Comptes Rendus
no. 9-10
Topological insulators/Isolants topologiques
Fractional quantum Hall physics in topological flat bands
[Physique de lʼeffet Hall quantique fractionnaire dans des bandes plates topologiques]
Siddharth A. Parameswaran1  ; Rahul Roy2 ; Shivaji L. Sondhi3
1 Department of Physics, University of California, Berkeley, CA 94720, United States of America
2 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, United States of America
3 Department of Physics, Princeton University, Princeton, NJ 08544, United States of America
Comptes Rendus. Physique, Volume 14 (2013) no. 9-10, pp. 816-839.

Nous présentons une revue didactique sur la physique des isolants de Chern, qui se concentre plus particulièrement sur lʼeffet Hall quantique fractionnaire. Habituellement, cet effet apparaît typiquement dans des hétérostructures semiconductrices à basse température et sous champ magnétique fort. En revanche, les isolants de Chern peuvent abriter des phases topologiques aux propriétés similaires, mais stabilisées à lʼéchelle du paramètre de réseau, ce qui peut conduire un ordre topologique à haute température. Nous décrivons la construction des modèles avec bande(s) plate(s), passons en revue les résultats numériques et établissons une comparaison entre les isolants de Chern sur réseau et le problème de Landau défini dans le continuum. Nous discutons alors brièvement les aspects de la physique des isolants de Chern qui nont pas dʼanalogues dans le continuum, avant de passer aux possibles réalisations expérimentales. Nous concluons par une liste de perspectives et de problèmes encore ouverts dans ce domaine, ainsi que par une discussion des extensions de ces idées à des dimensions supérieures et à dʼautres phases topologiques.

We present a pedagogical review of the physics of fractional Chern insulators with a particular focus on the connection to the fractional quantum Hall effect. While the latter conventionally arises in semiconductor heterostructures at low temperatures and in high magnetic fields, interacting Chern insulators at fractional band filling may host phases with the same topological properties, but stabilized at the lattice scale, potentially leading to high-temperature topological order. We discuss the construction of topological flat band models, provide a survey of numerical results, and establish the connection between the Chern band and the continuum Landau problem. We then briefly summarize various aspects of Chern band physics that have no natural continuum analogs, before turning to a discussion of possible experimental realizations. We close with a survey of future directions and open problems, as well as a discussion of extensions of these ideas to higher dimensions and to other topological phases.

Publié le :
DOI : 10.1016/j.crhy.2013.04.003
Keywords: Chern insulators, Flat bands, Fractional quantum Hall effect, Topological order
Mot clés : Isolants de Chern, Bandes plates, Effet Hall fractionnaire, Ordre topologique
Siddharth A. Parameswaran 1 ; Rahul Roy 2 ; Shivaji L. Sondhi 3

1 Department of Physics, University of California, Berkeley, CA 94720, United States of America
2 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, United States of America
3 Department of Physics, Princeton University, Princeton, NJ 08544, United States of America 
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     pages = {816--839},
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Siddharth A. Parameswaran; Rahul Roy; Shivaji L. Sondhi. Fractional quantum Hall physics in topological flat bands. Comptes Rendus. Physique, Volume 14 (2013) no. 9-10, pp. 816-839. doi : 10.1016/j.crhy.2013.04.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.04.003/

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