Flat bands and strongly correlated Fermi systems

Abstract

Some materials can have the dispersionless parts in their electronic spectra. These parts are usually called flat bands and generate the corps of unusual physical properties of such materials. These flat bands are induced by the condensation of fermionic quasiparticles [1-3], being very similar to the Bose condensation. The difference is that fermions to condense, the Fermi surface should change its topology [1-4], leading to violation of time-reversal (T) and particle-hole (C) symmetries. Thus, the famous Landau theory of Fermi liquids does not work for the systems with fermion condensate (FC) so that several experimentally observable anomalies have not been explained so far.Here we use FC approach to explain recent observations of the asymmetric tunneling conductivity in heavy-fermion compounds and graphene [5][6][7] and its restoration in magnetic fields, as well as the violation of Leggett theorem [8,9], recently observed experimentally [10,11] in overdoped cuprates, and recent observation of the challenging universal scaling connecting linear-T -dependent resistivity to the superconducting superfluid density [12].

Effect of superconductivity on the shape of flat bands

“…1 (b) that both the particle -hole symmetry C and the time invariance T are violated resulting in the asymmetrical differential tunneling conductivity. This behavior has been predicted and evaluated [2,27,28], and turns out to be consistent with the experimental facts [14,[29][30][31].…”

Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review

“…The measured physical characteristic in the above methods is a differential tunneling conductivity or conductance. Asymmetric part of the conductance σ asym (V) ≡ I (V) − I (−V) (I ≡ dI/dV, where I is a tunneling current and V is a bias voltage) can be observed when a system with strongly correlated heavy fermions (like electrons and/or holes) is both in its normal and superconducting state [3][4][5][6][7][8][9]. We note that such an asymmetry does not occur in conventional metals, especially at low temperatures.…”

“…It is well known that partial C and T symmetries conserve for the systems of fermions, described by Landau theory. This implies that for these systems (like ordinary metals) σ d (V) is a symmetric function so that conductivity asymmetry is not observed in them at low T [8,10]. In the panel (a), at k i < k < k f (marked by dashed horizontal lines with k i and k f standing for initial and final momenta respectively) and T = 0.0001E F (blue curve), ε(k, T) is almost dispersionless and marked "Flat band".…”

“…In this case, to describe the observed asymmetric conductivity theoretically, one should inevitably use the FC approach [46]. We note that although fundamental microscopic interaction in the FC formalism is invariant with respect to quasiparticles and holes interchange, it yields spontaneous C and T symmetries breaking at low temperatures due to the topological reconstruction of the Fermi surface [1,3,[6][7][8]13,14]. This reconstruction yields the dependence of the quasiparticle spectrum ε(p) in FC phase on different external stimuli [11,12], which, in turn, generate NFL anomalies in observable properties of HF metals and high-T c superconductors.…”

Scattering Due to Non-magnetic Disorder in 2D Anisotropic d-wave High T&lt;sub&gt;c&lt;/sub&gt; Superconductors

“…For reviews on the question, whether a gap with nodes can explain experimental data on anisotropic HTSCs, please see [11,21,35]. For a discussion of other impurity effects affecting HTSCs and other unconventional superconductors, see [39].…”