Quasiparticle spectrum of<b><i>d</i></b>-wave superconductors in the mixed state

Marinelli, Luca; Halperin, B. I.; Simon, Steven H.

doi:10.1103/physrevb.62.3488

Cited by 57 publications

(137 citation statements)

References 22 publications

(30 reference statements)

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“…Unfortunately, the linearized approximation, on which these conclusions rest, has been found to be problematic. Within the linearized approximation, the QP spectrum is not 6,7 invariant under the large (singular) gauge transformations 8,9 , which were being employed in the calculations 5 of k xy . Because such large gauge invariance must hold, the validity of the results has been in doubt.…”

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confidence: 99%

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors

Cvetković

Vafek

2015

Nat Commun

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Bogolyubov quasiparticles move in a practically uniform magnetic field in the vortex state of high-temperature cuprate superconductors. When set in motion by an externally applied heat current, the quasiparticles' trajectories may bend, causing a temperature gradient perpendicular to the heat current and the applied magnetic field, resulting in the thermal Hall effect. Here we relate this effect to the Berry curvature of quasiparticle magnetic sub-bands, and calculate the dependence of the intrinsic thermal Hall conductivity on superconductor's temperature, magnetic field and the amplitude of the d-wave pairing. The intrinsic contribution to thermal Hall conductivity displays a rapid onset with increasing temperature, which compares favourably with existing experiments at high magnetic field on the highest purity samples. Because such temperature onset is related to the pairing amplitude, our finding may help to settle a much-debated question of the bulk value of the pairing strength in cuprate superconductors in magnetic field.

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confidence: 99%

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors

Cvetković

Vafek

2015

Nat Commun

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“…Initially Volovik [2] and Kopnin and Volovik [26] proposed that a semiclassical analysis of this type should be valid only down to a scale (∆ 2 0 /E F ) H/H c2 . Recent numerical work [24,25] indicated, however, that the true crossover scale is much smaller for realistic systems with ∆ 0 /E F ≪ 1. Such fine details of the true quantum quasiparticle band structure will also be smeared out by impurity effects.…”

Section: Introductionmentioning

confidence: 99%

“…We thus neglect states possibly localized in the vortex core, and other quasiparticle bandstructure effects in a periodic vortex lattice discussed recently by several authors [22][23][24][25]. Initially Volovik [2] and Kopnin and Volovik [26] proposed that a semiclassical analysis of this type should be valid only down to a scale (∆ 2 0 /E F ) H/H c2 .…”

Section: Introductionmentioning

confidence: 99%

Vortex state of ad-wave superconductor at low temperatures

Hirschfeld

Wölfle

2001

Phys. Rev. B

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A systematic perturbation theory is developed to describe the magnetic field-induced subdominant s-and dxy-wave order parameters in the mixed state of a d x 2 −y 2 -wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field Hc1 < ∼ H ≪ Hc2 from Tc down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant dxy pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.

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“…Applying the duality and a topological argument, we provide insights into the quasiparticle spectrum. In the quantum limit, interference effects become relevant especially at zero energy [3]. The existence of edge states is discussed as well.…”

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confidence: 99%

“…Two-dimensional Dirac fermions with a gauge field are of current interest, e.g., in the context of the vortex state in a two-dimensional d-wave superconductivity [1][2][3]. In our study, Dirac fermions with a gauge field are realized on a two-dimensional lattice.…”

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confidence: 99%

Duality in the Azbel-Hofstadter Problem and Two-Dimensionald-Wave Superconductivity with a Magnetic Field

Morita

Hatsugai

2001

Phys. Rev. Lett.

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A single-parameter family of lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter h = ∆/t (quantum parameter). A topological number is attached to each energy band. A duality between the classical limit (h = +0) and the quantum limit (h = 1) is revealed in the energy spectrum and the topological number.The model has a close relation to the two-dimensional dwave superconductivity with a magnetic field. Making use of the duality and a topological argument, we shed light on how the quasiparticles with a magnetic field behave especially in the quantum limit.Two-dimensional Dirac fermions with a gauge field are of current interest, e.g., in the context of the vortex state in a two-dimensional d-wave superconductivity [1][2][3]. In our study, Dirac fermions with a gauge field are realized on a two-dimensional lattice. It is a single-parameter deformation of the Azbel-Hofstadter problem [4,5]. In this paper, the parameter h is called quantum parameter [6]. A topological number is assigned for each energy band [7][8][9]. As the quantum parameter is varied continuously from the classical limit (h = +0) to the quantum limit (h = 1), the energy spectrum is reconstructed through the change of each topological number (plateau transition [9][10][11]). Although the two limits are not connected adiabatically, we found that there is a duality between the classical and the quantum regime.The model has a close relation to the two-dimensional d-wave superconductivity with a magnetic field. Applying the duality and a topological argument, we provide insights into the quasiparticle spectrum. In the quantum limit, interference effects become relevant especially at zero energy [3]. The existence of edge states is discussed as well. It reflects a non-trivial topology of each energy band [9,12].Let us define a key Hamiltonian in our paper, which is a single-parameter family of lattice fermion model. It is a deformation of the Azbel-Hofstadter problem. The Hamiltonian is H = l,m c † l H lm c m with One of the basic observables is a topological number for the n-th band, C n [7][8][9]. It iswhere ∇ = ∂/∂k and |u n (k) is a Bloch vector of the n-th band. The integration dk runs over the Brillouin zone (torus). The non-zero topological number results in the existence of edge states. In order to see it, put the system on a cylinder and introduce a fictitious flux through the cylinder (it is equivalent to a twist in the boundary condition) [13]. The edge states move from one boundary to the other as the fictitious flux quanta hc/e is added adiabatically. The number of carried edge states coincides with the summation of topological numbers below the Fermi energy [9,12]. Due to the topological stability, a singularity necessarily occurs with the change of the topological number (plateau transition [9][10][11]). The singularity is identified with an energy-gap closing on some points in the Brillouin zone. In Figs. 1-3, the energy spectra are shown. As h is varied continuously from the classical l...

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Quasiparticle spectrum ofd-wave superconductors in the mixed state

Cited by 57 publications

References 22 publications

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors

Vortex state of ad-wave superconductor at low temperatures

Duality in the Azbel-Hofstadter Problem and Two-Dimensionald-Wave Superconductivity with a Magnetic Field

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