arXiv subjects

Jainendra K. Jain

Publications and source records attributed to Jainendra K. Jain.

At least 37 records · Page 2Linked to original sources

arXiv2013

State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons

Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands, which is responsible for the fascinating phenomenology of this system. The theory of nearly free composite fermions has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between an excited composite-fermion particle and the hole it leaves behind. This interaction, the form of which we derive from the microscopic composite fermion theory, eliminates configurations containing certain tightly bound composite-fermion excitons. With this modification, the composite-fermion theory reproduces,for all well-defined excited bands seen in exact diagonalization studies, an exact counting for $ν>1/3$, and an almost exact counting for $ν\leq 1/3$. The resulting insight clarifies that the corrections to the nearly free composite fermion theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the composite-fermion Fermi sea.

cond-mat.str-el↗

arXiv2013

Competing Crystal Phases in the Lowest Landau Level

We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall states arises from an extremely delicate interplay between type-1 and type-2 composite fermion crystals, clearly demonstrating its nontrivial, strongly correlated character. We also compute the phase diagram of various crystals occurring over a wide range of filling factors, and demonstrate that the elastic constants exhibit non-monotonic behavior as a function of the filling factor, possibly leading to distinctive experimental signatures that can help mark the phase boundaries separating different kinds of crystals.

cond-mat.str-el↗

arXiv2013

Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings

We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $ν=2/3$, 4/5 and 4/3, and spin-partially-polarized states at filling factors 3/4 and 3/2, where "spin" serves as a generic label for the two components. We study ground states, excitations, edge states and entanglement spectrum for systems with up to 16 bosons, and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $ν=2/3$, 4/5 and 3/4, although it is less satisfactory for the $ν=3/2$ state. For $ν=4/3$ a "non-Abelian spin-singlet" state has been proposed to occur for a 2-body contact interaction; we find that it is more likely that the actual state here is a spin-singlet state of reverse-flux-attached composite fermions at filling $ν^*=4$. We also consider incompressible states at integral filling factors $ν=1$ and 2. The incompressible state at $ν=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $ν=2$ as the spin-singlet state of reverse-flux-attached composite fermions at $ν^*=2$.

cond-mat.str-el↗

arXiv2013

Phase diagram of the Two-Component Fractional Quantum Hall Effect

We calculate the phase diagram of the two component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or valley degree of freedom is active.

cond-mat.str-el↗

arXiv2012

Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $ν=2/3$ Fractional Quantum Hall Effect

The edge of spin unpolarized or spin polarized $ν=2/3$ fractional quantum Hall states is predicted by the effective theory to support a backward moving neutral mode in addition to a forward moving charge mode. We study this issue from a microscopic perspective where these states are identified with effective filling factor of 2 of composite fermions, but with an effective magnetic field that is antiparallel to the external field. A simple counting from the composite fermion description suggests that there might be two backward moving edge modes, but explicit calculations show that one of these is projected out of the low energy sector, while the remaining mode provides a good microscopic account of the actual counter propagating edge mode. The forward moving modes are identified as "Schur modes," obtained by multiplying the ground state wave function by the symmetric Schur polynomials. The edge of the 2/3 spin unpolarized state provides a particularly striking realization of "spin charge separation" in a one dimensional Tomonaga Luttinger liquids, with the spin and charge modes moving in opposite directions.

cond-mat.mes-hall↗

arXiv2012

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effect in different parameter regions. We argue that some, though not all, apparently puzzling features observed in recent experiments are consistent with a two-component fractional quantum Hall effect, with the electron spin frozen but the Dirac-valley symmetry approximately intact. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7 etc.; SU(4) skyrmions are not relevant for the low-energy physics.

cond-mat.str-el↗

arXiv2011

Microscopic study of the 2/5 fractional quantum Hall edge

This paper reports on our study of the edge of the 2/5 fractional quantum Hall state, which is more complicated than the edge of the 1/3 state because of the presence of a continuum of quasi-degenerate edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a non-perturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N_1, N_2] sector, where N_1 and N_2 are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N_1 + 1, N_2] or [N_1, N_2 + 1] sector; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N_1 + 1 + k, N_2 - k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed and substantial comparison with the two-boson model of the 2/5 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and non-universal, their sum is consistent with an effective two-boson description of the 2/5 edge.

cond-mat.str-el↗

arXiv2011

Higher Energy Composite Fermion Levels in the Fractional Quantum Hall Effect

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.

cond-mat.str-el↗

arXiv2011

Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor ν = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.

cond-mat.str-el↗

arXiv2011

Unpaired composite fermion, topological exciton, and zero mode

The paired state of composite fermions is expected to support two kinds of excitations: vortices and unpaired composite fermions. We construct an explicit microscopic description of the unpaired composite fermions, which we demonstrate to be accurate for a 3-body model interaction, and, possibly, adiabatically connected to the Coulomb solution. This understanding reveals that an unpaired composite fermion carries with it a charge-neutral "topological" exciton, which, in turn, helps provide microscopic insight into the origin of zero modes, fusion rules, and energetics.

cond-mat.str-el↗

arXiv2010

Fractional quantum Hall effect arising from repulsive three body interaction

We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion. Recent theoretical and experimental breakthroughs in ultra-cold atoms and molecules have facilitated the realization of such a system, where this physics can be tested.

cond-mat.str-el↗

arXiv2010

Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect

We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect nonabelian braid statistics.

cond-mat.str-el↗

arXiv2010

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also formulate an effective field theory to describe the behavior of a reconstructed edge, taking into account multiple edge modes. Experimental consequences are discussed.

cond-mat.str-el↗

arXiv2010

Testing the topological nature of the fractional quantum Hall edge

We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb interaction. This enables us to perform substantial tests of the predicted universality of the edge physics. Our results provide compelling evidence that the behavior of the FQH edge is intrinsically nonuniversal, even in the absence of edge reconstruction, and therefore does not bear a sharp and unique relation to the bulk FQH state.

cond-mat.str-el↗

arXiv2009

Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect

It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian during which the gap does not close. We show in this article that, at least for finite systems, as the interaction is changed from a model three body interaction to Coulomb, the ground state at filling factor $ν=2/5$ evolves continuously from the so-called Gaffnian wave function to the composite fermion wave function, but the quasiholes alter their character in a nonperturbative manner. This is attributed to the fact that the Coulomb interaction opens a gap in the Gaffnian quasihole sector, pushing many of the states to very high energies. Interestingly, the states below the gap are found to have a one-to-one correspondence with the composite fermion theory, suggesting that the Gaffnian model contains composite fermions, and that the Gaffnian quasiholes are unstable to the formation of composite fermions when a two-body interaction term is switched on. General implications of this study are discussed.

cond-mat.str-el↗

arXiv2008

States of interacting composite fermions at Landau level fillig $ν=2+3/8$

There is increasing experimental evidence for fractional quantum Hall effect at filling factor $ν=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $ν=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.

cond-mat.mes-hall↗

arXiv2007

Theoretical study of even denominator fractions in graphene: Fermi sea versus paired states of composite fermions

The physics of the state at even denominator fractional fillings of Landau levels depends on the Coulomb pseudopotentials, and produces, in different GaAs Landau levels, a composite fermion Fermi sea, a stripe phase, or, possibly, a paired composite fermion state. We consider here even denominator fractions in graphene, which has different pseudopotentials as well as a possible four fold degeneracy of each Landau level. We test various composite fermion Fermi sea wave functions (fully polarized, SU(2) singlet, SU(4) singlet) as well as the paired composite fermion states in the n=0 and $n=1$ Landau levels and predict that (i) the paired states are not favorable, (ii) CF Fermi seas occur in both Landau levels, and (iii) an SU(4) singlet composite fermion Fermi sea is stabilized in the appropriate limit. The results from detailed microscopic calculations are generally consistent with the predictions of the mean field model of composite fermions.

cond-mat.mes-hall↗

arXiv2007

Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at nu=5/2. We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies, and off-diagonal long range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.

cond-mat.mes-hall↗