BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electron-like particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the many-body interactions that exist inside a metal, even in the so-called heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the high-temperature phase of some of the best superconductors available. Understanding high-temperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their poster-child: the copper oxide high-temperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameter-free universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the low-energy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the single-particle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independent-particle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of non-quasiparticles will also be formalized. The correlation between the strength of the linear-in-temperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravity-inspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gauge-gravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely D-branes (the horseshoe-shaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.
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Acausality in superfluid dark matter and MOND-like theories
Abstract There has been much interest in novel models of dark matter that exhibit interesting behavior on galactic scales. A primary motivation is the observed Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the quartic power of rotation speed. This scaling is not obviously accounted for by standard cold dark matter. This has prompted the development of dark matter models that exhibit some form of so-called MONDian phenomenology to account for this galactic scaling, while also recovering the success of cold dark matter on large scales. A beautiful example of this are the so-called superfluid dark matter models, in which a complex bosonic field undergoes spontaneous symmetry breaking on galactic scales, entering a superfluid phase with a 3/2 kinetic scaling in the low energy effective theory, that mediates a long-ranged MONDian force. In this work we examine the causality and locality properties of these and other related models. We show that the Lorentz invariant completions of the superfluid models exhibit high energy perturbations that violate global hyperbolicity of the equations of motion in the MOND regime and can be superluminal in other parts of phase space. We also examine a range of alternate models, finding that they also exhibit forms of non-locality.
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- Award ID(s):
- 2013953
- NSF-PAR ID:
- 10348704
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2021
- Issue:
- 11
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 015
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Context. We make rotation curve fits to test the superfluid dark matter model. Aims. In addition to verifying that the resulting fits match the rotation curve data reasonably well, we aim to evaluate how satisfactory they are with respect to two criteria, namely, how reasonable the resulting stellar mass-to-light ratios are and whether the fits end up in the regime of superfluid dark matter where the model resembles modified Newtonian dynamics (MOND). Methods. We fitted the superfluid dark matter model to the rotation curves of 169 galaxies in the SPARC sample. Results. We found that the mass-to-light ratios obtained with superfluid dark matter are generally acceptable in terms of stellar populations. However, the best-fit mass-to-light ratios have an unnatural dependence on the size of the galaxy in that giant galaxies have systematically lower mass-to-light ratios than dwarf galaxies. A second finding is that the superfluid often fits the rotation curves best in the regime where the superfluid’s force cannot resemble that of MOND without adjusting a boundary condition separately for each galaxy. In that case, we can no longer expect superfluid dark matter to reproduce the phenomenologically observed scaling relations that make MOND appealing. If, on the other hand, we consider only solutions whose force approximates MOND well, then the total mass of the superfluid is in tension with gravitational lensing data. Conclusions. We conclude that even the best fits with superfluid dark matter are still unsatisfactory for two reasons. First, the resulting stellar mass-to-light ratios show an unnatural trend with galaxy size. Second, the fits do not end up in the regime that automatically resembles MOND, and if we force the fits to do so, the total dark matter mass is in tension with strong lensing data.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1475-7516/2021/11/015
