arXiv subjects

J. K. Jain

Publications and source records attributed to J. K. Jain.

At least 37 records · Page 2Linked to original sources

arXiv2023

Composite fermion pairing induced by Landau level mixing

Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors $ν=1/2$ and $ν=1/4$ in the $l=-3$ relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.

cond-mat.str-el↗

arXiv2022

Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction ($\hat{V}^\text{Pf}_3$) between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three- body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles with exact lowest Landau level projection. We further demonstrate adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level $\hat{V}^\text{Pf}_3$ Hamiltonian.

cond-mat.str-el↗

arXiv2022

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 [Villegas Rosales {\it et al.}, Phys. Rev. Lett. {\bf 127}, 056801 (2021)] open the possibility of a better quantitative understanding of this important issue. 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 $n/(2n\pm 1)$ states as $Δ_{n/(2n\pm 1)} = Ce^2/[(2n\pm 1)\varepsilon l]-Γ$, where $\varepsilon$ 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.

cond-mat.str-el↗

arXiv2022

Electrically switchable tunneling across a graphene pn junction: evidence for canted antiferromagnetic phase in $ν=0$ state

The ground state of a graphene sheet at charge neutrality in a perpendicular magnetic field remains enigmatic, with various experiments supporting canted antiferromagnetic, bond ordered, and even charge density wave phases. A promising avenue to elucidating the nature of this state is to sandwich it between regions of different filling factors, and study spin-dependent tunneling across the edge modes at the interfaces. Here we report on tunnel transport through a $ν=0$ region in a graphite-gated, hexagonal boron nitride ($hBN$) encapsulated monolayer graphene device, with the $ν=0$ strip sandwiched by spin-polarized $ν=\pm1$ quantum Hall states. We observe finite tunneling ($t \sim 0.3-0.6$) between the $ν=\pm1$ edges at not too small magnetic fields ($B>3T$) and low tunnel bias voltage ($<30-60μV$), which is surprising because electrons at the edge states nominally have opposite spins. Hartree-Fock calculations elucidate these phenomena as being driven by the formation of a CAF order parameter in the $ν=0$ region at zero bias (for wide enough junctions) leading to non-orthogonal spins at the edges. Remarkably, this tunneling can be controllably switched off by increasing bias; bias voltage leads to a pileup of charge at the junction, leading to a collapse of the CAF order and a suppression of the tunneling.

cond-mat.mes-hall↗

arXiv2022

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spinless electrons on a Hofstadter lattice with nearest neighbor attractive interaction, and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge invariant solutions that display a rich phase diagram as a function of the chemical potential, magnetic field and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically non-trivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no low energy Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana fermions are indicated.

cond-mat.supr-con↗

arXiv2021

Composite anyons on a torus

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Finally, we obtain from these wave functions, both analytically and numerically, various topological quantities, such as ground-state degeneracy, the Chern number, and the Hall viscosity.

cond-mat.mes-hall↗

arXiv2021

Anderson localization in fractional quantum Hall effect

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $ν=n/(2n+1)$ has a striking {\it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.

cond-mat.mes-hall↗

arXiv2021

Bardeen-Cooper-Schrieffer pairing of composite fermions

Topological pairing of composite fermions has led to remarkable ideas, such as excitations obeying non-Abelian braid statistics and topological quantum computation. We construct a $p$-wave paired Bardeen-Cooper-Schrieffer (BCS) wave function for composite fermions in the torus geometry, which is a convenient geometry for formulating momentum space pairing as well as for revealing the underlying composite-fermion Fermi sea. Following the standard BCS approach, we minimize the Coulomb interaction energy at half filling in the lowest and the second Landau levels, which correspond to filling factors $ν=1/2$ and $ν=5/2$ in GaAs quantum wells, by optimizing two variational parameters that are analogous to the gap and the Debye cut-off energy of the BCS theory. Our results show no evidence for pairing at $ν=1/2$ but a clear evidence for pairing at $ν=5/2$. To a good approximation, the highest overlap between the exact Coulomb ground state at $ν=5/2$ and the BCS state is obtained for parameters that minimize the energy of the latter, thereby providing support for the physics of composite-fermion pairing as the mechanism for the $5/2$ fractional quantum Hall effect. We discuss the issue of modular covariance of the composite-fermion BCS wave function, and calculate its Hall viscosity and pair correlation function. By similar methods, we look for but do not find an instability to $s$-wave pairing for a spin-singlet composite-fermion Fermi sea at half-filled lowest Landau level in a system where the Zeeman splitting has been set to zero.

cond-mat.str-el↗

arXiv2021

Crystalline Solutions of 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 {\it ad hoc} multiplicative factor. 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.

cond-mat.str-el↗

arXiv2021

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 almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption 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 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, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.

cond-mat.str-el↗

arXiv2020

Thirty Years of Composite Fermions and Beyond

This chapter appears in "Fractional Quantum Hall Effects: New Development," edited by B. I. Halperin and J. K. Jain (World Scientific, 2020). The chapter begins with a primer on composite fermions, and then reviews three directions that have recently been pursued. It reports on theoretical calculations making detailed quantitative predictions for two sets of phenomena, namely spin polarization transitions and the phase diagram of the crystal. This is followed by the Kohn-Sham density functional theory of the fractional quantum Hall effect. The chapter concludes with recent applications of the parton theory of the fractional quantum Hall effect to certain delicate states.

cond-mat.str-el↗

arXiv2020

Hall Effect for Dirac Electrons in Graphene Exposed to an Abrikosov Flux Lattice

The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system of Dirac electrons exposed to an Abrikosov flux lattice. We theoretically find that non-uniform magnetic field causes a carrier-density dependent reduction of the Hall conductivity. Our studies show that this reduction originates from a rather subtle effect: a levitation of the Berry curvature within Landau levels broadened by the non-uniform magnetic field. Experimentally, we measure the magneto-transport in a monolayer graphene-hexagonal boron nitride - niobium diselenide (NbSe$_2$) heterostructure, and find a density-dependent reduction of the Hall resistivity of graphene as the temperature is lowered from above the superconducting critical temperature of NbSe$_2$, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice.

cond-mat.mes-hall↗

arXiv2020

Kohn-Sham Density Functional Theory of Abelian Anyons

We develop a density functional treatment of non-interacting abelian anyons, which is capable, in principle, of dealing with a system of a large number of anyons in an external potential. Comparison with exact results for few particles shows that the model captures the behavior qualitatively and semi-quantitatively, especially in the vicinity of the fermionic statistics. We then study anyons with statistics parameter $1+1/n$, which are thought to condense into a superconducting state. An indication of the superconducting behavior is the mean-field result that, for uniform density systems, the ground state energy increases under the application of an external magnetic field independent of its direction. Our density-functional-theory based analysis does not find that to be the case for finite systems of anyons, which can accommodate a weak external magnetic field through density transfer between the bulk and the boundary rather than through transitions across effective Landau levels, but the "Meissner repulsion" of the external magnetic field is recovered in the thermodynamic limit as the effect of the boundary becomes negligible. We also consider the quantum Hall effect of anyons, and show that its topological properties, such as the charge and statistics of the excitations and the quantized Hall conductance, arise in a self-consistent fashion.

cond-mat.str-el↗

arXiv2020

Bloch Ferromagnetism of Composite Fermions

In 1929 Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully-magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy. We report here the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism that has eluded experiments for the last ninety years. Our platform is the exotic two-dimensional Fermi sea of composite fermions at half-filling of the lowest Landau level. Via quantitative measurements of the Fermi wavevector, which provides a direct measure of the spin polarization, we observe a sudden transition from a partially-spin-polarized to a fully-spin-polarized ground state as we lower the composite fermions' density. Our detailed theoretical calculations provide a semi-quantitative account of this phenomenon.

cond-mat.str-el↗

arXiv2020

Interplay between fractional quantum Hall liquid and crystal phases at low filling

The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ν\lesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ν=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ν=n/(6n\pm 1)$ and $ν=n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$ν$ states, specifically $ν=1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

cond-mat.str-el↗

arXiv2020

A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level

We consider a non-Abelian candidate state at filling factor $ν=3/7$ state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e. at filling factor $ν=2+3/7$), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that \emph{if} a fractional quantum Hall effect is observed at $ν=3/7$ in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.

cond-mat.str-el↗

arXiv2020

It's anyon's game: the race to quantum computation

In 1924, Satyendra Nath Bose dispatched a manuscript introducing the concept now known as Bose statistics to Albert Einstein. Bose could hardly have imagined that the exotic statistics of certain emergent particles of quantum matter would one day suggest a route to fault-tolerant quantum computation. This non-technical Commentary on "anyons," namely particles whose statistics is intermediate between Bose and Fermi, aims to convey the underlying concept as well as its experimental manifestations to the uninitiated.

physics.pop-ph↗

arXiv2020

Hall Viscosity of Composite Fermions

Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form $ν=n/(2pn\pm 1)$, where $n$ and $p$ are integers, from the explicit wave functions for these states. The calculated Hall viscosities $η^A$ agree with the expression $η^A=(\hbar/4) {\cal S}ρ$, where $ρ$ is the density and ${\cal S}=2p\pm n$ is the "shift" in the spherical geometry. We discuss the role of modular invariance of the wave functions, of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for $ν={n\over 2pn+1}$ may be derived analytically from the microscopic wave functions, provided that the overall normalization factor satisfies a certain behavior in the thermodynamic limit. This derivation should be applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction.

cond-mat.str-el↗