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Bose-Einstein condensate-mediated BCS-like superconductivity in graphene

Meng Juan Sun, Anton V. Parafilo, Kristian Hauser A. Villegas, V. M. Kovalev, Ivan G. Savenko

Published Sep 2, 2020• 0 citations
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Abstract

We propose a mechanism of robust BCS-like superconductivity in graphene placed in the vicinity of a Bose-Einstein condensate. Thus electrons in graphene interact with the excitations above the condensate, called the Bogoliubov quasiparticles (or bogolons). It turns out that bogolon-pair-mediated interaction allows us to surpass the long-standing problem of vanishing density of states of particles with a linear spectrum in the vicinity of the Dirac points. It results in a dramatic enhancement of the superconducting properties of graphene while keeping its relativistic dispersion. We study the behavior of the superconducting gap and calculate critical temperatures in the cases of single-bogolon and bogolon-pair-mediated pairing processes, accounting for the complex band structure of graphene. Surprisingly, both intravalley and intervalley bogolon-mediated pairings turn out equally possible.

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We propose a mechanism of robust BCS-like superconductivity in graphene placed in the vicinity of a Bose-Einstein condensate. Thus electrons in graphene interact with the excitations above the condensate, called the Bogoliubov quasiparticles (or bogolons). It turns out that bogolon-pair-mediated interaction allows us to surpass the long-standing problem of vanishing density of states of particles with a linear spectrum in the vicinity of the Dirac points. It results in a dramatic enhancement of the superconducting properties of graphene while keeping its relativistic dispersion. We study the behavior of the superconducting gap and calculate critical temperatures in the cases of single-bogolon and bogolon-pair-mediated pairing processes, accounting for the complex band structure of graphene. Surprisingly, both intravalley and intervalley bogolon-mediated pairings turn out equally possible.
Abstract We propose a mechanism for robust Bardeen–Cooper–Schrieffer-like superconductivity in graphene placed in the vicinity of a Bose–Einstein condensate. Electrons in the graphene interact with the excitations above the condensate, called Bogoliubov quasiparticles (or bogolons). It turns out that bogolon-pair-mediated interaction allows us to surpass the long-standing problem of the vanishing density of states of particles with a linear spectrum. This results in a dramatic enhancement of the superconducting properties of graphene while keeping its relativistic dispersion. We study the behavior of the superconducting gap and calculate critical temperatures in cases with single-bogolon and bogolon-pair-mediated pairing processes, accounting for the complex band structure of graphene. We also compare the critical temperature of the superconducting transition with the BKT temperature.
Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap E_{g}. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction-driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the Bose-Einstein condensate (BEC) regime at low densities. At a given larger density, a band gap E_{g}∼80-120 meV can carry the system into the strong-pairing multiband BCS-BEC crossover regime, the optimal range for realization of high-T_{c} superfluidity.
Achieving strong interactions in fermionic many-body systems is a major theme of research in condensed matter physics. It is well-known that interactions between fermions can be mediated through a bosonic medium, such as a phonon bath or Bose-Einstein condensate (BEC). Here we show that such induced attraction can be resonantly enhanced when the bosonic medium is a two-component spinor BEC. The strongest interaction is achieved by tuning the boson-boson scattering to the quantum critical spinodal point of the BEC where the sound velocity vanishes. The fermion pairing gap and the superconducting critical temperature can thus be dramatically enhanced. We propose two experimental realizations of this scenario, with exciton-polariton systems in two-dimensional semiconductors and ultracold atomic Bose-Fermi mixtures.
Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF ≤ 10-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.
The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.
We investigate the electromagnetic wave absorption process in a coherently coupled two-component Bose-Einstein condensate model in different dimensionality at zero temperature. As the analog of phonon in the solid state physics, the elementary excitation of the Bose-Einstein condensate is described by Bogoliubov quasiparticle or bogolon for short. Due to the small magnitude of the sound velocity of the bogolon, the absorption process is prohibited by the conservation of energy and momentum. To surmount this depression, the additional degree of freedom must be considered inside of the simple Bose gas model. In this article, we develop a microscopical theory for electromagnetic wave absorption by a two-component Bose-Einstein condensate and investigate the absorption rate dependence in different dimensions. Our calculation shows the possibility of manipulating the absorption property by tuning the parameters of the condensates.