Response, Relaxation and Transport in Unconventional Superconductors

Einzel, Dietrich; Klam, Ludwig

doi:10.1007/s10909-007-9519-2

Cited by 5 publications

(7 citation statements)

References 37 publications

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“…Now, we make use of an analogy between electron-phonon and electron-photon scattering, where the electrons scatter from a phonon rather than a photon and the electron-phonon coupling vertex replaces the Raman vertex (35). In particular, for the case of stress phonons, the electron-phonon coupling vertex is given by the electronic stress tensor, which is proportional to the inverse effective mass tensor (36)(37)(38)(39). As a result, for the system studied here, the electron-phonon coupling vertex, like the Raman vertex, is highly anisotropic in momentum space.…”

Section: Cdw Amplitude Mode Excitations and Electron-phonon Couplingmentioning

confidence: 99%

Alternative route to charge density wave formation in multiband systems

Eiter

Lavagnini

Hackl

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

103

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Charge and spin density waves, periodic modulations of the electron, and magnetization densities, respectively, are among the most abundant and nontrivial low-temperature ordered phases in condensed matter. The ordering direction is widely believed to result from the Fermi surface topology. However, several recent studies indicate that this common view needs to be supplemented. Here, we show how an enhanced electron-lattice interaction can contribute to or even determine the selection of the ordering vector in the model charge density wave system ErTe 3 . Our joint experimental and theoretical study allows us to establish a relation between the selection rules of the electronic light scattering spectra and the enhanced electron-phonon coupling in the vicinity of band degeneracy points. This alternative proposal for charge density wave formation may be of general relevance for driving phase transitions into other brokensymmetry ground states, particularly in multiband systems, such as the iron-based superconductors.electron-phonon interactions | nonconventional mechanism | Raman spectroscopy | solid-solid phase transitions T he common view of charge density wave (CDW) formation was originally posed in the work by Kohn (1). Using Kohn's reasoning (1), the tendency to ordering is particularly strong in low dimensions, because the Fermi surface has parallel parts, referred to as nesting. This nesting leads to a divergence in the Lindhard susceptibility, determining the magnitude and direction of the ordering vector Q (2). This divergence in the electronic susceptibility is conveyed to the lattice by the electron-phonon coupling: a phonon softens to zero frequency at Q, and a static lattice distortion develops when the system enters the CDW state, a behavior known as the Kohn anomaly.However, several publications raise the question as to whether nesting alone is sufficient to explain the observed ordering direction Q (3-7), particularly in dimensions higher than 1D. A central question is whether the selection of the CDW ordering vector is always driven by an electronic instability or if the ordering vector could, instead, be determined by a lattice distortion driven by some other mechanism exploiting the role of the electron-phonon coupling. In the latter case, the selected ordering vector would not necessarily nest the Fermi surface. The importance of strongly momentum-dependent electron-phonon coupling on CDW formation was pointed out in refs. 3 and 4, where the relevance of the Fermi surface for determining the ordering vector was indeed found to decrease as the coupling strength increases. In a recent paper on inelastic X-ray scattering measurements on 2H-NbSe 2 , acoustic phonons were observed to soften to zero frequency over an extended region around the CDW ordering vector (8). The authors argue that this behavior is not consistent with a Kohn anomaly picture, where sharp dips are expected (8). Therefore, the phonon softening must be driven by another mechanism, which they identify as a wave vector-dependent e...

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Section: Cdw Amplitude Mode Excitations and Electron-phonon Couplingmentioning

confidence: 99%

Alternative route to charge density wave formation in multiband systems

Eiter

Lavagnini

Hackl

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

103

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“…In this section, we study the quasiparticle spin relaxation in the superconducting GaAs (100) QWs. We first derive the KSBEs for the quasiparticle in the quasiparticle approximation, 18,21,[60][61][62][63][64][65][66][67][68][69] via the nonequilibrium Green function method with the generalized Kadanoff-Baym (GKB) ansatz 9,89,90 (Sec. IV A), and then show the numerical results for the SRTs without (Sec.…”

Section: Quasiparticle Spin Relaxationmentioning

confidence: 99%

“…With a small Fermi energy in the semiconductor QWs, the derivation of the KSBEs is based on the quasiparticle approximation. 18,21,[60][61][62][63][64][65][66][67][68][69]89 In the quasiparticle space, the contour-ordered non-equilibrium Green function is defined as 9,61,89…”

Section: Derivation With Full Hamiltonianmentioning

confidence: 99%

“…It is noted that in the study of the dynamics in superconducting system, different kinetic equations based on the quasiclassical [13][14][15][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] and quasiparticle 18,21,[60][61][62][63][64][65][66][67][68][69] approximations are used. The quasiclassical approximation is applicable for the system with a large Fermi energy, in which the dependence on the momentum magnitude is neglected in the Green function, whereas the frequency and angle-of-momentum dependencies are explicitly considered.…”

Section: Introductionmentioning

confidence: 99%

“…18,21,[60][61][62][63][64][65][66][67] When there exists the SOC, Einzel et al derived the kinetic equation based on the quasiparticle approximation, nevertheless in which the scattering is not considered. 68,69 The kinetic equations of quasiparticle with the scattering term explicitly considered in the presence of the SOC are still absent, even for the simplest case with the s-wave order parameter.…”

Section: Introductionmentioning

confidence: 99%

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A novel superconducting-velocity--tunable quasiparticle state and spin relaxation in GaAs (100) quantum wells in proximity to $s$-wave superconductor

Yu,

2016

Preprint

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We present a novel quasiparticle state driven by a supercurrent in GaAs (100) quantum wells in proximity to an s-wave superconductor, which can be tuned by the superconducting velocity. Rich features such as the suppressed Cooper pairings, large quasiparticle density and non-monotonically tunable momentum current can be realized by varying the superconducting velocity. In the degenerate regime, the quasiparticle Fermi surface is composed by two arcs, referred to as Fermi arcs, which are contributed by the electron-and hole-like branches. The D'yakonov-Perel' spin relaxation is explored, and intriguing physics is revealed when the Fermi arc emerges. Specifically, when the order parameter tends to zero, it is found that the branch-mixing scattering is forbidden in the quasi-electron band. When the condensation process associated with the annihilation of the quasi-electron and quasi-hole is slow, this indicates that the electron-and hole-like Fermi arcs in the quasi-electron band are independent. The open structure of the Fermi arc leads to the nonzero angular-average of the effective magnetic field due to the spin-orbit coupling, which acts as an effective Zeeman field. This Zeeman field leads to the spin oscillations even in the strong scattering regime. Moreover, in the strong scattering regime, we show that the open structure of the Fermi arc also leads to the insensitiveness of the spin relaxation to the momentum scattering, in contrast to the conventional motional narrowing situation. Nevertheless, with a finite order parameter, the branch-mixing scattering can be triggered, opening the inter-branch spin relaxation channel, which is dominant in the strong scattering regime. In contrast to the situation with an extremely small order parameter, due to the inter-branch channel, the spin oscillations vanish and the spin relaxation exhibits motional narrowing feature in the strong scattering regime.

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Kinetic Theory for Response and Transport in Non-centrosymmetric Superconductors

Klam

Manske

Einzel

2012

Non-Centrosymmetric Superconductors

Self Cite

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We formulate a kinetic theory for non-centrosymmetric superconductors at low temperatures in the clean limit. The transport equations are solved quite generally in spin-and particle-hole (Nambu) space by performing first a transformation into the band basis and second a Bogoliubov transformation to the quasiparticle-quasihole phase space. Our result is a particle-hole-symmetric, gauge-invariant and charge conserving description, which is valid in the whole quasiclassical regime (|q| ≪ kF and ω ≪ EF). We calculate the current response, the specific heat capacity, and the Raman response function. For the Raman case, we investigate within this framework the polarization-dependence of the electronic (pair-breaking) Raman response for the recently discovered non-centrosymmetric superconductors at zero temperature. Possible applications include the systems CePt3Si and Li2PdxPt3−xB, which reflect the two important classes of the involved spinorbit coupling. We provide analytical expressions for the Raman vertices for these two classes and calculate the polarization-dependence of the electronic spectra. We predict a two-peak structure and different power laws with respect to the unknown relative magnitude of the singlet and triplet contributions to the superconducting order parameter, revealing a large variety of characteristic fingerprints of the underlying condensate.

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Response, Relaxation and Transport in Unconventional Superconductors

Cited by 5 publications

References 37 publications

Alternative route to charge density wave formation in multiband systems

Alternative route to charge density wave formation in multiband systems

A novel superconducting-velocity--tunable quasiparticle state and spin relaxation in GaAs (100) quantum wells in proximity to $s$-wave superconductor

Kinetic Theory for Response and Transport in Non-centrosymmetric Superconductors

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