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 the parameters of the system and generic. We discuss here the class of gapless topological media, which contains the quantum vacuum of Standard Model in its symmetric phase, and also the condensed matter systems with zeroes in the fermionic 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 the stability of the others the 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 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 thus can be essentially higher. So the p-space topology may give us the general recipe for the search or artificial fabrication of the room-temperature superconductors.PACS numbers: I. WEYL POINT, LEVEL CROSSING AND BERRY PHASE MONOPOLESome features of topological matter can be formulated in terms of the Berry's connection in momentum space p. For example, the Weyl points in the fermionic spectrum in Standard Model (SM) or in condensed matter Weyl materials such as superfluid 3 He-A, can be viewed as the Berry's phase monopoles in momentum space 1 . Such monopole represents the topologically nontrivial point of level crossing (the conical or diabolical point) in the 3D space of parameters, where the parameters are three components of the (quasi)particle momentum (p x , p y , p z ). Fig. 1 demonstrates the elementary case of the level crossing, where only two branches of spectra touch each other. Near the crossing point the complex n × n Hamiltonian is effectively reduced to the 2 × 2 matrixwhere σ are the Pauli matrices. In the vicinity of the Weyl point p (0) , only linear terms in expansion of the Hamiltonian are important, and one obtains the effective HamiltonianIn the non-uniform situation the parameters of expansion e i k and p (0) become the fields, and then the Hamiltonian (2) describes the Weyl relativis...

Scaling behavior of the thermopower of the archetypal heavy-fermion metal YbRh2Si2

“…In such an event, quasiparticles of energy ε remain welldefined excitations near the chemical potential µ, ε ∼ µ [3,4], while the FC state itself is protected by topological invariants [17,18]. In the vicinity of FCQPT it is helpful to use "internal" scales to measure such quantities as e.g.…”

The influence of topological phase transition on the superfluid density of overdoped copper oxides

“…These observations representing the intrinsic LSCO properties provide unique opportunities for checking and expanding our understanding of the physical mechanisms responsible for high-T c superconductivity. We note, that that knowing the responsible mechanism can open avenue for chemical preparation of high-T c materials with T c as high as room temperature [8][9][10][11][12] .…”

“…Here we show that the physical mechanism, responsible for above non-BCS behavior of overdoped LSCO, stems from the topological fermion condensation quantum phase transition (FCQPT) accompanied by so-called fermion condensation (FC) phenomenon generating flat bands [8][9][10][11][12][13][14] . We note that flat bands and extended saddle point singularity play important role in the theory of HTSC, see e.g.…”

“…We emphasize that the quantum physics of all seemingly different strongly correlated Fermi systems (and overdoped HTSC among them) is universal and emerges regardless of their underlying microscopic details like the symmetries of their crystal lattices. Because we deal effectively with momenta transfers that are small compared to those of the order of the reciprocal lattice length (Brillouin zone boundaries), whose contributions have no effect on the topological properties of the systems under consideration [9][10][11][12]14 . Note that despite the highly anisotropic electronic band dispersion in overdoped cuprate HTSC and hence their Fermi surface, our theory still applies for this case.…”

“…We demonstrate that: i) at T = 0, the superfluid density n s turns out to be a small fraction of the total density of electrons; ii) the critical temperature T c is controlled by n s rather than by doping, and is a linear function of the n s . Since FCQPT generates flat electronic bands [8][9][10][11][12] , the system under consideration exhibits non-Fermi liquid (NFL) behavior and the resistivity ρ(T ) varies linearly with temperature, ρ(T ) ∝ αT . Since at x → x c α diminishes with T c decreasing, the system exhibits Landau Fermi liquid (LFL) behavior at x > x c and at low temperatures.…”