arXiv subjects

Sudhansu S. Mandal

Publications and source records attributed to Sudhansu S. Mandal.

At least 37 records · Page 2Linked to original sources

arXiv2019

Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect

Motivated by the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor $ν= 1/m$, I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for $1/m$ state. Each of these wave functions is interpreted as expelled electron into a different Hilbert subspace from the original Hilbert space of Laughlin condensate while still maintaining its correlation (although changed) with the electrons in the condensate such that the expelled electron behaves as a CF with respect to the electrons in the condensate. With this interpretation, I show that the ground state wavefunctions for general states at filling fractions $ν_{n,m}^{\pm} = n/[n(m\mp 1)\pm 1]$, respectively, can be constructed as coherent superposition of $n$ coupled Laughlin condensates and their conjugates, formed at different Hilbert subspaces. The corresponding wave functions, specially surprising for $ν_{n,m}^{-}$ sequence of states, are identical with those proposed in the theory of noninteracting CFs. The states which were considered as fractional quantum Hall effect of interacting CFs, can also be treated in the same footing as for the prominent sequences of states describing as the coupled condensates among which one is a non-Laughlin condensate in a different Hilbert subspace. Further, I predict that the half filling of the lowest Landau level is a quantum critical point for phase transitions between two topologically distinct phases each corresponding to a family of states.

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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

Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9

We determine the lowest and higher order collective modes in both spin-conserving and spin-reversed sectors by calculating energy differences of the appropriate linear combinations of different levels of composite-fermion-excitons and the fully spin-polarized ground states at filling factors $ν=1/3$, 2/5, 3/7, and 4/9. Apart from providing the detailed study of previously reported modes that have also been observed in the experiments, we predict additional higher energy modes at different filling factors. The lowest and the next higher spin-conserving modes have equal number of "magneto-rotons" and the number is the same as the number of filled effective Landau-like levels of composite fermions. The higher energy modes at $ν=1/3$ merge with the lowest mode at long-wavelength. The spin-conserving modes do not merge at other filling factors. Apart from showing zero-energy spin-wave mode at zero momentum, thanks to Larmor's theorem, the lowest spin-reversed modes at the ferromagnetic ground states of $ν=2/5$, 3/7, and 4/9 display one or more "spin-rotons" at negative energies signalling the unstable fully polarized ground states at sufficiently small Zeeman energies. The high energy spin-reversed modes also have spin-rotons but at positive energies. The energies of these excitations depend on the finite width of the quantum well as the Coulomb interaction gets screened. We determine finite thickness correction to the Coulomb interaction by the standard method of local density approximation and use them to calculate the critical energies such as rotons, long-wavelength, and short-wavelength modes which are detectable in inelastic light scattering experiments.

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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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arXiv2013

Amplitude Fluctuations Driven by the Density of Electron Pairs within Nanosize Granular Structuters inside Strongly Disordered Superconductors: Evidence for a Shell-Like Effect

Motivated by the recent observation of the shell effect in a nanoscale pure superconductor by Bose {\em et al} [Nat. Mat. {\bf 9}, 550 (2010)], we explore the possible shell-like effect in a strongly disordered superconductor as it is known to produce nanosize superconducting puddles (SPs). We find a remarkable change in the texture of the pairing amplitudes that is responsible for forming the SP, upon monotonic tuning of the average electron density, $\langle n \rangle$, and keeping the disorder landscape unaltered. Both the spatially averaged pairing amplitude and the quasiparticle excitation gap oscillate with $\langle n \rangle$. This oscillation is due to a rapid change in the low-lying quasiparticle energy spectra and thereby a change in the shapes and positions of the SPs. We establish a correlation between the formation of SPs and the shell-like effect. The experimental consequences of our theory are also discussed.

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arXiv2012

Correlated pair-amplitude fluctuations in disordered BCS superconductors

More than fifty years old "Anderson's theorem" suggests disorder-independent pair-amplitude and critical temperature at low to moderate strength of disorders. In spite of the extension of this paradigm and several subsequent theoretical proposals, mechanism for the superconductor-insulator transition (SIT) at large disorder is still an open problem. The understanding of experimental data at intermediate disorder is also lacking. Here, we proceed beyond "Anderson's theorem" by calculating disorder-averaged two-point pair-amplitude fluctuations. We find this correlation to be finite and long-ranged, activating scattering of quasiparticles in the novel "Cooper" channel. Without invoking any further parameter, this mechanism quantitatively predicts several testable properties: reduction of pair-amplitude at zero temperature; reduction of temperature, T_Δ, at which pair-amplitude vanishes; suppression and broadening of coherence peak; and decrease of hard-gap in quasiparticle density of states, with the increase of disorder. We interpret old and new data at intermediate disorder in light of our predictions. The robustness of this theory will hopefully provide insight to unravel the true mechanism for SIT.

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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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arXiv2012

Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peak-value of AHC is as high as the bare-buble contribution. We find that the wave number, q, at which the peaks occur is the inverse of the geometric mean of the mean free path of an electron and the spin-exchange length scale. Although the Rashba energy is responsible for the peak-value of AHC, the peak position is independent of it.

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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.

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arXiv2011

Fermionic Chern-Simons Theory of SU(4) Fractional Quantum Hall Effect

We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin and the valley degrees of freedom, which involves four distinct CS gauge fields. We choose the corresponding elements of the CS coupling matrix such that an even number of spin and valley quantum number dependent flux quanta is attached to all electrons and that any electron with a given spin and valley quantum number sees an integer number of flux attached to other electrons with different (spin and valley) quantum numbers. Using this CS matrix, we obtain a list of possible fractional quantum Hall states that might occur in graphene and propose wavefunctions for those states. Our analysis also applies to fractional quantum Hall states of both bilayer quantum Hall systems without spin polarization and bilayer spin polarized graphene.

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arXiv2009

Manifestation of helical edge states as zero-bias magneto-tunneling-conductance peaks in non-centrosymmetric superconductors

Helical edge states exist in the mixed spin-singlet and -triplet phase of a noncentrosymmetric superconductor (NCSS) when the pair amplitude (PA) in the negative helicity band, $Δ_-$, is smaller than the PA in the positive helicity band, $Δ_+$, i.e., when the PA in the triplet component is more than the same in the singlet component. We numerically determine energies of these edge states as a function of $γ= Δ_-/Δ_+$. The presence of these edge states is reflected in the tunneling process from a normal metal to an NCSS across a bias energy $eV$: (i) Angle resolved spin conductance (SC) obeying the symmetry $g_s(ϕ) =-g_s(-ϕ)$ shows peaks when the bias energy equals the available quasiparticle edge state energy provided $|eV| \lesssim Δ_-$. (ii) The total SC, $G_s$, is zero but modulates with $eV$ for finite magnetic field $H$. (iii) The zero bias peaks of $G_s$ and total charge conductance, $G_c$, at finite $H$ split into two at finite $eV$ for moderate $H$. (iv) At zero bias, $G_c$ and $G_s$ increase with $H$ and show peaks at $|H|\sim γH_0$ where $H_0$ is a characteristic field.

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arXiv2008

Frequency- and transverse wave-vector-dependent spin Hall conductivity in two-dimensional electron gas with disorder

We determine wave number $q$ and frequency $ω$ dependent spin Hall conductivity $σ_{yx}^s(q, ω)$ for a disordered two dimensional electron system with Rashba spin orbit interaction when $\q$ is {\it transverse} to the electric field. Both the conventional definition of spin current and its new definition which takes care of the conservation of spins, have been considered. The spin Hall conductivitivities for both of these definitions are qualitatively similar. $σ_{yx}^s(q, ω)$ is zero at $q=0, ω=0$ and is maximum at $q=0$ and at small but finite $ω$ whose value depends on different parameters of the system. Interestingly for $ω\to 0$, $σ_{yx}^s(q)$ resonates when $Λ\simeq L_{so}$ which are the wavelength $(Λ= 2π/q)$ of the electric field's spatial variation and the length for one cycle of spin precession respectively. The sign of the out-of-plane component of the electrons' spin flips when the sign of electric field changes due to its spatial variation along transverse direction. It changes the mode of spin precession from clockwise to anti-clockwise or {\it vice versa} and consequently a finite spin Hall current flows in the bulk of the system.

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arXiv2007

Ginzburg-Landau theory of noncentrosymmetric superconductors

The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\it et al.}, \phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin split band and pair scattering is allowed to occur between two spin split bands. The GL theory of such a system predicts two transition temperatures, the higher of which is the conventional critical temperature $T_c$ while the lower one $T^*$ corresponds to the cross-over from a mixed singlet-triplet phase at lower temperatures to only spin-singlet or spin-triplet (depending on the sign of the interband scattering potential) phase at higher temperatures. As a consequence, $n_s (T)$ shows a kink at this cross-over temperature. We attribute the temperature at which sudden change of slope occurs in the observed $n_s (T)$ to the temperature $T^*$. This may also be associated with the observed kink in the penetration depth data of CePt$_3$Si. We have also estimated critical field near critical temperature.

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