What makes a crystal supersolid ?

For nearly half a century the supersolid phase of matter has remained mysterious, not only eluding experimental observation, but also generating a great deal of controversy among theorists. Recent discovery of what is interpreted as a non-classical moment of inertia at low temperature in solid He-4 has elicited much excitement as a possible first observation of a supersolid phase. In the two years following the discovery, however, more puzzles than answers have been provided to the fundamental issue of whether the supersolid phase exists, in helium or any other naturally occurring condensed matter system. Presently, there is no established theoretical framework to understand the body of experimental data on He-4. Different microscopic mechanisms that have been suggested to underlie superfluidity in a perfect quantum crystal do not seem viable for \he4, for which a wealth of experimental and theoretical evidence points to an insulating crystalline ground state. This perspective addresses some of the outstanding problems with the interpretation of recent experimental observations of the apparent superfluid response in He-4 (seen now by several groups) and discusses various scenarios alternative to the homogeneous supersolid phase, such as superfluidity induced by extended defects of the crystalline structure which include grain boundaries, dislocations, anisotropic stresses, etc. Can a metastable superfluid "glassy" phase exist, and can it be relevant to some of the experimental observations ? One of the most interesting and unsolved fundamental questions is what interatomic potentials, given the freedom to design one, can support an ideal supersolid phase in continuous space, and can they be found in Nature.Comment: Perspective to appear in Advances in Physics, 25 pages, 7 figure

Vanishing of phase coherence in underdoped Bi_2Sr_2CaCu_2O_8+d

Coherent time-domain spectroscopy is used to measure the screening and dissipation of high-frequency electromagnetic fields in a set of underdoped Bi_2Sr_2CaCu_2O_8+d thin films. The measurements provide direct evidence for a phase-fluctuation driven transition from the superconductor to normal state, with dynamics described well by the Berezinskii-Kosterlitz-Thouless theory of vortex-pair unbinding.Comment: Nature, Vol. 398, 18 March 1999, pg. 221 4 pages with 4 included figure

Single vortex-antivortex pair in an exciton polariton condensate

In a homogeneous two-dimensional system at non-zero temperature, although there can be no ordering of infinite range, a superfluid phase is predicted for a Bose liquid. The stabilization of phase in this superfluid regime is achieved by the formation of bound vortex-antivortex pairs. It is believed that several different systems share this common behaviour, when the parameter describing their ordered state has two degrees of freedom, and the theory has been tested for some of them. However, there has been no direct experimental observation of the phase stabilization mechanism by a bound pair. Here we present an experimental technique that can identify a single vortex-antivortex pair in a two-dimensional exciton polariton condensate. The pair is generated by the inhomogeneous pumping spot profile, and is revealed in the time-integrated phase maps acquired using Michelson interferometry, which show that the condensate phase is only locally disturbed. Numerical modelling based on open dissipative Gross-Pitaevskii equation suggests that the pair evolution is quite different in this non-equilibrium system compared to atomic condensates. Our results demonstrate that the exciton polariton condensate is a unique system for studying two-dimensional superfluidity in a previously inaccessible regime

Collapse of superconductivity in a hybrid tin-graphene Josephson junction array

When a Josephson junction array is built with hybrid superconductor/metal/superconductor junctions, a quantum phase transition from a superconducting to a two-dimensional (2D) metallic ground state is predicted to happen upon increasing the junction normal state resistance. Owing to its surface-exposed 2D electron gas and its gate-tunable charge carrier density, graphene coupled to superconductors is the ideal platform to study the above-mentioned transition between ground states. Here we show that decorating graphene with a sparse and regular array of superconducting nanodisks enables to continuously gate-tune the quantum superconductor-to-metal transition of the Josephson junction array into a zero-temperature metallic state. The suppression of proximity-induced superconductivity is a direct consequence of the emergence of quantum fluctuations of the superconducting phase of the disks. Under perpendicular magnetic field, the competition between quantum fluctuations and disorder is responsible for the resilience at the lowest temperatures of a superconducting glassy state that persists above the upper critical field. Our results provide the entire phase diagram of the disorder and magnetic field-tuned transition and unveil the fundamental impact of quantum phase fluctuations in 2D superconducting systems.Comment: 25 pages, 6 figure

Dislocations and vortices in pair density wave superconductors

With the ground breaking work of the Fulde, Ferell, Larkin, and Ovchinnikov (FFLO), it was realized that superconducting order can also break translational invariance; leading to a phase in which the Cooper pairs develop a coherent periodic spatially oscillating structure. Such pair density wave (PDW) superconductivity has become relevant in a diverse range of systems, including cuprates, organic superconductors, heavy fermion superconductors, cold atoms, and high density quark matter. Here we show that, in addition to charge density wave (CDW) order, there are PDW ground states that induce spin density wave (SDW) order when there is no applied magnetic field. Furthermore, we show that PDW phases support topological defects that combine dislocations in the induced CDW/SDW order with a fractional vortex in the usual superconducting order. These defects provide a mechanism for fluctuation driven non-superconducting CDW/SDW phases and conventional vortices with CDW/SDW order in the core.Comment: 6 pages,1 figure, 1 tabl

Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas

Any state of matter is classified according to its order, and the kind of order a physical system can posses is profoundly affected by its dimensionality. Conventional long-range order, like in a ferromagnet or a crystal, is common in three-dimensional (3D) systems at low temperature. However, in two-dimensional (2D) systems with a continuous symmetry, true long-range order is destroyed by thermal fluctuations at any finite temperature. Consequently, in contrast to the 3D case, a uniform 2D fluid of identical bosons cannot undergo Bose-Einstein condensation. Nevertheless, it can form a "quasi-condensate" and become superfluid below a finite critical temperature. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. Above the critical temperature, proliferation of unbound vortices is expected. Here we report the observation of a BKT-type crossover in a trapped quantum degenerate gas of rubidium atoms. Using a matter wave heterodyning technique, we observe both the long-wavelength fluctuations of the quasi-condensate phase and the free vortices. At low temperatures, the gas is quasi-coherent on the length scale set by the system size. As the temperature is increased, the loss of long-range coherence coincides with the onset of proliferation of free vortices. Our results provide direct experimental evidence for the microscopic mechanism underlying the BKT theory, and raise new questions regarding coherence and superfluidity in mesoscopic systems.Comment: accepted for publication in Natur

Phase Structure and Compactness

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $\beta^2 = 8\pi$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.Comment: 21 pages, 5 figures, minor changes, final version, accepted for publication in JHE

Intertwined superfluid and density wave order in two-dimensional 4He

Superfluidity is a manifestation of the operation of the laws of quantum mechanics on a macroscopic scale. The conditions under which superfluidity becomes manifest have been extensively explored experimentally in both quantum liquids (liquid 4He being the canonical example) and ultracold atomic gases1, 2, including as a function of dimensionality3, 4. Of particular interest is the hitherto unresolved question of whether a solid can be superfluid5, 6. Here we report the identification of a new state of quantum matter with intertwined superfluid and density wave order in a system of two-dimensional bosons subject to a triangular lattice potential. Using a torsional oscillator we have measured the superfluid response of the second atomic layer of 4He adsorbed on the surface of graphite, over a wide temperature range down to 2 mK. Superfluidity is observed over a narrow range of film densities, emerging suddenly and subsequently collapsing towards a quantum critical point. The unusual temperature dependence of the superfluid density in the limit of zero temperature and the absence of a clear superfluid onset temperature are explained, self-consistently, by an ansatz for the excitation spectrum, reflecting density wave order, and a quasi-condensate wavefunction breaking both gauge and translational symmetry

Superconducting spintronics

The interaction between superconducting and spin-polarized orders has recently emerged as a major research field following a series of fundamental breakthroughs in charge transport in superconductor-ferromagnet heterodevices which promise new device functionality. Traditional studies which combine spintronics and superconductivity have mainly focused on the injection of spin-polarized quasiparticles into superconducting materials. However, a complete synergy between superconducting and magnetic orders turns out to be possible through the creation of spin-triplet Cooper pairs which are generated at carefully engineered superconductor interfaces with ferromagnetic materials. Currently, there is intense activity focused on identifying materials combinations which merge superconductivity and spintronics in order to enhance device functionality and performance. The results look promising: it has been shown, for example, that superconducting order can greatly enhance central effects in spintronics such as spin injection and magnetoresistance. Here, we review the experimental and theoretical advances in this field and provide an outlook for upcoming challenges related to the new concept of superconducting spintronics.J.L. was supported by the Research Council of Norway, Grants No. 205591 and 216700. J.W.A.R. was supported by the UK Royal Society and the Leverhulme Trust through an International Network Grant (IN-2013-033).This is the accepted manuscript. The final version is available at http://www.nature.com/nphys/journal/v11/n4/full/nphys3242.html