Non-Interacting Fermi Sea of Dipolar CFs

• Non-interacting Fermi sea of dipolar CFs is a framework where composite fermions bind with flux quanta to yield a Fermi-liquid state with a sharp Fermi surface.
• The model accurately describes momentum distributions and structure factors, confirming a q³ scaling without logarithmic corrections as seen in experiments and simulations.
• Experimental realizations in ultracold atoms and anisotropic lattices demonstrate controlled phase transitions and Fermi surface distortions, validating the non-interacting approximation.

A non-interacting Fermi sea of dipolar composite fermions (CFs) is a paradigm underpinning the emergent metallic state observed in fractional quantum Hall and cold atomic systems where electrons bind to flux quanta or neutral fermions possess large magnetic/electric dipole moments. Such systems, when interactions and correlations are sufficiently weak or "dressed out," exhibit Fermi-liquid-like properties that are accurately modeled by noninteracting composite dipolar fermions occupying a well-defined Fermi sea. This formalism enables precise descriptions of response functions, phase behavior, and quantum correlations across a wide spectrum of filling factors, external field strengths, and lattice geometries.

1. Theoretical Framework and Definitions

A composite fermion is canonically defined by the attachment of flux quanta (vortices) to a charged particle (electron), yielding a fermion–vortex bound state with dipolar character. In dipolar cold atom systems, the particles possess intrinsic electric or magnetic dipole moments, resulting in long-range, anisotropic dipole–dipole interactions. For high magnetic field two-dimensional electron gases at filling fraction $\nu=1/2$ (or other even denominator fractions), CFs experience an effective zero magnetic field and form a Fermi sea described by a Fermi wave vector

$k^*_F = \sqrt{4\pi n^*}$

where $n^*$ is the effective CF density, determined by either the total carrier density or, crucially, the minority carrier density in the lowest Landau level (Kamburov et al., 2014, Hossain et al., 2020). In fully spin-polarized systems, $k^*_F = \sqrt{4\pi \rho_e}$ where $\rho_e$ is the electron density (Balram et al., 2017).

2. Fermi Sea Properties: Momentum Distribution and Structure Factor

The non-interacting Fermi sea of dipolar CFs manifests in the momentum distribution $n(k)$ as a sharp discontinuity at $k=k_F$, indicative of a well-defined Fermi surface. The static structure factor $S(q)$, quantifying density–density correlations, reveals in extensive microscopic studies a leading small-$q$ behavior

$S(q) \approx \frac{2k_F}{3\pi} q^3$

for electrons at $\nu=1/2, 1/4$ and bosons at $\nu=1, 1/3$ (Anakru et al., 8 Sep 2025). This result matches the expectation from a non-interacting dipolar CF model, utilizing a projected density operator

$$\bar{\rho}(q) = e^{-q^2/4} \sum_k [i \ell_B^2 (q \times k)] c^\dagger_{k+q} c_k$$

and a circular Fermi sea. Notably, field-theory treatments incorporating gauge field Landau damping via random phase approximation (RPA) predict a nonanalytic $q^3\ln q$ correction, which is absent in accurate microscopic calculations. This alignment between theory and simulation confirms that dipolar CFs effectively behave as non-interacting Fermi liquids in terms of their density response at long wavelengths.

3. Fermi Surface Geometry, Anisotropy, and Lifshitz Transitions

In two-dimensional lattices and optical traps, the topology and geometry of the Fermi surface can undergo abrupt changes—Lifshitz transitions—when system parameters such as dipolar interaction strength or transverse hopping are tuned (Carr et al., 2010). For dipolar CFs in anisotropic lattices, the model dispersion

$$\xi_0(k) = -2t_{||} \cos k_x - 2t_\perp \cos k_y - \mu$$

is subject to interaction-induced renormalization of $t_\perp \to t^*_\perp$, potentially yielding a discontinuous meta-nematic transition. This transition signals a shift from quasi-one-dimensional Fermi sheets to a two-dimensional Fermi pocket, occurring via a first-order quantum phase change associated with van Hove singularities and BCS-like order parameter behavior

$$\Delta t^*_\perp \approx 2 \exp\left(-\frac{1}{bV_c}\right)$$

in the vicinity of the critical endpoint.

Dipolar interactions aligned along specific axes also deform the Fermi surface, introducing pronounced anisotropy observable in both experiments and simulations (Baarsma et al., 2016, Hossain et al., 2019). The extent of this anisotropy, and its dependence on filling factor and applied in-plane field, encodes valuable information about underlying mass renormalization and proximity to competing orders such as Wigner crystallization.

4. Spin and Minority Carrier Effects

Away from half-filling, particle-hole symmetry is generically broken, and the Fermi wave vector is determined by the density of minority carriers (Kamburov et al., 2014, Hossain et al., 2020). For non-fully spin-polarized CF Fermi seas,

$$k^*_{F\uparrow, \downarrow} = \sqrt{4\pi \rho_e^{\uparrow, \downarrow}}$$

with $\rho_e^{\uparrow, \downarrow}$ the respective spin densities (Balram et al., 2017). The observed asymmetries in commensurability resistance resonance experiments demonstrate the necessity of utilizing minority carrier densities, particularly for $\nu > 1/2$, refining models for metallic dipolar CF states. Large-scale simulations confirm that residual interactions between CFs are largely perturbative, validating the non-interacting model for the Fermi sea area, even with significant electron–electron correlations and Landau level mixing (Anakru et al., 8 Sep 2025).

5. Phase Behavior: Quantum Liquid, Wigner Crystal, and Absence of Stripe Phases

Quantum Monte Carlo studies reveal the equation of state for dipolar CFs in the Fermi-liquid phase is well described by Hartree–Fock theory with logarithmic corrections (Matveeva et al., 2012). As the dimensionless interaction parameter $k_F r_0$ increases, the effective mass $m^*/m$ reduces and the quasiparticle weight $Z$ at the Fermi surface decreases, corresponding to enhanced correlations. At a critical $k_F r_0 \approx 25 \pm 3$, a first-order liquid–solid (Wigner crystal) transition occurs, characterized by a narrow phase coexistence region $\delta(k_F r_0) \sim 0.01$. The Wigner crystal phase forms a triangular lattice with energy per particle

$$E_{WC} = N \frac{\varepsilon_F}{2} \frac{k_F r_0}{4} \left[1.597 + \frac{2.871}{\sqrt{k_F r_0}} \right]$$

Stripe phases, characterized by one-dimensional density modulations, are energetically disfavored across all studied interaction strengths, even when variationally optimized wave functions are employed.

6. Experimental Signatures and Construction in Ultracold Atom Systems

Production of dipolar Fermi seas is achievable in ultracold atomic gases, e.g. via sympathetic cooling of $^{53}$Cr atoms with bosonic $^{52}$Cr (Naylor et al., 2014). Here, the moderate dipolar interaction strengths and vanishing s-wave collisions among polarized fermions yield a near-ideal non-interacting Fermi sea. Manipulation of dipolar strength and hopping parameters in optical lattices affords precision control over dimensional crossover, Fermi surface topology, and phase transitions. Momentum-resolved time-of-flight imaging, geometric resonance, and structure factor measurements furnish robust diagnostics for Fermi surface geometry, anisotropy, and quantum phase transitions.

Key experimental protocols utilize patterning of superlattices for geometric resonance, commensurability analysis, and detection of abrupt changes in density profile under harmonic traps—directly attributable to interaction-driven Fermi surface reorganization (Carr et al., 2010, Hossain et al., 2019).

7. Field Theory, Dirac Composite Fermions, and Gauge Field Effects

Field-theoretical HLR models predict a Fermi sea of CFs coupled to an emergent Chern–Simons gauge field, leading to non-Fermi-liquid corrections such as Landau damping. However, recent large-scale microscopic studies employing quaternion-formulated Jain–Kamilla wave function projection challenge this scenario, consistently finding $q^3$ corrections to $S(q)$ without the RPA-predicted $q^3 \ln q$ term (Anakru et al., 8 Sep 2025). This suggests the non-interacting Fermi sea model of dipolar CFs accurately captures density–density correlations in the long-wavelength limit.

Dirac composite fermion theory and the dipole picture formally encode Berry curvature and half-quantized Hall conductance, producing an effective description wherein response functions and transport coefficients mirror those of massless Dirac CFs at long wavelengths (Ji et al., 2021). Corrections from electric quadrupoles and magnetic moments become relevant for short-wavelength probes, manifesting as deviations from Dirac CF predictions.

Summary Table: Non-Interacting Dipolar CF Fermi Sea Features

Feature	Description	Reference
Fermi wave vector ($k_F$)	$k_F = \sqrt{4\pi n^*}$ (minority carrier density)	(Kamburov et al., 2014, Balram et al., 2017, Hossain et al., 2020)
Structure factor $S(q)$	$S(q) \sim (2k_F/3\pi)q^3$ (no logarithmic correction)	(Anakru et al., 8 Sep 2025)
Fermi surface	Sharp, with possible anisotropy under dipolar interaction	(Carr et al., 2010, Baarsma et al., 2016)
Phase transitions	Lifshitz/meta-nematic, liquid–solid, (no stripe phase)	(Carr et al., 2010, Matveeva et al., 2012)
Gauge field effects	RPA-predicted $q^3\ln q$ not observed; $q^3$ matches dipolar model	(Anakru et al., 8 Sep 2025)

This synthesis consolidates the non-interacting Fermi sea picture for dipolar composite fermions—emphasizing its broad applicability and experimental accessibility, the robustness of Fermi surface properties and structure factor corrections, the nuances of symmetry and spin polarization, and the domains of validity relative to interaction strengths and emergent gauge field physics.