arXiv subjects

Ajit C. Balram

Publications and source records attributed to Ajit C. Balram.

At least 73 records · Page 4Linked to original sources

arXiv2019

Current-induced gap opening in interacting topological insulator surfaces

Two-dimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized two-terminal conductance. Quantization is protected by time-reversal symmetry, which forbids elastic backscattering. Paradoxically, the current-carrying state itself breaks the time-reversal symmetry that protects it. Here we show that the combination of electron-electron interactions and momentum-dependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Current-induced gap opening is manifested via a nonlinear contribution to the system's $I-V$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous current-induced gap opening mechanism for the surface states of three-dimensional TIs.

cond-mat.mes-hall↗

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

Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea

The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k^*_{\rm F}=\sqrt{4πρ_e}$, where $ρ_e$ is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from $ν=1/2$, the area is seen to be consistent with $k^*_{\rm F}=\sqrt{4πρ_e}$ for $ν<1/2$ but $k^*_{\rm F}=\sqrt{4πρ_h}$ for $ν>1/2$, where $ρ_h$ is the density of holes in the lowest Landau level. This result is consistent with particle-hole symmetry in the lowest Landau level. We investigate in this article the Fermi wave vector of the spin-singlet CF Fermi sea (CFFS) at $ν=1/2$, for which particle-hole symmetry is not a consideration. Using the microscopic CF theory, we find that for the spin-singlet CFFS the Fermi wave vectors for up and down spin CFFSs at $ν=1/2$ are consistent with $k^{*\uparrow,\downarrow}_{\rm F}=\sqrt{4πρ^{\uparrow,\downarrow}_e}$, where $ρ^{\uparrow}_e=ρ^{\downarrow}_e=ρ_e/2$, which implies that the residual interactions between composite fermions do not cause a non-perturbative correction for non-fully spin polarized CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by $k^{*\uparrow}_{\rm F}=\sqrt{4πρ^{\uparrow}_e}$ and $k^{*\downarrow}_{\rm F}=\sqrt{4πρ^{\downarrow}_e}$.

cond-mat.str-el↗

arXiv2019

Charge and spin textures of Ising quantum Hall ferromagnet domain walls

We investigate the charge and spin structures associated with arbitrary smooth polarization textures in Ising (integer) quantum Hall ferromagnets. We consider the case where the two polarizations (denoted "pseudospin" up and down) correspond to states with opposite physical spin and different Landau level indices, $n\uparrow$ and $m\downarrow$. We derive analytic expressions for the charge and spin densities, as functions of the underlying pseudospin texture, and use these results to investigate different types of linear domain walls, both analytically and numerically. We find that any smooth domain wall between two oppositely polarized domains carries a universal quantized charge dipole density proportional to the difference of Landau level indices, $n-m$. Additionally, non-uniformities in the domain wall may give rise to excess net charge localized at the domain wall. Interestingly, the physical spin density associated with the domain wall generally exhibits a much more complex multipolar structure than that of the pseudospin texture. These results should for example help to elucidate the mechanisms underlying nuclear electric resonance and nuclear polarization oscillations in Ising quantum Hall systems.

cond-mat.mes-hall↗

arXiv2019

Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $ν= k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted "$\bar{2}^{k}1^{k+1}$," and show that they lie in the same universality classes as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results imply that a $(U(1)_{k+1} \times U(2k)_{-1})/(SU(k)_{-2} \times U(1)_{-1})$ coset conformal field theory describes the edge excitations of the $\bar{2}^{k}1^{k+1}$ state, suggesting non-trivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence "$\bar{n}\bar{2}^{2}1^{4}$," with $n=1,2,3$, to describe the FQH states observed at $ν=2+1/2,~2+2/5$ and $2+3/8$.

cond-mat.str-el↗

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

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.

cond-mat.str-el↗

arXiv2018

Parton construction of a wave function in the anti-Pfaffian phase

In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL} Φ_{1}^3[Φ_{2}^{*}]^{2}\simΨ^{2}_{2/3}/Φ_{1}$ and in the spherical geometry it occurs at the same flux as the anti-Pfaffian state. This state has a good overlap with the anti-Pfaffian state and with the ground state obtained by exact diagonalization, using the second Landau level Coulomb interaction pseudopotentials for an ordinary semiconductor such as GaAs. By calculating the entanglement spectrum we show that this state lies in the same phase as the anti-Pfaffian state. A major advantage of this parton state is that its wave function can be evaluated for large systems, which makes it amenable to variational calculations. In the appendix of this work we have numerically assessed the validity of another candidate state at filling factor $ν=5/2$, namely the particle-hole-symmetric Pfaffian (PH-Pfaffian) state. We find that the proposed candidate wave function for the PH-Pfaffian state is particle-hole symmetric to a high degree but it does not appear to arise as the ground state of any simple Hamiltonian with two-body interactions.

cond-mat.str-el↗

arXiv2018

Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene

Motivated by recent experiments that reveal expansive fractional quantum Hall states in the $n=1$ graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet {\em et al.}, Nat. Common. {\bf 6}, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the $n=0$ Landau level. In particular, for the states at filling factors $n/(2n\pm 1)$, both exact diagonalization and the composite fermion theory show that the ground state is fully spin polarized and supports a robust spin wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the $n=1$ graphene Landau level, indicating a lack of fractional quantum Hall effect at half filling in the $n=1$ graphene Landau level.

cond-mat.str-el↗

arXiv2018

Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect

The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This article investigates an emergent symmetry in the fractional quantum Hall effect, namely the PH symmetry of {\em composite fermions}, which relates states at composite fermion filling factors $ν^*=n+\barν$ and $ν^*=n+1-\barν$, where the integer $n$ is the $Λ$ level index and $0\leq \barν\leq 1$. Detailed calculations using the microscopic theory of composite fermions demonstrate that for low lying $Λ$ levels (small $n$): (i) the 2-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $Λ$ level; and (ii) the 3-body interaction for composite fermions is an order of magnitude smaller than the 2-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $Λ$ levels, which is also supported by exact diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $ν={n+\barν\over 2(n+\barν)\pm 1}$ and $ν={n+1-\barν\over 2(n+1-\barν)\pm 1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $Λ$ level index, the 2-body and 3-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $ν=1/2$.

cond-mat.str-el↗

arXiv2017

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like $Λ$ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called "magnetoroton" minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B {\bf 48}, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar \emph{et al.} [Phys. Rev. Lett. {\bf 117}, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence $s/(2s+1)$ and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar \emph{et al.}'s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar \emph{et al.}'s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence $s/(2s\pm 1)$ in the lowest Landau level and the $n=1$ Landau level of graphene.

cond-mat.str-el↗

arXiv2017

Dynamical phase transitions, temporal orthogonality and the dynamics of observables in one dimensional ultra-cold quantum gases: from the continuum to the lattice

We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singularities of the rate functions, have been suggested to indicate the emergence of dynamical criticality and we address the question of whether such zeros can be tied to the dynamics of physically relevant observables and hence order parameters in the systems. For this we first numerically analyze the dynamics of a hard-core boson gas in a one-dimensional waveguide when a quenched lattice potential is commensurate with the particle density. Such a system can undergo a pinning transition to an insulating state and we find non-analytic behavior in the evolution of the rate function which is indicative of dynamical phase transitions. In addition, we perform simulations of the time dependence of the momentum distribution and compare the periodicity of this collapse and revival cycle to that of the non-analyticities in the rate function: the two are found to be closely related only for deep quenches. We then confirm this observation by analytic calculations on a closely related discrete model of hard-core bosons in the presence of a staggered potential and find expressions for the rate function for the quenches. By extraction of the zeros of the Loschmidt amplitude we uncover a non-equilibrium timescale for the emergence of non-analyticities and discuss its relationship with the dynamics of the experimentally relevant parity operator.

cond-mat.quant-gas↗

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.

cond-mat.mes-hall↗

arXiv2016

Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states

Numerical studies by Wójs, Yi and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors $ν=$ 1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel dominates. The interaction between composite fermions in the second $Λ$ level (composite fermion analog of the electronic Landau level) satisfies this property, and recent studies have supported unconventional fractional quantum Hall effect of composite fermions at $ν^*=$ 4/3 and 5/3, which manifests as fractional quantum Hall effect of electrons at $ν=$ 4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at $ν=$ 4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at $ν^*=$ 4/3, 5/3 and 6/5, and find that all these fractional quantum Hall states are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman energies for the spin phase transitions between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and compare them against recent experiments.

cond-mat.str-el↗

arXiv2016

The nature of composite fermions and the role of particle hole symmetry: A microscopic account

Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well established microscopic theory of the fractional quantum Hall effect and the 1/2 state, which is based on {\em non-relativistic} composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor $ν=1/2$ corresponds to an effective time reversal transformation (i.e. $\{\vec{k}_j\}$$\rightarrow$$\{-\vec{k}_j\}$) for composite fermions, and discuss how this connects to the absence of $2k_{\rm F}$ backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion $Λ$ levels (analogs of electronic Landau levels) we determine the $Λ$ level spacing and find it to be very nearly independent of the $Λ$ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a "normal form" for the unprojected wave functions of the $n/(2pn-1)$ states that correctly capture the topological properties even without lowest Landau level projection.

cond-mat.str-el↗

arXiv2016

Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment

The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. We obtain accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. We find that the observed phase diagram is in good quantitative agreement with theory that neglects Landau level mixing, but the agreement becomes significantly worse when Landau level mixing is incorporated assuming that the corrections to the energies are linear in the Landau level mixing parameter $λ$. This implies that a first order perturbation theory in $λ$ is inadequate for the current experimental systems, for which $λ$ is typically on the order of or greater than one. We also test the accuracy of the composite-fermion theory and find that all lowest Landau level projection methods used in the literature are very accurate for the states of the form $n/(2n+1)$ but for the states at $n/(2n-1)$ the results are more sensitive to the projection method. An earlier prediction of an absence of spin transitions for the $n/(4n+1)$ states is confirmed by more rigorous calculations, and new predictions are made regarding spin physics for the $n/(4n-1)$ 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.

cond-mat.str-el↗