Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

Pokrovsky, S. V.; Pokrovsky, V. L.

doi:10.1103/physrevlett.75.1150

Cited by 24 publications

(18 citation statements)

References 10 publications

(17 reference statements)

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“…͑This general proof has been given in our work. 10 For special situations the fact of appearance of the gap at a finite impurity concentration has been found earlier in Refs. 8, 9, and 7.…”

Section: ͑97͒mentioning

confidence: 86%

“…8, 9, and 7. We became aware of these articles after the submission of our work 10 and did not cite them. We regret this omission and use this opportunity to restore the priority.͒ ϭ͑Wϩ1/͒sin␣; ϭ͑Wϩ1/ ͒cos␣.…”

Section: ͑97͒mentioning

confidence: 99%

“…As it will be demonstrated below, an initially gapless excitation spectrum of a clean superconductor may acquire a gap due to the scattering of electrons by nonmagnetic impurities. 8,9,7,10 Thus, the layered anisotropic superconductors are potentially predisposed to a sort of phase transition at zero temperature. The latter may exhibit itself, e.g., in the quasiparticle tunneling and the temperature correction to the penetration depth in single crystals of Y-Ba-Cu-O doped by Pr or subject to the radiation damage.…”

Section: Introductionmentioning

confidence: 99%

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Density of states and order parameter in dirty anisotropic superconductors

Pokrovsky

1996

Phys. Rev. B

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We analyze in detail how the scattering by nonmagnetic impurities affects the shape and amplitude of the order parameter ͑OP͒ and the density of states in anisotropic superconductors in the framework of BCS theory. Special attention is paid to the case when the OP is a mixture of d and s waves changing its sign on the Fermi surface. The critical temperature is shown to decay with the increase of the residual resistance according to the power law. At zero temperature impurity scattering gives rise to a peculiar phase transition from a gapless regime to a state with a finite gap in the quasiparticle spectrum. ͓S0163-1829͑96͒02342-9͔

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Section: ͑97͒mentioning

confidence: 86%

Section: ͑97͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Density of states and order parameter in dirty anisotropic superconductors

Pokrovsky

1996

Phys. Rev. B

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“…Indeed, the impurity effect in an extended s-wave state with nodes in the gap was studied by many authors, [6][7][8][9][10][11][12][13] in pursuit of determination of the order parameter symmetry in high-T c superconductors, and some peculiar behaviors such as the impurity-induced opening of the gap ͑in the case of sign-changing order parameter͒ were found. [9][10][11][12][13][14] However, the order parameter in the high-T c superconductors turned out to be of d-wave symmetry. 15 Moreover, it appears difficult for extended s-wave order parameter with sign change to be realized in actual materials.…”

Section: Introductionmentioning

confidence: 99%

Superconducting state in a crystal of low symmetry: Impurity effect in an extendeds-wave superconductor with nodes in the excitation gap

Yamashita

Hirashima

2009

Phys. Rev. B

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It is argued that an extended s-wave superconducting state having order parameter that changes its sign on the Fermi surface is likely to occur in crystals of low symmetry such as organic conductors, if the pairing interaction is of electronic origin. Impurity effects in those superconducting states are then studied. Special attention is paid to the nuclear magnetic relaxation rate 1 / T 1 . It is found that impurities give rise to peculiar behavior of 1 / T 1 such as a coherence peak just below the transition temperature and T-linear variation, caused by impurity-induced finite density of states at the chemical potential, at low temperatures, at moderate impurity concentration.

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“…One could expect different types of transformations of these lines of zeroes that depend on the perturbation. Impurities, for example, can (i) produce the gap in the fermionic spectrum (32), thus transforming the system to class 2 (see Fig. 2d); (ii) lead to a finite density of states (33), thus transforming the system to class 1; (iii) produce zeroes of fractional dimension, which means that the exponent in the density of states N(E) ϰ E 2ϪD is nonintegral (34) and thus corresponds to a fractional dimension D of the manifold of zeroes; and (iv) lead to localization (35).…”

Section: Systems With a Fermi Linementioning

confidence: 99%

Field theory in superfluid ³ He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

Volovik

1999

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

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There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superf luid 3 He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superf luid 3 He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis.3 He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3 He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a ''relativistic'' spectrum close to gap nodes, which allows application of ideas developed for superf luid 3 He-A.It is now well understood that the universe and its symmetrybroken ground state, the physical vacuum, may behave like a condensed matter system with a complicated and possibly degenerate ground state (1-5). If the analogy of the quantum mechanical physical vacuum with condensed matter systems is taken seriously, the first question that arises is: which system of condensed matter reproduces most closely the properties of the quantum vacuum? Because particle physics deals with interacting Fermi and Bose quantum fields, the system should be fermionic. This requirement excludes superfluid 4 He, which contains only Bose fields. In Fermi systems, such as metals, superconductors, and normal and superfluid 3 He, in addition to the fermionic degrees of freedom that come from the bare fermions, electrons, and 3 He-atoms, the quantum Bose fields appear as low-energy collective modes. Therefore, these systems do represent interacting Fermi and Bose quantum fields.Which Fermi system is the best? To answer this question we first must realize that the main feature that differentiates between various Fermi systems is the topology of the quasiparticle spectrum in the low energy (infra-red) corner. I will consider only systems whose ground state is spatially homogeneous, which is one of the least disputed properties of the physical vacuum. When the topology of the quasiparticle spectrum is taken into account, the homogeneous Fermi systems can be organized into very few classes (see Fig. 1).

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Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

Cited by 24 publications

References 10 publications

Density of states and order parameter in dirty anisotropic superconductors

Density of states and order parameter in dirty anisotropic superconductors

Superconducting state in a crystal of low symmetry: Impurity effect in an extendeds-wave superconductor with nodes in the excitation gap

Field theory in superfluid ³ He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

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Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

Cited by 24 publications

References 10 publications

Density of states and order parameter in dirty anisotropic superconductors

Density of states and order parameter in dirty anisotropic superconductors

Superconducting state in a crystal of low symmetry: Impurity effect in an extendeds-wave superconductor with nodes in the excitation gap

Field theory in superfluid 3 He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

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Field theory in superfluid ³ He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?