Composite FermionsEdit
Composite fermions are emergent quasiparticles that arise in two-dimensional electron systems subjected to strong perpendicular magnetic fields at low temperatures. By binding an even number of magnetic flux quanta to each electron, the strongly interacting electrons can be mapped onto a system of weakly interacting composite fermions moving in a reduced effective magnetic field. This idea provides a unifying framework for understanding the fractional quantum Hall effect, linking it to the more familiar integer quantum Hall effect through an elegant change of perspective. The concept was developed in the late 1980s and has since become a cornerstone of modern condensed matter physics, with broad experimental support in materials such as GaAs-based quantum wells and extensions to other platforms like graphene and oxide interfaces.
The core idea is best understood in the language of the two-dimensional electron gas, the standard medium in which the fractional quantum Hall effect is observed. In this setting, strong repulsive interactions among electrons drive the system into highly correlated states when Landau levels are partially filled. The composite fermion construction posits that each electron captures an even number (2p) of flux quanta to form a new particle—the composite fermion. In doing so, the electrons experience a reduced effective magnetic field B*, which can be viewed as the external field B minus the field associated with the attached flux quanta. When this effective field is such that composite fermions fill an integer number p of their own Landau-like levels, the system exhibits a quantized Hall conductance at fractions of the form ν = p/(2p ± 1). This mapping explains the observed sequence of fractional quantum Hall states, notably 1/3, 2/5, 3/7, and so on, and it provides a natural route to understanding energy gaps and transport plateaus without invoking prohibitively complicated many-body wavefunctions for every fraction. See two-dimensional electron gas and fractional quantum Hall effect for related background.
The theoretical framework that underpins composite fermions blends a physically intuitive picture with a precise mathematical toolset. The flux attachment is often implemented in field-theoretic language via a Chern-Simons gauge field. In this picture, electrons and the attached flux are reinterpreted as composite fermions moving in an effective field B*. This mean-field approach captures the essential physics of the observed Jain sequences and the corresponding integer quantum Hall effect of CFs. The approach is closely associated with the notion of the Jain sequence, named after Jain sequence on constructing fractions from integer fillings of CF Landau-like levels. See Chern-Simons theory for the gauge-theoretic underpinning and Landau level for the quantization story.
In the half-filled and near-half-filled regimes, a complementary perspective has gained traction. Some physicists advocate a particle-hole symmetric formulation in which the composite fermions behave as Dirac fermions, a viewpoint that emphasizes symmetry between electrons and holes in a half-filled Landau level. This Dirac composite fermion theory has been advanced to address gaps in symmetry that the original flux-attachment construction can obscure. See Dirac composite fermion theory and particle-hole symmetry for details. The Dirac formulation does not collapse the successes of the standard CF picture, but it provides a framework that aligns more naturally with certain symmetry considerations and with some experimental observations at ν ≈ 1/2. See also discussions surrounding the compatibility between the Dirac picture and the traditional CF construction.
Experimental evidence for composite fermions is robust and multifaceted. In high-mquality GaAs/AlGaAs quantum wells, precise transport measurements reveal robust fractional quantum Hall plateaus at ν = 1/3, 2/5, 3/7, and related fractions, consistent with the CF mapping to integer quantum Hall states. Commensurability measurements and observations of CF cyclotron motion provide direct evidence for the reduced effective field and the CF picture of Landau-like levels. Activation gaps extracted from temperature-dependent transport scale with Coulomb energy scales, confirming the interaction-driven nature of these states. In addition, experiments at ν = 1/2 have revealed signatures compatible with a CF Fermi sea: a compressible state with a Fermi surface-like character in the absence of a conventional gap, consistent with CFs forming a Fermi liquid in zero net magnetic field B*. Platform-dependent studies in graphene and other materials have extended the reach of CF physics beyond traditional GaAs systems, demonstrating the universality of the underlying ideas. See Fractional quantum Hall effect, two-dimensional electron gas, and GaAs for context.
Extensions and ongoing developments keep this area vibrant. The CF framework has been adapted to bilayer systems, where interlayer correlations give rise to rich phenomenology and new quantum Hall states. The enigmatic state at ν = 5/2 remains a focal point of debate, with candidates including the Pfaffian and anti-Pfaffian states that host non-Abelian anyons, as well as competing Abelian descriptions; the relationship of these states to CF concepts is an active line of inquiry. See Pfaffian state, anti-Pfaffian state, and non-Abelian anyons for related topics. Contemporary research also explores the role of Landau level mixing, finite thickness, and disorder, all of which can influence gaps and stability of observed states. In parallel, the Dirac composite fermion program continues to be refined, particularly in its treatment of particle-hole symmetry and its connection to experiments near ν = 1/2. See Read–Rezayi state for broader non-Abelian contexts and Dirac composite fermion theory for symmetry-focused developments.
Controversies and debates within the field center on how best to formulate the theory at a fundamental level and how to interpret certain experimental observations. Critics of the earliest flux-attachment approach have argued that it is a powerful phenomenological device rather than a unique microscopic description, and that a complete, symmetry-respecting theory would ideally account for particle-hole symmetry more transparently. Proponents of the Dirac composite fermion view contend that particle-hole symmetry is essential in the half-filled regime and that a Dirac description brings this symmetry to the fore, without discarding the empirical successes of the conventional CF picture. See particle-hole symmetry and Dirac composite fermion theory.
The 5/2 state—long associated with the Moore–Read Pfaffian (and the related anti-Pfaffian) state—is frequently discussed in CF circles because it sits at the intersection of CF ideas and non-Abelian anyon physics. While CF concepts illuminate many fractions, the precise nature of the 5/2 state and its potential non-Abelian character remains under active investigation, with competing interpretations and experimental tests. See Pfaffian state and non-Abelian anyons.
Overall, the composite fermion framework remains a highly successful and pragmatic tool for understanding the fractional quantum Hall effect. It reconciles a wide array of experimental observations with a coherent theoretical narrative, while continuing to adapt to new data and new platforms. See Fractional quantum Hall effect and Chern-Simons theory for foundational context.