arXiv subjects

Jainendra K. Jain

Publications and source records attributed to Jainendra K. Jain.

At least 19 recordsLinked to original sources

arXiv2025

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, fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multi-component FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multi-component FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature was 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 multi-component 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-flux and reverse-flux 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.

cond-mat.mes-hall↗

arXiv2024

Crossover from Integer to Fractional Quantum Hall Effect

The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical particles. Field theoretical formulations execute the gluing process through the device of emergent gauge fields. Here we study numerically the process of going from the integer quantum Hall effect of two species of fermionic partons to the fractional quantum Hall effect of bosons by introducing an attractive interaction between the fermions of different species and continuously increasing its strength to glue them into bosons. To properly capture the physics in the bulk, we implement this process in a lattice version of the spherical geometry, which allows us to keep the full Hilbert space. Even though the two end-point states are topologically distinct, we find that, for the small system sizes accessible to our study, the energy gap remains open, indicating a crossover between these two states.

cond-mat.str-el↗

arXiv2022

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 [Y. Kim $\textit{et al.}$, Nature Physics $\textbf{15}$, 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 $1$ graphene Landau levels. The relevance of these results to experiments is discussed.

cond-mat.str-el↗

arXiv2020

Unconventional $\mathbb{Z}_{n}$ parton states at $ν= 7/3$: The role of finite width

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. ${\bf 2}$, 013349 (2020)] has suggested that an unconventional state describing $\mathbb{Z}_{n}$ superconductivity of composite bosons, which supports excitations with charge $1/(3n)$ of the electron charge, is energetically better than the Laughlin wave function at $ν=7/3$ in GaAs systems. All experiments to date, however, are consistent with the latter. To address this discrepancy, we study the effect of finite width on the ground state and predict a phase transition from an unconventional $\mathbb{Z}_{n}$ state at small widths to the Laughlin state for widths exceeding $\sim$ 1.5 magnetic lengths. We also determine the parameter region where an unconventional state is stabilized in the one third filled zeroth Landau level in bilayer graphene. The roles of Landau level mixing and spin are also considered.

cond-mat.str-el↗

arXiv2019

Theoretical phase diagram of two-component composite fermions in double layer graphene

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layer-correlated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors $ν=3/7$, $4/9$, $6/11$, $4/7$, $3/5$, $2/3$, and $4/5$) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings $ν=3/7$ and $ν=3/5$ are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as $ν=3/7$, interlayer correlations are predicted to survive to surprisingly large interlayer separations.

cond-mat.str-el↗

arXiv2019

Even denominator fractional quantum Hall states in higher Landau levels of graphene

An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from a chiral $p$-wave paired state of composite fermions which are topological bound states of electrons and quantized vortices. This state is theoretically described by a "Pfaffian" wave function or its hole partner called the anti-Pfaffian, whose excitations are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics. This has inspired ideas on fault-tolerant topological quantum computation and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even-denominator fractional quantum Hall physics in the $n=3$ Landau level. We numerically investigate the known candidate states for the even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistics

cond-mat.mes-hall↗

arXiv2019

Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells

We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to $f$-wave pairing of composite fermions. This state is topologically distinct from the familiar $p$-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.

cond-mat.str-el↗

arXiv2018

Microscopic verification of topological electron-vortex binding in the lowest-Landau-level crystal state

When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular Wigner crystal. We demonstrate that, in the entire crystal phase, this crystal is very well represented by a composite-fermion-crystal wave function, revealing that it is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a non-perturbative binding of quantized vortices to electrons, which establishes a long range quantum coherence in it. It is suggested that this has qualitative consequences for experiment.

cond-mat.mes-hall↗

arXiv2018

Exotic Bilayer Crystals in a Strong Magnetic Field

Electron bilayers in a strong magnetic field exhibit insulating behavior for a wide range of interlayer separation $d$ for total Landau level fillings $ν\leq 1/2$, which has been interpreted in terms of a pinned crystal. We study theoretically the competition between many strongly correlated liquid and crystal states and obtain the phase diagram as a function of quantum well width and $d$ for several filling factors of interest. We predict that three crystal structures can be realized: (a) At small $d$, the Triangular Ising AntiFerromagnetic (TIAF) crystal is stabilized in which the particles overall form a single-layer like triangular crystal while satisfying the condition that no nearest-neighbor triangle has all three particles in the same layer. (b) At intermediate $d$, a Correlated Square (CS) crystal is stabilized, in which particles in each layer form a square lattice, with the particles in one layer located directly across the centers of the squares of the other. (c) At large $d$, we find a Bilayer Graphene (BG) crystal in which the A and B sites of the graphene lattice lie in different layers. All crystals that we predict are strongly correlated crystals of composite fermions; a theory incorporating only electron Hartree-Fock crystals does not find any crystals besides the `trivial' ones occurring at large interlayer separations for total filling factor $ν\leq1/3$ (when layers are uncorrelated and each layer is in the long familiar single-layer crystal phase). The TIAF, CS and BG crystals come in several varieties, with different flavors of composite fermions and different interlayer correlations. The appearance of these exotic crystal phases adds to the richness of the physics of electron bilayers in a strong magnetic field, and also provides insight into experimentally observed bilayer insulator as well as transitions within the insulating part of the phase diagram.

cond-mat.str-el↗

arXiv2017

Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling $1/2$ FQH effect observed in bilayer graphene [Kim {\em et al.}, Nano Lett. {\bf 15}, 7445 (2015)], and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.

cond-mat.str-el↗

arXiv2016

Role of exciton screening in the 7/3 fractional quantum Hall effect

The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud. Their wide extent has implications for experiments as well as for analysis of finite system exact diagonalization studies.

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arXiv2015

Emergent Fermi sea in a system of interacting bosons

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The fermions forming the SU(2) singlet Fermi sea are bound states of bosons and quantized vortices, formed as a result of the repulsive interaction between bosons in the lowest Landau level.

cond-mat.quant-gas↗

arXiv2015

Analytical Theory of Strongly Correlated Wigner Crystals in the Lowest Landau Level

In this work, we present an analytical theory of strongly correlated Wigner crystals (WCs) in the lowest Landau level (LLL) by constructing an approximate, but accurate effective two-body interaction for composite fermions (CFs) participating in the WCs. This requires integrating out the degrees of freedom of all surrounding CFs, which we accomplish analytically by approximating their wave functions by delta functions. This method produces energies of various strongly correlated WCs that are in excellent agreement with those obtained from the Monte Carlo simulation of the full CF crystal wave functions. We compute the compressibility of the strongly correlated WCs in the LLL and predict discontinuous changes at the phase boundaries separating different crystal phases.

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arXiv2014

Theoretical investigation of edge reconstruction in the $ν$=5/2 and 7/3 fractional quantum Hall states

The edge physics of the $ν=5/2$ fractional quantum Hall state is of relevance to several recent experiments that use it as a probe to gain insight into the nature of the bulk state. We perform calculations in a semi-realistic setup with positive background charge at a distance $d$, by exact diagonalization both in the full Hilbert space (neglecting Landau level mixing) and in the restricted Pfaffian basis of edge excitations. Our principal finding is that the 5/2 edge is unstable to a reconstruction except for very small $d$. In addition, the interactions between the electrons in the second Landau level and the lowest Landau level enhance the tendency toward edge reconstruction. We identify the bosonic and fermionic modes of edge excitations and obtain their dispersions by back-calculating from the energy spectra as well as directly from appropriate trial wave functions. We find that the edge reconstruction is driven by an instability in the fermionic sector for setback distances close to the critical ones. We also study the edge of the $ν=7/3$ state and find that edge reconstruction occurs here more readily than for the $ν=1/3$ state. Our study indicates that the $ν=5/2$ and 7/3 edge states are reconstructed for all experimental systems investigated so far and thus must be taken into account when analyzing experimental results. We also consider an effective field theory to gain insight into how edge reconstruction might influence various observable quantities.

cond-mat.str-el↗

arXiv2014

Collective excitations of a system of coupled relativistic and non-relativistic two-dimensional electron gases

We study collective excitations of a two-dimensional electron system consisting of two kinds of charge carriers: relativistic or Dirac electrons with linear dispersion and non-relativistic electrons with parabolic dispersion. We find that the strength of the interaction between the different charge carriers, i.e., the inter-species interaction, plays a significant role in determining the number of plasmon modes as well as their dispersions in certain parameter regimes.

cond-mat.mes-hall↗

arXiv2014

Quantum bubble defects in the lowest Landau level crystal

A longstanding puzzle for the lowest Landau level crystal phase has been an order of magnitude discrepancy between the theoretically calculated energy of the defects and the measured activation gap. We perform an extensive study of various kinds of defects in the correlated composite fermion crystal and find that the lowest energy defect is a six-fold symmetric "hyper-correlated bubble interstitial," in which an interstitial particle forms a strongly correlated bound state with a particle of the crystal. The energy of the bubble defect is a factor of $\sim$3 smaller than that of the lowest energy defect in a Hartree-Fock crystal. The anomalously low activation energies measured in transport experiments are thus a signature of the unusual quantum nature of the crystal and its defects.

cond-mat.str-el↗

arXiv2014

A note contrasting two microscopic theories of the fractional quantum Hall effect

Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the relation between them, ranging from their being distinct to their being completely equivalent. This article attempts to provide a clarification of the issue. It is shown that the two theories postulate distinct microscopic mechanisms for the origin of the fractional quantum Hall effect, and make substantially different predictions that have allowed experiments to distinguish between them.

cond-mat.str-el↗

arXiv2014

Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect

The origin of fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, FQHE here results from the suppression of pairs with relative angular momentum {\em three} rather than one, confirming the exotic mechanism proposed by Wójs, Yi and Quinn [Phys. Rev. B {\bf 69}, 205322 (2004)]. We predict that the 4/11 state reported a decade ago by Pan {\em et al.} [Phys. Rev. Lett. {\bf 90}, 016801 (2003)] is a conventional partially spin polarized FQHE of composite fermions, and estimate the Zeeman energy where a phase transition into the unconventional fully spin polarized state will occur.

cond-mat.mes-hall↗