Common quantum phase transition in quasicrystals and heavy-fermion metals

Abstract

Extraordinary new materials named quasicrystals and characterized by noncrystallographic rotational symmetry and quasiperiodic translational properties have attracted scrutiny. Study of quasicrystals may shed light on the most basic notions related to the quantum critical state observed in heavy-fermion metals. We show that the electronic system of some quasicrystals is located at the fermion condensation quantum phase transition without tuning. In that case the quasicrystals possess the quantum critical state with the non-Fermi liquid behavior which in magnetic fields transforms into the Landau Fermi-liquid one. Remarkably, the quantum critical state is robust despite the strong disorder experienced by the electrons. We also demonstrate for the first time that quasicrystals exhibit the typical scaling behavior of their thermodynamic properties such as the magnetic susceptibility, and belong to the famous family of heavy-fermion metals. Our calculated thermodynamic properties are in good agreement with recent experimental observations.

5 pages, 3 figures, typos corrected, some references and comments added

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• Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice
• Local Electron Correlations in a Two-dimensional Hubbard Model on the Penrose Lattice
• Pressure-Driven Quantum Criticality and T/H Scaling in the Icosahedral Au-Al-Yb Approximant
• Quasi-classical physics and T-linear resistivity in both strongly correlated and ordinary metals
• New state of matter: heavy-fermion systems, quantum spin liquids, quasicrystals, cold gases, and high temperature superconductors
• Fermion condensation, $T$-linear resistivity and Planckian limit
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Topological basis for understanding the behavior of the heavy-fermion metal $\beta -\mathrm{YbAl}{\mathrm{B}}_4$ under application of magnetic field and pressure
• Cooper instability and superconductivity on the Penrose lattice
• Doped Mott insulator on Penrose tiling
• Strongly correlated Fermi systems as a new state of matter
• Quasi-one-dimensional quantum spin liquid in the $\mathrm{Cu}({\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2)(\mathrm{N}{\mathrm{O}}_3{)}_2$ insulator
• Unconventional superfluidity of superconductivity on Penrose lattice
• Direct observation of heterogeneous valence state in Yb-based quasicrystalline approximants
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Universal $T/B$ scaling behavior of heavy fermion compounds
• Precursor to Quantum Criticality in Ce-Au-Al Quasicrystal Approximants
• Quantum Critical Scaling of Specific Heat in a Quasicrystal
• Fermion condensate generates a new state of matter by making flat bands