inclusion or nanoholes of the size of the coherence length is considered using the Bogoliubov-deGennes equations beyond the semiclassical approximation. While the lowest excitation, mini-gap, in the unpinned (or pinned by a metallic defect) vortex is of the order of Delta(2)/epsilon(F), it becomes of the order of the superconducting gap Delta. The reconstruction of the quasiparticle excitations' spectrum has a significant impact on optical properties and on the tunneling density of states. We calculate the absorption amplitude and point out that, while in STM the energy gap Delta(DOS) is between a quasiparticles state with angular momentum mu(e) = mu(s) > 1/2 and quasi-hole with mu(h) = mu(s) the microwave absorption gap, Delta(dir) is between states with mu(e) = mu(h) + 1. It is shown that Delta(dir) > Delta(DOS). The large mini-gap might play a role in magneto-transport phenomena broadly associated with the "superconductor-insulator" transition in quasi 2D systems in which small insulating inclusions are generally present. (C) 2012 Elsevier B. V. All rights reserved.
On investigation of high T(c) superconductors with Electron Paramagnetic Resonance spectrometers
(2010-11-15)
Shaltiel, D.
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von Nidda, H. -A. Krug
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Shapiro, B. Ya.
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Bogoslavsky, B.
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Rosenstein, B.
Following the discovery of high T(c) superconductors, many researchers have applied EPR spectrometers to investigate their properties using the regular instructions to operate the spectrometer. As no substantial information was obtained it was soon practically abandoned. Investigations performed recently with the EPR technique, using a different operating method than the conventional one and the introduction of a detailed theoretical study related to the interaction of the JV with the microwave magnetic field lead to new and important results related to properties of high anisotropy superconductors indicating that the EPR spectrometer can be used to investigate properties of high anisotropy superconductors. The failures when using conventional operating method to obtain meaningful results and the method used in the present work to carry out the measurements in a proper manner are presented. Some important results obtained in investigating high anisotropy superconductors by the EPR technique are presented. (C) 2010 Elsevier B.V. All rights reserved.