Towards A Possible Charge-Kondo effect in Optical Lattices

📝 Abstract

The Kondo effect underpins a large body of recent developments in the physics of $d $- and $f $-band compounds. Although its {\it charge} analog is a rarity in solids, the recent observations of the charge Kondo effect and the consequent rise in superconducting T $_c$ encourage a search for other accessible systems. Motivated by the possibility of wilfully tuning the {\it sign} of the inter-electronic interaction in optical lattices, we study conditions for the elusive {\it charge Kondo liquid} (CKL) state to manifest. We propose that a combination of Feshbach resonances and sequentially controlled laser pulses may produce the CKL. We show that the CKL is {\it never} a stable ground state, appearing only when the ordered ground states are destabilized. Finally, we discuss interesting analogies with nuclear matter.

💡 Analysis

The Kondo effect underpins a large body of recent developments in the physics of $d $- and $f $-band compounds. Although its {\it charge} analog is a rarity in solids, the recent observations of the charge Kondo effect and the consequent rise in superconducting T $_c$ encourage a search for other accessible systems. Motivated by the possibility of wilfully tuning the {\it sign} of the inter-electronic interaction in optical lattices, we study conditions for the elusive {\it charge Kondo liquid} (CKL) state to manifest. We propose that a combination of Feshbach resonances and sequentially controlled laser pulses may produce the CKL. We show that the CKL is {\it never} a stable ground state, appearing only when the ordered ground states are destabilized. Finally, we discuss interesting analogies with nuclear matter.

📄 Content

arXiv:0811.1737v2 [cond-mat.str-el] 13 Aug 2009 Towards A Possible Charge-Kondo Effect in Optical Lattices M. S. Laad1, L. Craco2, and A. Taraphder1,4 1 Lehrstuhl f¨ur Theoretische Physik, Technische Universit¨at Dortmund, 44221 Dortmund, Germany 2Max-Planck-Institut f¨ur Chemische Physik fester Stoffe, 01187 Dresden, Germany 3Department of Physics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302 India 4Max-Planck-Institut f¨ur Physik komplexer Systeme, 01187 Dresden, Germany (Dated: November 3, 2018) The Kondo effect underpins a large body of recent developments in the physics of d- and f-band compounds. Although its charge analog is a rarity in solids, the recent observations of the charge Kondo effect and the consequent rise in superconducting Tc encourage a search for other accessible systems. Motivated by the possibility of wilfully tuning the sign of the inter-electronic interaction in optical lattices, we study conditions for the elusive charge Kondo liquid (CKL) state to manifest. We propose that a combination of Feshbach resonances and sequentially controlled laser pulses may produce the CKL. We show that the CKL is never a stable ground state, appearing only when the ordered ground states are destabilized. Finally, we discuss interesting analogies with nuclear matter. PACS numbers: 03.75.Ss, 71.10.Fd, 71.10.Hf The Kondo effect has historically played a monumental role in solid state physics [1], where quasi-bound state (singlet) formation involving a local moment screened by the itinerant electron spins leads a renormalized Fermi liquid (FL) with huge enhancements of quasiparticle masses, whence the name “heavy fermion”. Subsequently, more exotic, quadrupolar [2] and orbital [3] versions were invoked in other contexts. The destruction of FL behavior at quantum phase transitions near magnetic order in some f-electron systems is thought to be linked to “unbinding” of this Kondo quasi-bound singlet state [4]. However, the intriguing possibility of observing a charge analogue of the Kondo effect, requiring an attractive, local interaction, has not been addressed carefully. In practice, materials such as Ba1−x(K, Pb)xBiO3 are modelled by variants of U < 0 Hubbard model [5, 6, 7, 8]. Recent experimental realization [9] of the charge Kondo effect (CKE), predicted theoretically some time back [10], and the consequent rise of superconducting Tc in doped PbT e [11] and SnT e [9], has re-ignited interest in the U < 0 models. Here, chemical doping (≤2%) generates a narrow impurity band in the semiconductor band gap, facilitating use of a U < 0 lattice models in the intermediate-to-strong coupling limit (|U|/Wimp > 1). The interesting issues for theory are thus: What are the precise conditions under which a charge-Kondo Fermi liquid state (the CKL state) can appear? Is it ever a stable phase at zero temperature? Might a quantum phase transition (QPT), reminiscent of its well-studied spin analogue, occur, and if so, how? What instabilities might one generically expect to arise near such a QPT? Advances in artificially engineered fermionic/bosonic optical lattices allowing wilful manipulation of parameters open up yet another route to test model Hamiltonian predictions. Such systems may hold more promise for CKE, given the paucity of real materials exhibiting U < 0. In contrast to real materials, these systems are free of inhomogeneities. In this context, various interacting models have already been realized [12, 13]. The physical conditions for this lie well within the regime of experimental techniques available. In practice, different hyperfine states of same or different atomic species (acting, as it may, as different fermionic/bosonic species) can be trapped and controlled independently. A particularly attractive feature is their ready tunability: it is even possible to choose the sign of the interaction in such systems; a mixture of two fermionic species interacting via an attractive interaction is achieved by forcing a mixture of two such atomic spin states through a Feshbach resonance, whence a bound state appears in the two particle problem. A p-wave Feshbach resonance [14] can even create a tunable asymmetry in the interactions, allowing one to access more complex “hidden” ordered states. Further, the periodic potential of each species of atoms was independently tuned in an optical lattice [15]. This could facilitate observation of the band insulator (driven by staggered periodic lattice potential) to Mott insulator (due to on-site interaction, U) transition, and possible emergence of correlated metallic phases sandwiched between them. Optical lattices thus provide a unique tool to address interesting questions posed above. A suitable model for a two-component fermionic system (having an attractive two-body interaction), with temporally separated laser pulses simulating inter-site hybridization between the two spinless fermionic species (a, b) is described by the Hamiltonian H

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