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arXiv:2002.08445 · Physical review. B./Physical review. B

Potential coexistence of exciton and fermion-pair condensations

LeeAnn M. Sager-Smith, Shiva Safaei, David A. Mazziotti

Published Feb 18, 2020• 19 citations
arXivHTMLPDF

Abstract

An extensive theoretical and experimental investigation has been conducted on fermion-pair condensation and exciton condensation as distinct classes of Bose-Einstein-like condensation. In this Rapid Communication, the existence of a fermion-exciton condensate---a single quantum state in which the characters of both fermion-pair and exciton condensates coexist---is established computationally in the low-particle-number ($N$) limit and theoretically in the large-$N$ thermodynamic limit. The trade-off between the fermion-pair and excitonic character of the fermion-exciton condensate is shown to be elliptic in nature. The possibility that the properties of fermion-exciton condensates could be a hybrid of the properties of fermion-pair condensates and exciton condensates is discussed, and future experimental and computational exploration of this class of condensate, which may potentially be realizable in a bilayer of superconductors, is anticipated.

DOI
10.1103/physrevb.101.081107

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An extensive theoretical and experimental investigation has been conducted on fermion-pair condensation and exciton condensation as distinct classes of Bose-Einstein-like condensation. In this Rapid Communication, the existence of a fermion-exciton condensate---a single quantum state in which the characters of both fermion-pair and exciton condensates coexist---is established computationally in the low-particle-number (NNN) limit and theoretically in the large-NNN thermodynamic limit. The trade-off between the fermion-pair and excitonic character of the fermion-exciton condensate is shown to be elliptic in nature. The possibility that the properties of fermion-exciton condensates could be a hybrid of the properties of fermion-pair condensates and exciton condensates is discussed, and future experimental and computational exploration of this class of condensate, which may potentially be realizable in a bilayer of superconductors, is anticipated.
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Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state two-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phases, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.
Fermion-exciton condensates (FECs)---computationally and theoretically predicted states that simultaneously exhibit the character of superconducting states and exciton condensates---are novel quantum states whose properties may involve a hybridization of superconductivity and the dissipationless flow of energy. Here, we exploit prior investigations of superconducting states and exciton condensates on quantum devices to identify a tuneable quantum state preparation entangling the wave functions of the individual condensate states. Utilizing this state preparation, we prepare a variety of FEC states on quantum computers---realizing strongly correlated FEC states on current, noisy intermediate-scale quantum devices---and verify the presence of the dual condensate via postmeasurement analysis. This confirmation of the previously predicted condensate state on quantum devices as well as the form of its wave function motivates further theoretical and experimental exploration of the properties, applications, and stability of FECs.
In this thesis we study the spin or pseudospin singlet pair condensation of two different kinds of polarized fermion systems.Using generalized BCS mean-field theories we study how pairing adapts to unequal spin or pseudospin populations.After briefly reviewing the basic physics of superconductivity in Chapter 2, in Chapter 3 the mean-field theory for electron-hole bilayer systems is derived to describe the condensation of excitons which is analogous to the Cooper pair condensation in superconductors.Self-consistent solution of the exciton system gap equation shows that the excitation energy spectrum is qualitatively the same as in superconductors.In Chapter 4 the role of the spin degree of freedom in the bilayer system is investigated by generalizing the two-component mean-field theory developed in Chapter vi 3 to four-component cases.The main consequence is that population polarization leads to ferromagnetism.The interplay between exciton condensation and spontaneous spin-order is the most important consequence of the presence of both spin and pseudospin degrees of freedom in excitonic condensates.In a sense that we explain in this Chapter, both normal and condensed fluids are present in the ferromagnetic excitonic state.Using the Rashba spin-orbit interaction model derived in the appendix, we show that an external electric field can alter the characteristics of the ferromagnetic condensate phase.The spin splitting by the spin-orbit interaction and its different spin state structures lead to qualitatively different magnetic properties for electron and hole layers.In Chapter 5 we turn our attention to a second class of polarized fermion systems that is of great current interest.A fully quantum mechanical treatment of a rotating fermion atom cloud is developed and implicit equations determining the critical temperatures for all center-of-mass Landau level pairings are obtained.In Chapter 6 the condition for the realization of higher center-of-mass Landau level pairing, which corresponds to FFLO state in spin split superconductors, is determined by calculating the critical temperatures for all possible pairing channels.It is shown that FFLO states can be realized in the strong interaction and low rotation frequency regimes in parameter space, where the pairing energy can survive the high polarization.
Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.
Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.