arXiv subjects

Sutirtha Mukherjee

Publications and source records attributed to Sutirtha Mukherjee.

13 recordsLinked to original sources

arXiv2021

From the Gaffnian critical point to the incompressible 2/5 quantum Hall state

Despite the high overlap with the exact Coulomb ground state, the so-called Gaffnian state fails to describe the incompressibility at the 2/5 quantum Hall filling factor and consequently it was conjectured to be a quantum critical state. To achieve a gapped state starting from the Gaffnian wavefunction, which we interpret as the inter-flavor pairing of the composite fermions, we propose a minimally `modified Gaffnian' wavefunction keeping the pairing intact. We find that a suitable hybridization of these two wavefunctions is an excellent description of the 2/5 quantum Hall state. It has a very high overlap with the exact Coulomb state and their entanglement spectra match up to reasonably higher levels. Interestingly, this hybridized wavefunction being a representative of a paired state suggests an exotic possibility of non-Abelian quasiparticle excitations at 2/5 filling.

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arXiv2021

Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State

In view of the evolution from the integer to fractional quantum Hall effect, the next frontier in the research of topological insulators is to investigate what happens in fractionally filled topological flat bands. A particularly pressing question is if there exists the lattice analogue of the Laughlin state in the 1/3-filled Chern flat band, dubbed as the Chern-Laughlin state. The answer depends crucially on the form of the electron-electron interaction, which can generate various competing ground states such as the Laughlin, stripe/nematic, parafermion, and parton states. Unfortunately, it is difficult to precisely characterize the exact ground state as any of these candidate ground states due to the lack of appropriate order parameters. Here, we propose that the existence of an adiabatic path from fractional Chern insulators to the Tao-Thouless state, i.e., the root partition state of the Laughlin state in the thin torus limit, can serve as an effective order parameter for the Chern-Laughlin state. Specifically, by devising the piecewise hybrid adiabatic path of first transforming the electron-electron interaction and then taking the thin torus limit, it is shown that Chern flat bands with the nearest-neighbor interaction can indeed host the Chern-Laughlin state at 1/3 filling. This method can be extended to possible FCIs at other general fillings of the Jain sequence.

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arXiv2018

Fractional Quantum Hall Effect at $ν=2+6/13$: The Parton Paradigm for the Second Landau Level

The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at $ν=2+6/13$~ [Kumar \emph{et al.}, Phys. Rev. Lett. {\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "$\bar{3}\bar{2}111$" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $\bar{3}\bar{2}111$ state to be a good candidate for the $ν=2+6/13$ FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "$\bar{n}\bar{2}111$" family of parton states naturally describes many observed SLL FQHE plateaus.

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arXiv2017

Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator

Motivated by the close analogy with the fractional quantum Hall states (FQHSs), fractional Chern insulators (FCIs) are envisioned as strongly correlated, incompressible states emerging in a fractionally filled, (nearly) flat band with non-trivial Chern number. Built upon this vision, fractional topological insulators (FTIs) have been proposed as being composed of two independent copies of the FCI with opposite Chern numbers for different spins, preserving the time-reversal symmetry as a whole. An important question is if the correlation between electrons with different spins can be really ignored. To address this question, we investigate the effects of correlation in the presence of spin-dependent holomorphicity, i.e., electrons of one spin species reside in the holomorphic lowest Landau level, while those of the other in the antiholomorphic counterpart. By constructing and performing exact diagonalization of an appropriate model Hamiltonian, here, we show that generic, strongly correlated, fractionally filled states with spin-dependent holomorphicity cannot be described as two independent copies of the FQHS, suggesting that FTIs in the lattice cannot be described as those of the FCI either. Fractionally filled states in this system are generally compressible except at half filling, where an insulating state called the half-filled spin-holomorphic FTI occurs. It is predicted that the half-filled spin-holomorphic FTI is susceptible to an inherent spontaneous symmetry breaking, leading to the spatial separation of spins.

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arXiv2017

Jastrow form of the Ground State Wave Functions for Fractional Quantum Hall States

The topological morphology--order of zeros at the positions of electrons with respect to a specific electron--of Laughlin state at filling fractions $1/m$ ($m$ odd) is homogeneous as every electron feels zeros of order $m$ at the positions of other electrons. Although fairly accurate ground state wave functions for most of the other quantum Hall states in the lowest Landau level are quite well-known, it had been an open problem in expressing the ground state wave functions in terms of flux-attachment to particles, {\em a la}, this morphology of Laughlin state. With a very general consideration of flux-particle relations only, in spherical geometry, we here report a novel method for determining morphologies of these states. Based on these, we construct almost exact ground state wave-functions for the Coulomb interaction. Although the form of interaction may change the ground state wave-function, the same morphology constructs the latter irrespective of the nature of the interaction between electrons.

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arXiv2017

Topological Structure and an Accurate Wave Function for the Enigmatic 5/2 Fractional Quantum Hall State

We comprehensively show the topological structure--order of zeros felt by an electron at the positions of other electrons --for the enigmatic filling factor 5/2 at the "Pfaffian-shift" in a spherical geometry. A set of linearly independent antisymmetric functions that are constructed from the possible graphs preserving this topological structure provides complete basis for determining an accurate ground state wave function for any interaction, in particular the Coulomb interaction. One of the graphs describes $Z_2$ para-fermion equivalently the Pfaffian wave function, but some of the other graphs also contribute to form the exact ground state for the Coulomb interaction. We further show that our wave function for the Coulomb interaction supports clustering up to half of the composite bosons, signifying a strong-coupling regime.

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arXiv2017

Determination of many-electron basis functions for a Quantum Hall ground state using Schur polynomials

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles.

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arXiv2017

The enigma of the $ν=2+\frac{3}{8}$ fractional quantum Hall effect

The fractional quantum Hall effect at $ν=2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class of of exotic states described by the Bonderson-Slingerland wave function. Its excitations are non-Abelian anyons similar to those of the well studied Pfaffian state at 5/2, but its wave function has a more complex structure. Using the effective edge theory, we make predictions for various measurable quantities that should enable a confirmation of the underlying topological order of this state.

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arXiv2015

Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $ν=4/13$, 5/17, and 3/10

By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states at the filling factors $ν= 3/10$, 4/13, and 5/17 in the range $2/7 <ν< 1/3$. These observed states correspond to partially filled second effective Landau level, for the composite fermions carrying four vortices, with filling factor $\barν = 1/2$, 1/3, and 2/3 respectively, analogous to the previously studied states of composite fermions with two attached vortices in the range $1/3 <ν<2/5$. We show that the character of these states in the range $2/7 <ν< 1/3$ replicates the same for the states in the range $1/3 <ν<2/5$ having identical $\barν$: Chiral p-wave pairing with anti-Pfaffian correlation of composite fermions carrying six quantized vortices produces incompressible state at $ν= 3/10$; an unconventional interaction between composite fermions, resulting from the suppression of fermion pairs with relative angular momentum three and producing fractional quantum Hall effect of composite fermions in the second effective Landau level with $\barν =1/3$ and its particle-hole conjugate filling factor 2/3, reproduces incompressible states at $4/13$ and $5/17$ filling factors. We further estimate the thermodynamic limit of the ground state energies and calculate the lowest energy gap for neutral collective excitations of these states.

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arXiv2015

Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions

We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect (FQHE) states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wavevectors with {\em anomalously} low energies which do not have any analogue to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states are responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted before for these FQHE states. Experimental consequences of our theory are also discussed.

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arXiv2014

Possible realization of a chiral p-wave paired state in a two component system

There is much interest in the realization of systems with p-wave pairing in one dimension or chiral p-wave pairing in two dimensions, because these are believed to support Majorana modes at the ends or inside vortices. We consider a two component system of composite fermions and provide theoretical evidence that, under appropriate conditions, the screened interaction between the minority composite fermions is such as to produce an almost exact realization of p-wave paired state described by the so-called anti-Pfaffian wave function. This state is predicted to occur at filling $ν=3/8$ or 13/8 in GaAs when the Zeeman energy is sufficiently small, and at $ν=\pm 3/8$ or $\pm 13/8$ in single layer graphene when either the Zeeman or the valley splitting is sufficiently small.

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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.

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arXiv2012

Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level

We predict that an incompressible fractional quantum Hall state is likely to form at $ν=3/8$ as a result of a chiral p-wave pairing of fully spin polarized composite fermions carrying four quantized vortices, and that the pairing is of the Anti-Pfaffian kind. Possible experimental ramifications are discussed.

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