2017/04/30 by Matteo Ippoliti, Scott Geraedts, Scott D. Geraedts +1 · 13 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Connection (principal bundle) #Dispersion relation #Field (mathematics) #Geometry #Kinetic energy #Landau quantization #Magnetic field #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum and electron transport phenomena #Quantum mechanics #Symmetry (geometry) #Topological Materials and Phenomena #Zero (linguistics) #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.96.045145
published in Physical review. B./Physical review. B 96(4) (American Physical Society) · 7 pages + references, 7 figures. Added many-body DMRG calculation
openalex created_date 2017/05/05 · arxiv created 2017/07/11 · openalex publication_date 2017/07/31 · arxiv updated 2017/08/09 · openalex updated_date 2026/08/05
We investigate the relation between the Fermi sea (FS) of zero-field carriers in two-dimensional systems and the FS of the corresponding composite fermions which emerge in a high magnetic field at filling \ensuremathν=(1)/(2), as the kinetic energy dispersion is varied. We study cases both with and without rotational symmetry and find that there is generally no straightforward relation between the geometric shapes and topologies of the two FSs. In particular, we show analytically that the composite Fermi liquid (CFL) is completely insensitive to a wide range of changes to the zero-field dispersion which preserve rotational symmetry, including ones that break the zero-field FS into multiple disconnected pieces. In the absence of rotational symmetry, we show that the notion of ``valley pseudospin'' in many-valley systems is generically not transferred to the CFL, in agreement with experimental observations. We also discuss how a rotationally symmetric band structure can induce a reordering of the Landau levels, opening interesting possibilities of observing higher-Landau-level physics in the high-field regime.