Pis’ma v ZhETF, vol. 111, iss. 2, pp. 86 - 87

January 25

Metamorphoses of electron systems hosting a fermion condensate

V. A. Khodel+∗1), J. W. Clark^∗×, M. V. Zverev+◦

⁺National Research Centre Kurchatov Institute, 123182 Moscow, Russia

^∗McDonnell Center for the Space Sciences & Department of Physics, Washington University, St. Louis, MO 63130, USA

^×Centro de Investigação em Matema’tica e Aplicações, University of Madeira, 9020-105 Funchal, Madeira, Portugal

^◦Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia

Submitted 31 October 2019

Resubmitted 3 December 2019

Accepted 4 December 2019

DOI: 10.31857/S0370274X2002006X

We present a theory of interaction-induced flat

significant advance toward a self-consistent theory of

bands, emergent in strongly correlated electron systems

fermion condensation has been made in microscopic

beyond a critical point, at which the topological sta-

calculations based on a Hubbard model, performed in

bility of the Landau state breaks down, and apply this

[11, 12] using well-established renormalization-group

theory to analysis of phenomena that, seemingly, have

methods. In addition, the original FC formalism was

little in common, including: (i) a specific metal-insulator

recently updated [13] to properly account for interac-

transition with formation of the so-called quantum elec-

tions between the FC and normal quasiparticles that

tron solid state in two-dimensional electron liquid, re-

has made it possible to explain the topological na-

siding in MOSFETs and SiGe/Si/SiGe quantum wells,

ture of the metal-insulator transition in two-dimensional

(ii) a second-order high-temperature superconducting

high-mobility electron systems of SiGe/Si/SiGe quan-

phase transition in copper oxides, whose critical tem-

tum wells [14-16].

perature T_c turns out to be proportional to the Fermi

The recent “second wind” of the original FC scenario

energy TF = p2F/2me and (iii) non-Fermi-liquid low-

has received specific impetus from the rapid progress in

temperature chaotic-like behavior of many strongly cor-

experimental (e.g., see [17-20]) and theoretical [21, 22]

related electron systems, documented in experimental

studies of doped monolayer graphene and, especially,

studies of their resistivity ρ(T ) for two last decades.

twisted bilayer graphene, where flattening of the single-

We propose that both these transitions are triggered

particle spectrum ϵ(p) can be engineered. In particular,

by a spontaneous topological rearrangement of the con-

in a recent experimental paper [23], the manifestation of

ventional Landau state that consists in formation of a

interaction-induced flat bands in the electron system of

so-called fermion condensate (FC) [1-3], an interaction-

monolayer graphene has been documented for the first

induced flat portion ϵ(p) = 0 of the single-particle

time. It is also expected [24, 25] that the dispersionless

spectrum ϵ(p). The analogy with a boson condensate

FC spectrum with singular density of states is the trig-

(BC) is evident from the respective densities of states

ger for possible granular room-temperature supercon-

ρ_FC(ε) = n_FCδ(ε) and ρ_BC(ε) = n_BCδ(ε), where n_FC

ductivity in highly oriented pyrolitic graphite [26, 27]

and n_BC denote the fermion and boson condensate den-

(and references therein).

sities. A distinctive feature of electron systems, harbor-

In dealing with 2D strongly correlated low-density

ing such flat bands, is the presence of a finite classical-

homogeneous electron liquid of MOSFETs we focus on

like entropy excess S0 = S(T = 0) ∝ nFC obtained

a specific metal-insulator transition uncovered long ago

upon substituting a zero-temperature FC momentum

in [28, 29], the nature of which remains unexplained

distribution 0 < n_∗(p) < 1 into the textbook Landau

yet. We demonstrate that proper accounting for interac-

formula.

tions between normal quasiparticles and the FC, emer-

The original model of fermion condensation was in-

gent at densities n, lower than the critical density n_t,

troduced and analyzed in [1-3] more than 25 years ago.

at which the topological stability of the original Lan-

With further theoretical development, evidence for its

dau state breaks down, results in formation of a spe-

essential role in coherent explanation of diverse non-

cific non-BCS gap Υ(p) in the single-particle spectrum,

Fermi-liquid behavior across a broad range of strongly

whose magnitude changes linearly with variation of the

correlated Fermi systems at low temperatures, has since

difference n_t - n. It is such a behavior of the activa-

been presented in numerous works, notably [1-10]. A

tion energy that has been uncovered in measurements

of the electrical resistivity of MOSFETs just in this

¹⁾e-mail: vak@wuphys.wustl.edu

density region [15] that reveals the topological nature

Письма в ЖЭТФ том 111 вып. 1 - 2

2020

Metamorphoses of electron systems hosting a fermion condensate

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Письма в ЖЭТФ том 111 вып. 1 - 2

2020