Possible realization of odd-frequency pairing in heavy fermion compounds

Abstract

Using Majorana fermions to represent spins we reexamine the Kondo lattice model for heavy fermions. The simplest decoupling procedure provides a realization of odd-frequency superconductivity, with resonant pairing and surfaces of gap zeros. Spin and charge coherence factors vanish linearly with the energy on the Fermi surface, predicting a linear specific heat, but a T 3 NMR relaxation rate. Possible application to heavy fermions is suggested. PACS numbers: 75.20.Hr, 75.30.Mb, 75.40.Gb Though a decade and a half has passed since the discovery of the heavy fermion metals and superconductors [1,2], many experimental anomalies remain. While the basic theoretical picture of resonantly scattered conduction electrons forming a highly renormalized /band is not in question, certain experimental features fit awkwardly into the standard model [3][4][5][6][7]. The underlying nature of the interactions [8], the nature of the pairing [9], and the excitation spectrum of heavy fermion insulators [10] are three areas of continuing uncertainty.Conventional approaches to heavy fermion physics represent the / moments as fermions by enforcing a "Gutzwiller constraint" of unit occupancy n/=\ at each site. This requires a projection of the physical Hilbert space of the local moments from the larger Hilbert space of pseudo fermions: a task that is difficult to do exactly, and usually only treated on the average. In this Letter we examine an approach to a simple Kondo lattice model for heavy fermions that avoids these difficulties.Various new features are predicted that differ qualitatively from the standard model of heavy fermion behavior; most notably a development of strong correlations between the spin and pair degrees of freedom, forming a ground state where the conduction electrons experience frequency dependent or "resonant" triplet pairing. The pairing fields actually diverge at low frequencies as the inverse frequency, providing a first stable realization of the phenomenon of odd-frequency pairing originally considered by Berezinskii [1 1,12]. For a wide range of conditions, including the presence of spin-orbit coupling, this theory predicts surfaces of gapless excitations, and a linear specific heat that survives in the superconducting state. Unlike a conventional superconductor, the charge and spin coherence factors vanish on the pseudo Fermi surface, giving rise to a T 3 NMR relaxation. In this scenario, the linear specific heat anomalies often observed in heavy fermion superconductors [13] might be interpreted as intrinsic.A key feature of our approach is the use of a special anticommuting representation of spin-j operators to describe the magnetic excitations within the low-lying crystal field doublets of the heavy fermion ions [14]. Recall that for individual S = j objects, the Pauli matrices are anticommuting variables {<J Q ,Ob\ = 2d a t> and consequently can be treated as real or Majorana (cr f = a) Fermi fields. Their Fermi statistics alone guarantee that the spin operator S= j icrxa satisfies both the SU(2) algeb...

Spin Dynamics from Majorana Fermions

“…The calculation of these quantities requires a knowledge of both the four-leg vertex and the single-particle Green's function. Typically, the vertex is simply neglected, or treated in a very approximate fashion.An alternative approach is to take advantage of the anticommuting properties of Pauli matrices, writing the spin operator in terms of Majorana fermions [6,7,8,9,10],where η = (η 1 , η 2 , η 3 ) is a triplet of Majorana fermions which satisfy {η a , η b } = δ ab . This representation does not require the imposition of a constraint: the fact that S 2 = 3/4 follows directly from the operator properties of the Majorana fermions.…”

Possible Odd-Frequency Superconductivity in Strong-Coupling Electron–Phonon Systems

“…1) Two decades later, Balatsky and Abrahams revisited the singlet type of the OF pairing in the context of cuprates superconductors. [2][3][4] Since then, the OF pairing has been discussed in a wide variety of theoretical models, e.g., the Kondo lattice, [5][6][7][8][9] the square-lattice 10) and the triangularlattice [11][12][13] Hubbard, and t-J 14) models. A universal feature of superconductivity so far stimulates to discuss the OF pairing in connection with experimental reality in the heavyfermion systems, 15,16) superconducting junctions, [17][18][19][20][21][22][23][24][25][26][27][28][29][30] vortex core, 31,32) proximity effect of superfluid 3 He 33) and the cold atoms.…”

Odd triplet superconductivity in a superconductor/ferromagnet system with a spiral magnetic structure

“…It turned out however that in reality the condensate function in He 3 is an even function of ω and an odd function of p. Later a possibility to realize the odd (in frequency) triplet superconductivity in solids was discussed for various models in Refs. [14,15,16].…”