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arXiv:cond-mat/0510519 · Physical Review B

Excitonic pairing between nodal fermions

Dmitri V. Khveshchenko, William Shively

Published Mar 10, 2006• 52 citations
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Abstract

We study excitonic pairing in nodal fermion systems characterized by a vanishing quasiparticle density of states at the pointlike Fermi surface and a concomitant lack of screening for long-range interactions. By solving the gap equation for the excitonic order parameter, we obtain a critical value of the interaction strength for a variety of power-law interactions and densities of states. We compute the free energy and analyze possible phase transitions, thus shedding further light on the unusual pairing properties of this peculiar class of strongly correlated systems.

DOI
10.1103/physrevb.73.115104

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We study excitonic pairing in nodal fermion systems characterized by a vanishing quasiparticle density of states at the pointlike Fermi surface and a concomitant lack of screening for long-range interactions. By solving the gap equation for the excitonic order parameter, we obtain a critical value of the interaction strength for a variety of power-law interactions and densities of states. We compute the free energy and analyze possible phase transitions, thus shedding further light on the unusual pairing properties of this peculiar class of strongly correlated systems.
We study excitonic pairing in nodal fermion systems characterized by a vanishing quasiparticle density of states at the pointlike Fermi surface and a concomitant lack of screening for long-range interactions. By solving the gap equation for the excitonic order parameter, we obtain a critical value of the interaction strength for a variety of power-law interactions and densities of states. We compute the free energy and analyze possible phase transitions, thus shedding further light on the unusual pairing properties of this peculiar class of strongly correlated systems.
Modern condensed matter physics owes much of its success to Fermi liquid theory. In recent times, however, the study of strongly correlated particle systems is opening up all-new territory in many-body physics. A peculiar class of such systems, that of nodal fermions, is characterized by the quasiparticle density of states vanishing at the point-like Fermi surface and long-range inter-particle interactions surviving unscreened. In the first part, I discuss fermion pairing in one such system, 2D graphene. By solving the gap equation for the excitonic order parameter, I obtain values of critical interaction strength for a variety of power-law interactions and densities of states. Furthermore, these results are then used to compute the respective free energies and analyze possible phase transitions. In the second part, I discuss the effects of lattice disorder and impurities on the density of states in nodal fermion systems. These results and predictions will be of interest to a broad range of physical problems involving nodal fermions, and can be tested in a variety of experimental directions.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles.
The Hubbard model of attractively interacting fermions provides a paradigmatic setting for fermion pairing. It features a crossover between Bose-Einstein condensation of tightly bound pairs and Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs, and a "pseudo-gap" region where pairs form above the superfluid critical temperature. We directly observe the nonlocal nature of fermion pairing in a Hubbard lattice gas, using spin- and density-resolved imaging of [Formula: see text]1000 fermionic potassium-40 atoms under a bilayer microscope. Complete fermion pairing is revealed by the vanishing of global spin fluctuations with increasing attraction. In the strongly correlated regime, the fermion pair size is found to be on the order of the average interparticle spacing. Our study informs theories of pseudo-gap behavior in strongly correlated fermion systems.