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Bighin, Giacomo (2016) Mean field and fluctuations for fermionic systems: from ultracold Fermi gases to cuprates. [Tesi di dottorato]

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Abstract (inglese)

This Thesis analyzes the role of a mean-field theory and of the fluctuations in two different fermionic systems: the BCS-BEC crossover and high-Tc superconducting cuprates.

In the first part of the Thesis we introduce the mean-field theory and the Gaussian-level fluctuations for the BCS-BEC crossover, i.e. the continuous evolution observed in ultracold neutral fermionic systems, from a weakly-coupled regime where fermions form Cooper pairs, to a strongly-coupled regime where the fermions at first form bosonic molecular dimers, subsequently undergoing Bose-Einstein condensation for low enough temperatures. We then analyze some problems related to the crossover: the condensate fraction for a spin-unbalanced Fermi gas, the Beliaev decay for collective excitations and the case of a two-dimensional Fermi gas, for which we calculate the first sound velocity and the Berezinskii-Kosterlitz-Thouless critical temperature, in very good agreement with recent experimental data. Finally we analyze a regularization procedure for the equation of state in the deep-BEC limit, allowing one to analytically derive the correct ratio between the fermionic and bosonic scattering lengths.

In the second part of the Thesis we introduce a gauge approach to superconductivity in cuprates in which the hole is decomposed as the product of a spinful neutral particle, the spinon, and a spinless charged particle, the holon. The statistics of each particle is modified by binding it to a gauge field providing a statistical flux, this approach being analogous to Chern-Simons bosonization. We thus obtain a model characterized by three characteristic temperatures corresponding, respectively, to the appearance of a finite density of incoherent holon pairs, of a finite density of incoherent spinon pairs and, finally, to the phase coherence leading to superconductivity.

Specifically in the present Thesis within this model we study the superfluid density, demonstrating that the spinon and holon contributions sum according to a Ioffe-Larking-like rule, analogous to that they found for resistivity, showing excellent agreement with experimental data in the moderate underdoping up to optimal doping region. We also demonstrated that the formalism reproduces the quasi-universality observed in experimental data at different dopings and allows for an analytical derivation of a relation that approximates the Uemura relation for moderate dopings.

Abstract (italiano)

Questa tesi analizza il ruolo della teoria di campo medio e delle fluttuazioni in due differenti sistemi fermionici: il crossover BCS-BEC e i cuprati superconduttori ad alta temperatura critica.

Nella prima parte della tesi si introduce la teoria di campo medio e le fluttuazioni a livello Gaussiano per il crossover BCS-BEC, i.e. l’evoluzione continua osservata in sistemi ultrafreddi di fermioni neutri, da un regime di accoppiamento debole dove i fermioni formano coppie di Cooper, ad un regime di accoppiamento forte dove i fermioni formano dapprima dimeri molecolari bosonici, i quali poi condensano a temperature sufficientemente basse. Si analizzano alcuni problemi correlati al crossover: la frazione condensata nel caso di un gas di Fermi con sbilanciamento di spin, il decadimento di Beliaev per le eccitazioni collettive e il caso di un gas di Fermi bidimensionale, per il quale in particolare si calcolano la velocità del primo suono e le temperatura critica di Berezinskii-Kosterlitz-Thouless, in accordo molto buono con recenti dati sperimentali. Infine si analizza una procedura di regolarizzazione per l’equazione di stato nel limite deep-BEC che permette di derivare analiticamente il corretto rapporto tra la lunghezza di scattering fermionica e bosonica.

Nella seconda parte della tesi si introduce un approccio di gauge alla superconduttività nei cuprati nel quale la buca è decomposta nel prodotto di una particella che porta solo spin, lo spinone, e una particella che porta solo carica, l’holone. La statistica di ciascuna particella è modificata accoppiandola ad un campo di gauge che fornisce un flusso statistico, in un approccio analogo alla bosonizzazione di Chern-Simons. Si ottiene quindi un modello che prevede tre temperature caratteristiche che corrispondono, rispettivamente, alla comparsa di una densità finita di coppie di holoni incoerenti, di una densità finita di coppie di spinoni incoerenti e infine alla coerenza di fase che dà luogo alla superconduttività.

In particolare in questa tesi all'interno di tale modello si studia la densità di superfluido, dimostrando che il contributo spinonico e quello holonico si sommano secondo una regola del tutto analoga a quella di Ioffe-Larkin per la resistività, mostrando un ottimo accordo con i dati sperimentali nella regione di doping moderato fino all'optimal doping. Si dimostra anche il formalismo riproduce la quasi-universalità in doping osservata nei dati sperimentali e permette la derivazione analitica di una relazione che approssima la relazione di Uemura per doping moderati.

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Tipo di EPrint:Tesi di dottorato
Relatore:Salasnich, Luca
Correlatore:Marchetti, Pieralberto
Dottorato (corsi e scuole):Ciclo 28 > Scuole 28 > FISICA
Data di deposito della tesi:01 Febbraio 2016
Anno di Pubblicazione:01 Febbraio 2016
Parole chiave (italiano / inglese):BCS-BEC crossover, ultracold Fermi gases, ultracold quantum matter, quantum matter, cuprates, superconductivity, condensed matter, bosonization
Settori scientifico-disciplinari MIUR:Area 02 - Scienze fisiche > FIS/03 Fisica della materia
Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Struttura di riferimento:Dipartimenti > Dipartimento di Fisica e Astronomia "Galileo Galilei"
Codice ID:9535
Depositato il:24 Ott 2016 14:36
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