Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1

The theory of composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level, which provides the relevant degrees of freedom in the limit of strong magnetic field. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor nu = 1 has been formulated by Dong and Senthil [Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)]. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of a composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor nu = 1. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, nu b = 1 - nu f. This tunability enables us to study the dilute limit nu b << 1, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate that gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau- Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of nu f << 1, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.

Automated summary

The theory of composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. Recently, a low-energy noncommutative field theory for bosons at Landau-level filling factor nu = 1 has been formulated, which reduces to the celebrated Halperin-Lee-Read theory in certain limits. In this work, a Bose-Fermi mixture at total filling factor nu = 1 is considered, and the number density and Fermi momentum of composite fermions can be tuned by changing the filling factor of bosons. In the dilute limit, the energy dispersion and effective mass of composite fermions can be calculated exactly, and the approximation of a commutative field theory is justified.