From Standard Model of particle physics to room-temperature superconductivity

Abstract

Topological media are gapped or gapless fermionic systems, whose properties are protected by topology, and thus are robust to deformations of parameters of the system and generic. We discuss the class of gapless topological media, which contains the quantum vacuum of Standard Model in its symmetric phase, and condensed matter systems with zeroes in the energy spectrum, which form Fermi surfaces, Weyl and Dirac points, Dirac lines, Khodel-Shaginyan flat bands, etc. Some zeroes are topologically protected, being characterized by topological invariants, expressed in terms of Green's function. For stability of the others the $\mathbf{p}$-space topology must be accompanied by symmetry. Vacua with Weyl points serve as a source of effective relativistic quantum fields emerging at low energy: chiral fermions, effective gauge fields and tetrad gravity emerge together in the vicinity of a Weyl point. The accompanying effects, such as chiral anomaly, electroweak baryo-production and chiral vortical effect, are expressed via the symmetry protected $\mathbf{p}$-space invariants. The gapless topological media exhibit the bulk-surface and bulk-vortex correspondence: which in particular may lead to the flat band on the surface of the system or in the core of topological defects. The materials with flat band in bulk, on the surface or within the dislocations have singular density of states, which crucially influences the critical temperature of the superconducting transition in such media. While in all the known superconductors the transition temperature is exponentially suppressed as a function of the pairing interaction, in the flat band the transition temperature is proportional to the pairing interaction, and can be essentially higher. The $\mathbf{p}$-space topology may give us the general recipe for search or artificial fabrication of the room-temperature superconductors.

8 pages, 8 figures, accepted for proceedings of Nobel Symposium 156 "New forms of Matter - Topological Insulators and Superconductors"

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• Classification of topological insulators and superconductors in three spatial dimensions
• Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Chiral magnetic effect in two-band lattice model of Weyl semimetal
• On the superconductivity of graphite interfaces
• Band-Contact Lines in Electron Energy Spectrum of Graphite
• Emergent Weyl spinors in multi-fermion systems
• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points
• Temperature dependence of the axial magnetic effect in two-color quenched QCD
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Andreev-Majorana bound states in superfluids
• Merging of Landau levels in a strongly-interacting two-dimensional electron system in silicon
• Interface size dependence of the Josephson critical behaviour in pyrolytic graphite

Cited by in corpus (27)

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• Topological Semimetals from first-principles
• Topological Nodal Line Semimetals in CaP3 family of materials
• Symmetry Demanded Topological Nodal-line Materials
• Nodal Line Spin-gapless Semimetals and High-quality Candidate Materials
• Topological nodal-line semimetals in ferromagnetic rare-earth-metal monohalides
• Topological Dirac line nodes and superconductivity coexist in SnSe at high pressure
• Indication of band flattening at the Fermi level in a strongly correlated electron system
• Recent developments in the field of the metal-insulator transition in two dimensions
• Tunable Dirac interface states in topological superlattices
• Pressure-induced Superconductivity in Sulfur-doped SnSe Single Crystal Using Boron-doped Diamond Electrode-prefabricated Diamond Anvil Cell
• New state of matter: heavy-fermion systems, quantum spin liquids, quasicrystals, cold gases, and high temperature superconductors
• The influence of topological phase transition on the superfluid density of overdoped copper oxides
• Three-dimensional graphdiyne as a topological nodal-line semimetal
• Weyl Nodal Line-Surface Half-metal in CaFeO${}_3$
• Topological basis for understanding the behavior of the heavy-fermion metal $\beta -\mathrm{YbAl}{\mathrm{B}}_4$ under application of magnetic field and pressure
• Drumhead surface states and their signatures in quasiparticle scattering interference
• Manifestation of strong correlations in transport in ultra-clean SiGe/Si/SiGe quantum wells
• Observation of a flat and extended surface state in a topological semimetal
• 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
• Band Flattening and Landau Level Merging in Strongly-Correlated Two-Dimensional Electron Systems
• Common behavior of the scaled condensation energy for both high-$T_c$ and conventional superconductors
• Scaling behavior of the thermopower of the archetypical heavy-fermion metal $\mathrm{YbR}{\mathrm{h}}_2\mathrm{S}{\mathrm{i}}_2$
• Transport properties of strongly correlated Fermi systems
• Scaling behavior of superconductors
• Orbital Limit and Gaussian Fluctuation Effects in Flat Band Superconductors with PseudoMagnetic Fields