Quantitative investigation of the de Haas-van Alphen effect in the superconducting state

Janssen, T. J. B. M.; Haworth, C.; Hayden, Stephen M; Meeson, P. J.; Springford, M; Wasserman, Allen L.

doi:10.1103/physrevb.57.11698

Cited by 69 publications

(56 citation statements)

References 60 publications

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“…However, for angles nearer to the plane, the Dingle plots become non-linear because of additional damping caused by the growth of the superconducting gap, as has been observed in many superconductors (see for example Ref. [18]). This observation proves that our dHvA signals arise from MgB 2 rather than any impurity phase.…”

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confidence: 98%

de Haas–van Alphen effect in single crystal MgB2

Carrington

Cooper

Hussey

et al. 2003

Physica C: Superconductivity

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We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from 0.44 − 0.68me. By comparing these with band masses calculated recently by three groups, we find that the electron-phonon coupling strength λ, is a factor ∼ 3 larger for the c-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.

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confidence: 98%

de Haas–van Alphen effect in single crystal MgB2

Carrington

Cooper

Hussey

et al. 2003

Physica C: Superconductivity

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“…The field-dependent damping of magnetic quantum oscillations is usually described by factors [2,45,46]…”

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confidence: 99%

“…Below the upper critical field, B c2 , the opening of a superconducting gap and the corresponding disappearance of the entire Fermi surface seem to contradict the existence of such oscillations. Nevertheless, they were observed in many type-II superconductors ( [2][3][4] …”

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Field-induced gapless electron pocket in the superconducting vortex phase ofYNi2B2Cas probed by magnetoacoustic quantum oscillations

et al. 2017

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By use of ultrasound studies we resolved magneto-acoustic quantum oscillation deep into the mixed state of the multiband nonmagnetic superconductor YNi2B2C. Below the upper critical field, only a very weak additional damping appears that can be well explained by the field inhomogeneity caused by the flux-line lattice in the mixed state. This is clear evidence for no or a vanishingly small gap for one of the bands, namely, the spheroidal α band. This contrasts de Haas-van Alphen data obtained by use of torque magnetometry for the same sample, with a rapidly vanishing oscillation signal in the mixed state. This points to a strongly distorted flux-line lattice in the latter case that, in general, can hamper a reliable extraction of gap parameters by use of such techniques. † This work is dedicated to the memory of Lev Petrovich Gor'kovThe observation of magnetic quantum oscillations is usually taken as evidence for the existence of a Fermi surface. The appearance of Landau levels in a magnetic field leads to an oscillating density of states at the Fermi level as a function of field. Experimentally, these oscillations can be detected in many thermodynamic and transport properties, with the most prominent being the de Haas-van Alphen (dHvA) effect in the magnetization. Consequently, the observation of dHvA oscillations in the mixed state of a superconductor first appeared as a surprise [1]. Below the upper critical field, B c2 , the opening of a superconducting gap and the corresponding disappearance of the entire Fermi surface seem to contradict the existence of such oscillations. Nevertheless, they were observed in many type-II superconductors ([2-4] and references therein).Motivated by the experimental evidence, however, it subsequently was shown by a number of theoretical studies that this phenomenon may be understood in principle in a rather general context. Thereby, different models are used to explain the occurrence of quantum oscillations below B c2 [5-9], but it still remains unclear which of them is the most appropriate. Usually, the validity of these theories is tested by comparing the predicted additional damping of the quantum oscillations below B c2 with experiment. Such analysis gives as the main fit parameter the superconducting gap at zero temperature, ∆ 0 , a value that largely depends on the used model.With the proper theory at hand dHvA data could, in principle, yield information on the field and angular evolution of the superconducting gap, ∆. However, considerable ambiguity in ∆ is introduced not only by the various theoretical predictions but even more from varying, sometimes contradictory, experimental data. In particular, for YNi 2 B 2 C and LuNi 2 B 2 C highly controversial results were reported [4,[10][11][12][13][14][15][16][17][18]. Thereby, for the so-called α band, an additional damping of the dHvA signal was found either in line with the opening of a weak-coupling gap [11][12][13]15], or yielding an unexpectedly small gap [4,10,14,17,18], or even an abrupt vanishing of the oscillatio...

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“…We find an analytic formulae for this damping which is due to tunnelling between semiclassical quasiparticle orbits comprising both particle-like and hole-like segments. The quantitative predictions of the theory are consistent with the available data.The revival of interest [1][2][3] in studying the de Haas-van Alphen (dHvA) effect in the superconducting state [4] is driven by the hope that this would provide new k-vector dependent information about the superconducting gap ∆(k). Evidently this would be of particular importance in connection with anisotropic superconductors where ∆(k) can have lines of zero's on the Fermi surface [5].…”

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confidence: 99%

“…Clearly, |∆| in the above analysis is an effective quantity whose value cannot be expected to agree with the zero field |∆| of 2.6 meV (see for example ref. [2]). A more detailed analysis of the existing data as well as a more complete presentation of the theory will be given elsewhere ( 1 ).…”

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A damping of the de Haas van Alphen oscillations in the superconducting state

Duncan¹,

Györffy²

2002

J. Phys.: Condens. Matter

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Abstract. -Deploying a recently developed semiclassical theory of quasiparticles in the superconducting state we study the de Haas-van Alphen effect. We find that the oscillations have the same frequency as in the normal state but their amplitude is reduced. We find an analytic formulae for this damping which is due to tunnelling between semiclassical quasiparticle orbits comprising both particle-like and hole-like segments. The quantitative predictions of the theory are consistent with the available data.The revival of interest [1][2][3] in studying the de Haas-van Alphen (dHvA) effect in the superconducting state [4] is driven by the hope that this would provide new k-vector dependent information about the superconducting gap ∆(k). Evidently this would be of particular importance in connection with anisotropic superconductors where ∆(k) can have lines of zero's on the Fermi surface [5]. Unfortunately at this stage there is no concensus concerning the mechanism of how the experimentally observed oscillations of the diamagnetic response of a Type II superconductor come about [6][7][8][9][10][11][12][13][14][15]. Using our recently developed very general semiclassical theory of quasiparticles in the superconducting state [16], in what follows we develop a semiclassical picture of Landau like orbits of quasiparticles suggested by the simple model calculation of Miller and Györffy [8]. Clearly the long term aim of a semiclassical theory is to provide an analogue of the Lifshitz-Kosevich formulae for superconductors. Hopefully such a formulae would allow the interpretation of experiments in terms of the Fermi surface and the variation of ∆(k) on the Fermi surface. At this stage we only deal with conventional superconductors with the usual s-wave pairing. As it happens this is the only case for which reliable data already exists. Within the limits of a number of simplifying assumptions the above semiclassical theory provides for Bohr-Sommerfeld like quantisation rules for quasiparticles. In particular it allows for the analogue of magnetic breakdown which involves tunnelling between distinct semiclassical orbits. We show that there are orbits which enclose areas that are precisely the same size as the Landau orbits in the normal state, but involve such tunnelling. As will be seen the consequence of these tunnelling events is a damping factor in the Lifshitz-Kosevich formulae in agreement with experiments [1][2][3].The theory we wish to use seeks the semiclassical spectrum of the following Bogoliubov-de c EDP Sciences

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Quantitative investigation of the de Haas-van Alphen effect in the superconducting state

Cited by 69 publications

References 60 publications

de Haas–van Alphen effect in single crystal MgB2

de Haas–van Alphen effect in single crystal MgB2

Field-induced gapless electron pocket in the superconducting vortex phase ofYNi2B2Cas probed by magnetoacoustic quantum oscillations

A damping of the de Haas van Alphen oscillations in the superconducting state

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