While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.
While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.
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 nonanalytic correction ∝q^{3}lnq to S(q) (with the magnetic length ℓ_{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 ν=1/2 and 1/4, and for completeness, also of bosons at ν=1 and 1/3. In the q→0 limit, our microscopic calculation reveals a q^{3} term in S(q) of the CF metals rather than q^{3}lnq. This behavior is well predicted by a model of a noninteracting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.
Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well established microscopic theory of the fractional quantum Hall effect and the 1/2 state, which is based on {\em non-relativistic} composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor ν=1/2 corresponds to an effective time reversal transformation (i.e. {kj}→{−kj}) for composite fermions, and discuss how this connects to the absence of 2kF backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion Λ levels (analogs of electronic Landau levels) we determine the Λ level spacing and find it to be very nearly independent of the Λ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a normal form for the unprojected wave functions of the n/(2pn−1) states that correctly capture the topological properties even without lowest Landau level projection.
Composite Fermi liquids (CFLs) are compressible states that can occur for 2D interacting fermions confined in the lowest Landau level at certain Landau level fillings. They have been understood as Fermi seas formed by composite fermions which are bound states of electromagnetic fluxes and electrons as reported by Halperin, Lee, and Read [Phys. Rev. B 47, 7312 (1993)PRBMDO0163-182910.1103/PhysRevB.47.7312]. At half filling, an explicitly particle-hole symmetric theory based on Dirac fermions was proposed by Son [Phys. Rev. X 5, 031027 (2015)PRXHAE2160-330810.1103/PhysRevX.5.031027] as an alternative low energy description. In this work, we investigate the Berry curvature of CFL model wave functions at a filling fraction of one-quarter, and observe that it is uniformly distributed over the Fermi sea except at the center where an additional π phase was found. Motivated by this, we propose an effective theory which generalizes Son's half filling theory, by internal gauge flux attachment, to all filling fractions in which fermionic CFLs can occur. The numerical results support the idea of internal gauge flux attachment.
In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that "composite fermions"--bound states of an electron with two magnetic flux quanta--can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2k(F) backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.
The physics of two-dimensional electron gas in a perpendicular magnetic field, i.e., the quantum Hall system, is remarkably rich. At half filling of the lowest Landau level, it has been predicted that "composite fermions"---emergent quasiparticles consisting of an electron attached to two magnetic flux quanta---experience zero net magnetic field and form a Fermi sea, dubbed composite Fermi liquid (CFL). However, despite its seemingly simple appearance, CFL is a strongly correlated quantum many-body state in disguise, and solving it in a controlled manner is extremely difficult, to the extent that the thermodynamic properties of CFL remain largely unknown. In this work, we perform state-of-the-art thermal tensor network simulations of the ν=1/2 Landau level system and observe low-temperature power-law behaviour of the specific heat, signaling the gapless nature of CFL. More importantly, the power is extracted to be close to 2/3, clearly deviating from the ordinary linear-T behaviour of Fermi liquid, suggesting coupling between the CFs and the dynamical emergent gauge field and thereby revealing the quantum many-body nature of the CFL state.
Here, the authors investigate the possibility that particle-hole symmetry in the lowest Landau level at half filling arises as an emergent low-energy symmetry. Specifically, they start with the traditional approach to the half-filled Landau level: an effective field theory known as the composite Fermi liquid pioneered by Halperin, Lee, and Read. In this theory, composite fermions arise when flux is attached to electrons in a half-filled Landau level. However, an equivalent starting point is one where one starts with a filled Landau level, depletes electrons (or equivalently, adds holes) to the point of half filling. One then attaches flux to the holes, and the resulting composite hole description is another viable description of the half-filled Landau level. The authors construct a particle-hole symmetric theory by studying a system consisting of alternating quasi-one-dimensional strips of composite Fermi liquid (CFL) and composite hole liquid (CHL), both of which break particle-hole symmetry. Gauge invariance requires the existence of gapless edge modes at the interface between the CFL and CHL. Out of these modes, they construct a neutral Dirac fermion coupled to an emergent U(1) gauge field. Thus, at distances long compared to the strip width, they demonstrate that the system is described by a Dirac fermion coupled to an emergent gauge field, with an anti-unitary particle-hole symmetry, precisely the form conjectured recently by Son to be the low-energy description of a particle-hole symmetric half-filled Landau level.