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arXiv:1202.3444 · Physical Review Letters

Microscopic Model of Quasiparticle Wave Packets in Superfluids, Superconductors, and Paired Hall States

S. A. Parameswaran, Steven Allan Kivelson, R. Shankar, Shivaji L. Sondhi, Boris Z. Spivak

Published Dec 5, 2012• 9 citations
arXivHTMLPDF

Abstract

We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

DOI
10.1103/physrevlett.109.237004

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We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.
We show that, in the presence of Coulomb interactions, the charge of a quasiparticle in a fully gapped superconductor is a sharp quantum observable. It follows that the familiar Bogoliubov quasiparticles are neutral, spin-1/2 fermions. Since the current-carrying collective modes are spinless, charge and spin are carried by separate excitations in a superconductor. The quantum numbers of these quasiparticles are identical to those of a spinon in a ``resonating-valence-bond'' (RVB) superconductor. This supports the notion that a RVB superconductor is simply a strong-coupling version of a BCS superconductor. We describe an experiment that would directly verify the separation of charge and spin in a bulk superconductor.
The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator 52\frac{5}{2}25​ occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper pairing of underlying quasiparticles, composite fermions (CFs), leads to the explanation of this effect. Such a state should have a Pfaffian form of the BCS wave function (due to the fully polarized spin) and non-Abelian statistics of possible vortexlike excitations (due to the ppp-wave nature of the pairing). Here we expose the origin of pairing by using the effective dipole representation of the problem and show that pairing is encoded in a Hamiltonian that describes the interaction of the charge density with dipoles, i.e., the current of CFs. The necessary condition for the paired state to exist is the effective dipole physics at the Fermi level as a consequence of the nontrivial topology of the ideal band in which electrons live, a Landau level (LL); the paired state is a resolution of the unstable, critical behavior characterized by the distancing of correlation hole with respect to electron (and thus dipole) at the Fermi level due to the topology. We describe analytically this deconfined critical point, at which deconfinement of Majorana neutral fermions takes place. In the presence of large, short-range repulsive interaction inside a LL, the critical behavior may be stabilized into a regularized Fermi-liquid-like state, like the one that characterizes the physics in the lowest LL, but in general, for an interaction with slowly decaying pseudopotentials, the system is prone to pairing.
This paper reviews progress on the Fractional Quantum Hall Effect (FQHE) based on what we term hamiltonian theories, i.e., theories that proceed from the microscopic electronic hamiltonian to the final solution via a sequence of transformations and approximations, either in the hamiltonian or path integral approach, as compared to theories based on exact diagonalization or trial wavefunctions. We focus on the Chern-Simons (CS) approach in which electrons are converted to CS fermions or bosons that carry along flux tubes and our Extended Hamiltonian Theory (EHT) in which electrons are paired with pseudo-vortices to form composite fermions (CF) whose properties are a lot closer to the ultimate low-energy quasiparticles. We address a variety of qualitative and quantitative questions: In what sense do electrons really bind to vortices? What is the internal structure of the Composite Fermion and what does it mean? What exactly is the dipole picture? How are (approximate) transport gaps, zero-temperature magnetic transitions, the temperature dependent polarizations of gapped and gapless states, the NMR relaxation rate 1/T11/T_11/T1​ in gapless states, and gaps in inhomogeneous states computed? It is seen that though the CS and EHT approaches agree whenever a comparison is possible, results that are transparent in one approach are typically opaque in the other, making them truly complementary.
The effects of possible superfluidity on the cranking moment of a large many-fermion system moving under periodic boundary conditions are investigated within the framework of the theory of superconductivity recently formulated by Bogolyubov. The Hamiltonian is initially subjected to Bogolyubov's general unitary transformation. The collective excitations of the fermions are then considered in the usual pair approximation; the appropriate cranking terms are linear in the boson pair operators. On performing a unitary transformation which transforms away these linear terms, one obtains an expression for the moment of inertia of the system which includes both the effects of possible superfluidity and collective excitation. This expression, by virtue of its being stationary with respect to arbitrary variations in the amplitude associated with the latter unitary transformation, is then utilized as a variational principle for the moment of inertia. For the normal state, the result previously obtained by the author, that the moment of inertia has the rigid value, is rederived in more compact form. For the superfluid state, one finds that collective excitations effect a marked increase in the superfluid moment at intermediate coupling strengths although the resulting moment is still quite small compared to the rigid value. In contrast to the normal state case, where particle-hole pairs play a major role, this increase is almost entirely due to excitations consisting of particle-pairs or hole-pairs. The precise magnitude of the apparent resonance in the moment produced by the ddd-wave part of the cranking interaction is dependent to some extent on the features of the particle-particle potential which leads to the superfluid state. Variational expressions for the moment are exhibited for both Yukawa and delta-function shell potentials. These results are identical in charged and neutral Fermi systems. A calculation of the cranking moment at finite temperatures is presented in an Appendix along with an interpretation of it in terms of Bardeen's two-fluid model of superconductivity.
We propose a modified BCS wavefunction as the ground state of a correlated superconductor with the correlation specified between kkk and −k-k−k electrons in the reciprocal space. Owing to this correlation, low-energy excitations are not conventional BCS Bogoliubov quasiparticles. They display at least four poles in the Green's function and their particle-hole weights in the tunneling and photon-emission spectrum become asymmetric. The superfluid density or superfluid stiffness also deviates from the BCS predictions with finite paramagnetic terms inside the total diamagnetic response. Moreover, a ddd-wave correlated pairing state becomes robust against weak disorders. Hence, this state can explain many mysterious features observed in unconventional superconductors like cuprates.