Criterion for stability of Goldstone modes and Fermi liquid behavior in a metal with broken symmetry

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 111; no. 46; pp. 16314 - 16318
• Main Authors: Watanabe, Haruki, Vishwanath, Ashvin
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 18.11.2014; National Acad Sciences
• Subjects: Bosons; Broken symmetry; Crystal lattices; Electrons; Fermi liquids; Fermi surfaces; Liquids; Magnetic fields; Metals; Particle physics; Phonons; Physical Sciences; Quantum physics; Rotation; Symmetry; Theorems; Goldstone modes; strong magnetic fields; spontaneous symmetry breaking; non-Fermi liquids
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1415592111

There are few general physical principles that protect the low-energy excitations of a quantum phase. Of these, Goldstone’s theorem and Landau–Fermi liquid theory are the most relevant to solids. We investigate the stability of the resulting gapless excitations—Nambu–Goldstone bosons (NGBs) and Landau quasiparticles—when coupled to one another, which is of direct relevance to metals with a broken continuous symmetry. Typically, the coupling between NGBs and Landau quasiparticles vanishes at low energies, leaving the gapless modes unaffected. If, however, the low-energy coupling is nonvanishing, non-Fermi liquid behavior and overdamped bosons are expected. Here we prove a general criterion that specifies when the coupling is nonvanishing. It is satisfied by the case of a nematic Fermi fluid, consistent with earlier microscopic calculations. In addition, the criterion identifies a new kind of symmetry breaking—of magnetic translations—where nonvanishing couplings should arise, opening a previously unidentified route to realizing non-Fermi liquid phases. Significance A remarkable feature of many particle systems is that although they are described by equations respecting various symmetries, they may spontaneously organize into a state that explicitly breaks symmetries. An example is a crystal that breaks the translation symmetry of space. In such cases, a celebrated theorem predicts an excitation, the Goldstone mode. In this paper we examine whether this continues to hold inside a metal, where electrons can collide with the Goldstone excitations. Our result is a one-equation criterion that specifies whether the interactions between electrons and Goldstone modes can be ignored or whether it completely changes their character. In the latter case, unusual phases of matter such as non-Fermi liquids or superconductors may arise.