Interacting Composite Fermions

There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\ensuremath{\nu}=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\ensuremath{\nu}=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\ensuremath{\nu}=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\ensuremath{\nu}=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.

arXiv:0804.1635Physical Review BJun 5, 200812 citations

POSSIBLE NEW PHASES OF COMPOSITE FERMIONS

V. W. Scarola, Seong-Young Lee, Jainendra K. Jain

When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].

International Journal of Modern Physics BAug 30, 20020 citations

Paired Composite Fermions

Gunnar M oller

Bulletin of the American Physical SocietyMar 19, 20100 citations

Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect

Ajit Coimbatore Balram, Jainendra K. Jain

The particle-hole (PH) symmetry of electrons is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. We investigate an emergent symmetry in the fractional quantum Hall effect, namely, the PH symmetry of composite fermions, which relates states at composite fermion filling factors ${\ensuremath{\nu}}^{*}=n+\overline{\ensuremath{\nu}}$ and ${\ensuremath{\nu}}^{*}=n+1\ensuremath{-}\overline{\ensuremath{\nu}}$, where the integer $n$ is the $\mathrm{\ensuremath{\Lambda}}$-level index and $0\ensuremath{\le}\overline{\ensuremath{\nu}}\ensuremath{\le}1$. Detailed calculations using the microscopic theory of composite fermions demonstrate the following for low-lying $\mathrm{\ensuremath{\Lambda}}$ levels (small $n$ ): (i) The two-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $\mathrm{\ensuremath{\Lambda}}$ level; and (ii) the three-body interaction for composite fermions is an order of magnitude smaller than the two-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $\mathrm{\ensuremath{\Lambda}}$ levels, which is also supported by exact-diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $\ensuremath{\nu}=\frac{n+\overline{\ensuremath{\nu}}}{2(n+\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$ and $\ensuremath{\nu}=\frac{n+1\ensuremath{-}\overline{\ensuremath{\nu}}}{2(n+1\ensuremath{-}\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $\mathrm{\ensuremath{\Lambda}}$-level index, the two-body and three-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $\ensuremath{\nu}=1/2$.The particle-hole (PH) symmetry of electrons is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. We investigate an emergent symmetry in the fractional quantum Hall effect, namely, the PH symmetry of composite fermions, which relates states at composite fermion filling factors ${\ensuremath{\nu}}^{*}=n+\overline{\ensuremath{\nu}}$ and ${\ensuremath{\nu}}^{*}=n+1\ensuremath{-}\overline{\ensuremath{\nu}}$, where the integer $n$ is the $\mathrm{\ensuremath{\Lambda}}$-level index and $0\ensuremath{\le}\overline{\ensuremath{\nu}}\ensuremath{\le}1$. Detailed calculations using the microscopic theory of composite fermions demonstrate the following for low-lying $\mathrm{\ensuremath{\Lambda}}$ levels (small $n$): (i) The two-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $\mathrm{\ensuremath{\Lambda}}$ level; and (ii) the three-body interaction for composite fermions is an order of magnitude smaller than the two-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $\mathrm{\ensuremath{\Lambda}}$ levels, which is also supported by exact-diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $\ensuremath{\nu}=\frac{n+\overline{\ensuremath{\nu}}}{2(n+\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$ and $\ensuremath{\nu}=\frac{n+1\ensuremath{-}\overline{\ensuremath{\nu}}}{2(n+1\ensuremath{-}\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $\mathrm{\ensuremath{\Lambda}}$-level index, the two-body and three-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $\ensuremath{\nu}=1/2$.

arXiv:1711.01771Physical review. B./Physical review. BDec 29, 201718 citations

Second Generation of Composite Fermions

M. O. Goerbig, Pascal Lederer, C. Morais Smith

arXiv:cond-mat/0308021Aug 1, 20030 citations

n

is the $\mathrm{\ensuremath{\Lambda}}$-level index and $0\ensuremath{\le}\overline{\ensuremath{\nu}}\ensuremath{\le}1$. Detailed calculations using the microscopic theory of composite fermions demonstrate the following for low-lying $\mathrm{\ensuremath{\Lambda}}$ levels (small

n

): (i) The two-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $\mathrm{\ensuremath{\Lambda}}$ level; and (ii) the three-body interaction for composite fermions is an order of magnitude smaller than the two-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $\mathrm{\ensuremath{\Lambda}}$ levels, which is also supported by exact-diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $\ensuremath{\nu}=\frac{n+\overline{\ensuremath{\nu}}}{2(n+\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$ and $\ensuremath{\nu}=\frac{n+1\ensuremath{-}\overline{\ensuremath{\nu}}}{2(n+1\ensuremath{-}\overline{\ensuremath{\nu}})\ifmmode\pm\else\textpm\fi{}1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $\mathrm{\ensuremath{\Lambda}}$-level index, the two-body and three-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $\ensuremath{\nu}=1/2$.