Fractional Chern Insulators in Twisted Bilayer MoTe 2 : A Composite Fermion Perspective
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Lu, Tianhong (ORCID:0000000165043798)↗
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Results for “composite fermions”
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Scaling and diffusion of Dirac composite fermions
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Lee, Chao-Jung (ORCID:0000000333391522)↗
Dirac composite fermion theory of general Jain sequences
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
New Experimental Results of Composite Fermions at the Half-Filled Landau Level.
Abstract not provided.
Pan, Wei↗
Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene
Motivated by the observation of even denominator fractional quantum Hall effect in the n = 3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n = 2 graphene Landau level, whereas no pairing instability is found at half filling in the n = 0 and n = 1 graphene Landau levels. The relevance of these results to experiments is discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Crystalline solutions of the Kohn-Sham equations in the fractional quantum Hall regime
A Kohn-Sham density functional approach has recently been developed for the fractional quantum Hall effect, which maps the strongly interacting electrons into a system of weakly interacting composite fermions subject to an exchange correlation potential as well as a density dependent gauge field that mimics the "flux quanta" bound to composite fermions. To get a feel for the role of various terms, we study the behavior of the self-consistent solution as a function of the strength of the exchange correlation potential, which is varied through an ad hoc multiplicative factor. Here, we find that a crystal phase is stabilized when the exchange correlation interaction is sufficiently strong relative to the composite-fermion cyclotron energy. Various properties of this crystal are examined.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Construction of a series of new $\textit{ν}$ = 2/5 fractional quantum Hall wave functions by conformal field theory
In this paper, a series of $\textit{ν}$ = 2/5 fractional quantum Hall wave functions are constructed from conformal field theory(CFT). They share the same topological properties with states constructed by Jain's composite fermion approach. Upon exact lowest Landau level (LLL) projection, some of Jain's composite fermion states would not survive if constraints on Landau level indices given in the appendices of this paper were not satisfied. By contrast, states constructed from CFT are always in LLL. These states are characterized by different topological shifts and multibody relative angular momenta. Further, as a by-product, in the appendices we prove the necessary conditions for general $\textit{ν = p}$/(2$\textit{p}$ + 1) composite fermion states to have nonvanishing LLL projection.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Revisiting excitation gaps in the fractional quantum Hall effect
Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples open the possibility of a better quantitative understanding of this important issue. Here we present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the n/(2n ± 1) states as Δ n/(2n+1) = Ce 2 /[(2n ± 1)ϵl]-Γ, where ϵ is the dielectric constant of the background semiconductor and l is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and Γ as a disorder-induced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that Γ can be nonzero even in the absence of disorder.
36 MATERIALS SCIENCE↗
Fluctuations and magnetoresistance oscillations near the half-filled Landau level
We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level (ν = 1/2) that result from the presence of a periodic one-dimensional electrostatic potential. In this work, we use the Dirac composite fermion theory of Son, where the ν = 1/2 state is described by a (2 + 1)-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge-field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger-Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field–dependent mass for the Dirac composite fermions away from ν = 1/2. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe 2 bilayers
Twisted bilayer transition metal dichalcogenides, such as MoTe 2 , provide a versatile platform for exploring correlated topological phases. This work investigates the interplay between perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer MoTe 2 (t-MoTe 2 ) across two distinct regimes: a low-twist-angle phase (θ ≈ 2.1°) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase (θ ≈ 3.89°) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain fractal FCIs with higher Chern numbers. As a result, the electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.
Anyons↗
Unlocking New Regimes in Fractional Quantum Hall Effect with Quaternions
We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously not amenable to quantitative theoretical investigation. As an illustration, we explore the possibility of a nematic or a charge-density wave instability of the composite-fermion Fermi sea at half-filled Landau level and of the nearby FQH states by looking for a gap closing instability of the neutral magneto-roton excitation. As a result, our quaternion formulation of the FQH effect has been inspired by mathematical developments in the theoretical analyses of gravitational wave modes and cosmic microwave background radiation, where an important role is played by spin-weighted spherical harmonics that are nothing but monopole harmonics appearing in the spherical geometry for the FQH effect.
Composite fermions↗
Chiral superconductivity from a parent Chern band and its non-Abelian generalization
Here, we propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetralayer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose-Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose-Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multilayer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the non-abelian Moore-Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore-Read quantum Hall phase. Our work suggests rhombohedral multilayer graphene as a potential platform for rich correlated topological phases.
Wang, Yan-Qi [University of Maryland, College Park↗
Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ ≃ 0.42. Here, in this study, we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor v = 1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels
One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO 3 /SrTiO 3 ) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) e 2 /h , where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.
Science & Technology - Other Topics↗
Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between 𝑁 = 0 and 𝑁 = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.
Bilayer graphene↗
Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions
Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall effect. Effective theory approach and exact diagonalization in a disk and torus geometries proves the existence of the counterpropagating edge modes with opposite spin polarizations at the boundary between the two neighboring regions of the two-dimensional electron liquid in spin-polarized and spin-unpolarized phases. By analytical and numerical analysis, we argue that these systems can host parafermions when coupled to an 𝑠-wave superconductor and are experimentally feasible. We investigate settings based on 𝜈 = 2/3, 4/3, and 5/3 spin transitions and analyze spin-flipping interactions that hybridize counterpropagating modes. Lastly, we discuss spin-orbit interactions of composite fermions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect
Here we propose a two-fluid description of fractional quantum Hall systems, in which one component is a condensate of composite bosons and the other a Fermi liquid formed by composite fermions (or simply electrons). We employ the theory to model the interface between a fractional quantum Hall liquid and a (composite) Fermi liquid metal, where we find a penetration of quantum Hall condensate into the metallic region reminiscent of the proximity effect in superconductor-metal interfaces. We also find a novel and physically reasonable set of gapped quasielectron and neutral modes in fractional quantum Hall liquids.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Origin of the $ν$ = 1/2 fractional quantum Hall effect in wide quantum wells
The nature of the fractional quantum Hall effect at ν = 1/2, observed in wide quantum wells al- most three decades ago, is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which assumes that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase diffusion Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, and also to two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations find that the one-component composite-fermion Fermi sea and the one-component Pfaffian states are very close in energy for a range of quantum well widths and densities, suggesting that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state. Furthermore, we hope that this will motivate further experimental studies of this state.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗