Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study

Abstract

Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within a random phase approximation, these theories predict that the Landau damping of the gauge field resulting from its coupling to the low-energy, long-wavelength CF particle-hole excitations modifies the electrons' density-density correlation function related to the static structure factor $S(q)$ at wave vector $q$. This produces a non-analytic correction $\propto q^3\ln q$ to $S(q)$ (with the magnetic length ${\ell }_B=1$). Thanks to the recently developed quaternion formulation for Jain-Kamilla projection of CF wave functions, the evaluation of $S(q)$ from the accurate microscopic theory of composite fermions has now become possible for systems containing as many as $N=900$ CFs, which enables a reliable determination of the small-$q$ behavior of $S(q)$. We study CF metals corresponding to electrons at Landau level filling factors $\nu =1/2$ and $1/4$, and for completeness, also of bosons at $\nu =1$ and $1/3$. In the $q\to 0$ limit, our microscopic calculation reveals a $q^3$ term in $S(q)$ of the CF metals rather than $q^3\ln q$. This behavior is well-predicted by a model of a non-interacting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.

arXiv commentMain: 5 pages + 1 fig. SM: 5 pages + 3 figs. We welcome all comments

References in corpus (59)

• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Holographic metals and the fractionalized Fermi liquid
• Is the Composite Fermion a Dirac Particle?
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Singular Fermi Liquids
• Condensation of `composite bosons' in a rotating BEC
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Low Energy Dynamics of the Spinon-Gauge System
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Theory of a continuous Mott transition in two dimensions
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Recent Developments in Non-Fermi Liquid Theory
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Ultra-high quality two-dimensional electron systems
• Band Structure of the Fractional Quantum Hall Effect
• The half-filled Landau level: the case for Dirac composite fermions
• Universal theory of strange metals from spatially random interactions
• A dipole interpretation of the $\nu =1/2$ state
• Large $N$ theory of critical Fermi surfaces
• Quantum Hall physics in rotating Bose-Einstein condensates
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Composite fermi liquids in the lowest Landau level
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Response Function of the Fractional Quantized Hall State on a Sphere II: Exact Diagonalization
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Fermi-sea-like correlations in a partially filled Landau level
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Response Function of the Fractional Quantized Hall State on a Sphere I: Fermion Chern-Simons Theory
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Localization of overdamped bosonic modes and transport in strange metals
• Hamiltonian Theory of the Fractional Quantum Hall Effect: Effect of Landau Level Mixing
• Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Reconstructing the electron in a fractionalized quantum fluid
• STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states
• Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
• Composite Fermions and the Fermion-Chern-Simons Theory
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Emergent Fermi sea in a system of interacting bosons
• Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Dipole representation of half-filled Landau level
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Bipartite Fluctuations of Critical Fermi Surfaces
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Electromagnetic response of composite Dirac fermions in the half-filled Landau level
• Quantitative theory of composite fermions in Bose-Fermi mixtures at $\nu =1$
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions

Cited by in corpus (1)

• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere