Symmetry breaking phase transitions occurring in the early Universe are expected to leave behind long-lived topologically stable structures such as monopoles, strings or domain walls1–6. Here I discuss the analogy between cosmological strings and vortex lines in the superfluid, and suggest a cryogenic experiment which tests key elements of the cosmological scenario for string formation. In a superfluid obtained through a rapid pressure quench, the phase of the Bose condensate wavefunction—the 4He analogue of the broken symmetry of the field-theoretic vacuum—will be chosen randomly in domains of some characteristic size d. When the quench is performed in an annulus of circumference C the typical value of the phase mismatch around the loop will be ∼(C/d)1/2. The resulting phase gradient can foe sufficiently large to cause the superfluid to flow with a measurable (mm s−1), randomly directed velocity.

Cosmological Experiments in Superfluid Helium

Interfaces between complex oxides are emerging as one of the most interesting systems in condensed matter physics. In this special setting, in which translational symmetry is artificially broken, a variety of new and unusual electronic phases can be promoted. Theoretical studies predict complex phase diagrams and suggest the key role of the charge carrier density in determining the systems' ground states. A particularly fascinating system is the conducting interface between the band insulators LaAlO(3) and SrTiO(3) (ref. 3). Recently two possible ground states have been experimentally identified: a magnetic state and a two-dimensional superconducting condensate. Here we use the electric field effect to explore the phase diagram of the system. The electrostatic tuning of the carrier density allows an on/off switching of superconductivity and drives a quantum phase transition between a two-dimensional superconducting state and an insulating state. Analyses of the magnetotransport properties in the insulating state are consistent with weak localization and do not provide evidence for magnetism. The electric field control of superconductivity demonstrated here opens the way to the development of new mesoscopic superconducting circuits.

Electric field control of the LaAlO3/SrTiO3 interface ground state.

We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

Impurity-induced states in conventional and unconventional superconductors

Discrete breathers — Advances in theory and applications

Tunneling spectroscopy has played a central role in the experimental verification of the microscopic theory of superconductivity in classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy and spectroscopy (STM and STS) on these compounds allowed the main difficulties to be overcome. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. The crucial efforts to gain control over the technique and to obtain reproducible results are first recalled. Then a discussion on how the STM and STS techniques have contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors is presented: the unusually large gap values and the absence of scaling with the critical temperature, the pseudogap and its relation to superconductivity, the unprecedented small size of the vortex cores and its influence on vortex matter, the unexpected electronic properties of the vortex cores, and the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states and in the vortex cores.

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Scanning tunneling spectroscopy of high-temperature superconductors

The Physics of Liquid and Solid Helium

The Physics of Superconductors

Superconductivity: Conventional and Unconventional Superconductors

Superconductivity: Novel Superconductors

Theoretical and experimental results of research on the properties of condensed helium are presented, with major emphasis on /sup 3/He and /sup 3/He--/sup 4/He solutions. Topics covered include: Landau--Fermi-liquid theory and low temperature properties of normal liquid /sup 3/He; low temperature properties of dilute solutions of /sup 3/He in superfluid /sup 4/He; theory of anisotropic superfluidity in /sup 3/He; superfluid /sup 3/He; helium monolayers; multilayer adsorbed helium in restricted geometries; and neutron scattering from helium. Abstracts of seven individual items from the book were prepared for the data base. (GHT)

K H Bennemann

Papers

The Physics of Liquid and Solid Helium

The Physics of Superconductors

Superconductivity: Conventional and Unconventional Superconductors

Superconductivity: Novel Superconductors

Physics of liquid and solid helium. Part I