Doping quantum spin liquids on the Kagome lattice

TL;DR

This paper reviews DMRG studies showing that lightly doping quantum spin liquids on the kagome lattice tends to produce insulating charge-density-wave states with short-range spin correlations, rather than high-temperature superconductivity.

Contribution

It demonstrates that doping kagome QSLs generally results in insulating CDW states, extending findings to various QSL types and analyzing the effects of second-neighbor hopping.

Findings

Doping leads to long-range CDW order with one doped hole per unit cell.

Superconducting correlations remain short-ranged but are enhanced by second-neighbor hopping.

Results are relevant to kagome materials and their potential phases.

Abstract

We review recent density-matrix renormalization group (DMRG) studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high-temperature superconductivity, have been theoretically anticipated we find instead a tendency toward fractionalized insulating charge-density-wave (CDW) states. In agreement with earlier work (Jiang, Devereaux, and Kivelson, Phys. Rev. Lett. ${\bf 119}$, 067002 (2017)), results for the $t$-$J$ model reveal that starting from a fully gapped QSL, light doping leads to CDW long-range order with a pattern that depends on lattice geometry and doping concentration such that there is one doped-hole per CDW unit cell, while the spin-spin correlations remain short-ranged. Alternatively, this state can be viewed as a stripe crystal or Wigner crystal of spinless holons, rather than doped holes. From here, by studying generalized versions of the $t$-$J$ model, we extend these results to light doping of other types of QSLs, including critical and chiral QSLs. Our results suggest that doping these QSLs also leads to insulating states with long-range CDW orders. While the superconducting correlations are short-ranged, they can be significantly enhanced by second-neighbor electron hopping. The relevance of our numerical results to Kagome materials is also discussed.