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arXiv:cond-mat/0310089 · Physical Review B

Non-Abelian Berry phase and Chern numbers in higher spin-pairing condensates

Chyh-Hong Chern, Han-Dong Chen, Congjun Wu, Jiangping Hu, Shoucheng Zhang

Published Jun 18, 2004• 17 citations
arXivHTMLPDF

Abstract

We show that the non-Abelian Berry phase emerges naturally in the $s$-wave and spin quintet pairing channel of spin-$3∕2$ fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This topological structure can be realized in ultracold atomic systems and in solid state systems with at least two Kramers doublets.

DOI
10.1103/physrevb.69.214512

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We show that the non-Abelian Berry phase emerges naturally in the sss-wave and spin quintet pairing channel of spin-3∕23∕23∕2 fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This topological structure can be realized in ultracold atomic systems and in solid state systems with at least two Kramers doublets.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from sss-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard sss-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.
Two-component fermionic superfluids on a lattice with an external non-Abelian gauge field give access to a variety of topological phases in the presence of a sufficiently large spin imbalance. We address here the important issue of superfluidity breakdown induced by spin imbalance by a self-consistent calculation of the pairing gap, showing which of the predicted phases will be experimentally accessible. We present the full topological phase diagram, and we analyze the connection between Chern numbers and the existence of topologically protected and non-protected edge modes. The Chern numbers are calculated via a very efficient and simple method.
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