arXiv subjects

Ajit C. Balram

Publications and source records attributed to Ajit C. Balram.

At least 37 records · Page 2Linked to original sources

arXiv2025

Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}{=}0$ and $\mathbf{n}{=}1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the $\mathbf{n}{=}0$ Landau level are bond-ordered, while those in the $\mathbf{n}{=}1$ Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [Amet, $\textit{et al.}$, Nat. Comm. $\mathbf{6}$, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

cond-mat.mes-hall↗

arXiv2025

Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions

The composite fermion Fermi liquid (CFL) state at $ν=1/2$ filling of a Landau level is a paradigmatic non-Fermi liquid borne out purely by Coulomb interactions. But in what ways is this exotic state of matter different from a Fermi liquid? The CFL entanglement entropy was indeed found to exhibit a significant enhancement compared to free electrons [Shao et al., Phys. Rev. Lett. 114, 206402 (2015)], which was subsequently ruled out as a finite-size effect by the study of a lattice CFL analog [Mishmash and Motrunich, Phys. Rev. B 94, 081110 (2016)]. Moreover, the enhancement was not observed in a quasi-one-dimensional limit of the Coulomb ground state at $ν=1/2$ [Geraedts et al., Science 352, 197 (2016)]. Here, we revisit the problem of entanglement scaling in the CFL state realized in a two-dimensional electron gas. Using Monte Carlo evaluation of the second Rényi entropy $S_2$ for the CFL variational wave function, we show that the entanglement enhancement is present not only at $ν=1/2$ but also at $ν=1/4$, as well as in bosonic CFL states at $ν=1$ and $ν=1/3$ fillings. In all cases, we find the scaling of $S_2$ with subsystem size to be enhanced compared to the non-interacting case, and insensitive to the choice of geometry and projection to the lowest Landau level. We also demonstrate that, for CFL states, the variance of the particle number in a subsystem obeys area-law scaling with a universal subleading corner contribution, in stark contrast with free fermions. Our results establish the enhanced entanglement scaling and suppressed charge fluctuations as fingerprints of non-Fermi-liquid correlations in CFL states.

cond-mat.str-el↗

arXiv2024

Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect

A fundamental manifestation of the nontrivial correlations of an incompressible fractional quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary particles, namely fractionally-charged composite fermions (CFs). We show here that the Girvin-MacDonald-Platzman (GMP) density-wave excitation of the $ν{=}n/(2pn{\pm }1)$ FQH states also splits into more elementary single CF excitons. In particular, the GMP graviton, which refers to the recently observed spin-2 neutral excitation in the vanishing wave vector limit [Liang {\it et al.}, Nature {\bf 628}, 78 (2024)], remains undivided for $ν{=}n/(2n{\pm} 1)$ but splits into two gravitons at $ν{=}n/(4n{\pm} 1)$ with $n{>}1$. A detailed experimental confirmation of the many observable consequences of the splitting of the GMP mode should provide a unique window into the correlations underlying the FQH effect.

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arXiv2024

Phase Separation in the Putative Fractional Quantum Hall A phases

We use several techniques to probe the wave functions proposed to describe the ${\cal A}$ phases by Das, Das, and Mandal [Phys. Rev. Lett. 131, 056202 (2023); Phys. Rev. Lett. 132, 106501 (2024); Phys. Rev. B 110, L121303 (2024).]. As opposed to representing fractional quantum Hall liquids, we find these wave functions to describe states that clearly display strong phase separation. In the process of exploring these wave functions, we have also constructed several new methods for diagnosing phase separation and generating such wave functions numerically. Finally, we uncover a new property of entanglement spectra that can be used as a check for the accuracy of numerics.

cond-mat.str-el↗

arXiv2024

Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene

We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the ``$\overline{(8/3)}\bar{2}1^{3}$" parton wave function, where a parton itself forms an FQHE state. This state is topologically distinct from the $8/17$ Levin-Halperin state, a daughter state of the Moore-Read state. We carry out extensive numerical exact diagonalization of the Coulomb interaction at 8/17 in the zeroth Landau level of bilayer graphene but find that our results cannot conclusively determine the topological order of the underlying ground state. We work out the low-energy effective theory of the $\overline{(8/3)}\bar{2}1^{3}$ edge and make predictions for experimentally measurable properties of the state which can tell it apart from the 8/17 Levin-Halperin state.

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arXiv2024

Fractional quantum Hall coexistence phases in higher Landau levels of graphene

Monolayer graphene under a strong magnetic field near charge neutrality manifests the integer and fractional quantum Hall effects. Since only some of the four spin/valley flavors available to the electrons in each Landau level manifold are filled, they also exhibit spontaneous symmetry breaking the in spin/valley sector, a phenomenon known as quantum Hall ferromagnetism. In this work, we study quantum Hall ferromagnets in the higher Landau level manifolds of monolayer graphene and show that there is an even richer set of symmetry-broken phases than in the lowest Landau level manifold. Specifically, both valley polarized and valley equatorial (where the occupied Landau levels are in an equal superposition of both valleys) ferromagnets, antiferromagnets, and canted antiferromagnets are found. Several types of spin valley entangled phases are found, all of which manifest the simultaneous spontaneous symmetry breaking of both magnetic and lattice symmetries.

cond-mat.mes-hall↗

arXiv2024

Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy

Composite fermion (CF) is a topological quasiparticle that emerges from a non-perturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to non-interacting fermions that form Landau levels in a magnetic field, CFs can fill analogous ``Lambda'' levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with the scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes low-energy properties of CFs, we show that \emph{high-energy} features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the non-interacting CF paradigm.

cond-mat.mes-hall↗

arXiv2024

Universal Modelling of Oscillations in Fractional Quantum Hall Fluids

Density oscillations in quantum fluids can reveal their fundamental characteristic features. In this work, we study the density oscillation of incompressible fractional quantum Hall (FQH) fluids created by flux insertion. For the model Laughlin state, we find that the complex oscillations seen in various density profiles in real space can be universally captured by a simple damped oscillator model in the occupation-number space. It requires only two independent fitting parameters or characteristic length scales: the decay length and the oscillation wave number. Realistic Coulomb quasiholes can be viewed as Laughlin quasiholes dressed by magnetorotons, which can be modeled by a generalized damped oscillator model. Our work reveals the fundamental connections between the oscillations seen in various aspects of FQH fluids such as in the density of quasiholes, edge, and the pair correlation function. The presented model is useful for the study of quasihole sizes for their control and braiding in experiments and large-scale numerical computation of variational energies.

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arXiv2024

Microscopic Model for Fractional Quantum Hall Nematics

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

cond-mat.str-el↗

arXiv2024

Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene

At and near charge neutrality, monolayer graphene in a perpendicular magnetic field is a quantum Hall ferromagnet. In addition to the highly symmetric Coulomb interaction, residual lattice-scale interactions, Zeeman, and sublattice couplings determine the fate of the ground state. Going beyond the simplest model with ultra-short-range residual couplings to more generic couplings, one finds integer phases that show the coexistence of magnetic and lattice order parameters. Here we show that fractional quantum Hall states in the vicinity of charge neutrality have even richer phase diagrams, with a plethora of phases with simultaneous magnetic and lattice symmetry breaking.

cond-mat.mes-hall↗

arXiv2023

Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene

We study the competition between the electron liquid and solid phases, such as Wigner crystal and bubbles, in partially filled Landau levels (LLs) of multilayer graphene. Graphene systems offer a versatile platform for controlling band dispersion by varying the number of its stacked layers. The band dispersion determines the LL wave functions, and consequently, the LL-projected Coulomb interaction in graphene and its multilayers is different from that in conventional semiconductors like GaAs. As a result, the energies of the liquid and solid phases are different in the different LLs of multilayer graphene, leading to an alternative phase diagram for the stability of these phases, which we work out. The phase diagram of competing solid and liquid phases in the LLs of monolayer graphene has been studied previously. Here, we primarily consider $AB{-}$ or Bernal$-$stacked bilayer graphene (BLG) and $ABC{-}$stacked trilayer graphene (TLG) and focus on the Laughlin fractions. We determine the cohesive energy of the solid phase using the Hartree-Fock approximation, and the energy of the Laughlin liquid is computed analytically via the plasma sum rules. We find that at the Laughlin fillings, the electron liquid phase has the lowest energy among the phases considered in the $\mathcal{N}{=}0, 1, 2$ LLs of BLG, as well as in the $\mathcal{N}{=}3, 4$ LLs of TLG, while in the $\mathcal{N}{>}2$ LLs of BLG and $\mathcal{N}{>}4$ LLs of TLG, the solid phases are more favorable. We also discuss the effect of impurities on the above-mentioned phase diagram.

cond-mat.mes-hall↗

arXiv2023

Composite-fermion pairing at half and quarter filled lowest Landau level

The Halperin-Lee-Read Fermi sea of composite fermions (CFs) at half-filled lowest Landau level is the realization of a fascinating non-Fermi liquid metallic phase. Remarkably, experiments have found that as the width of the quantum well is increased, this state makes a transition into a fractional quantum Hall (FQH) state, the origin of which has remained an important puzzle since its discovery more than three decades ago. We perform detailed and accurate quantitative calculations using a systematic variational framework for the pairing of CFs that closely mimics the BCS theory of superconductivity. We find: (i) as the quantum-well width is increased, the single-component CF Fermi sea occupying the lowest symmetric subband of the quantum well undergoes an instability into a single-component p-wave paired state of CFs; (ii) the theoretical phase diagram in the quantum-well width - electron density plane is in excellent agreement with experiments; (iii) a sufficient amount of asymmetry in the charge distribution of the quantum well destroys the FQH effect, as observed experimentally; and (iv) the two-component 331 state is energetically less favorable than the single component paired state. Evidence for FQH effect has been seen in wide quantum wells also at quarter-filled lowest Landau level; here our calculations indicate an f-wave paired state of CFs. We further investigate bosons in the lowest Landau level at filling factor equal to one and show that a p-wave pairing instability of CFs, which are bosons carrying a single flux quantum, in agreement with exact diagonalization studies. The general consistency of the composite-fermion BCS approach with experiments lends support to the notion of CF pairing as the mechanism of FQH effects at even-denominator filling factors. Various experimental implications are mentioned.

cond-mat.str-el↗

arXiv2023

Prediction of non-Abelian fractional quantum Hall effect at $ν= 2 + \frac{4}{11}$

The fractional quantum Hall effect (FQHE) in the second Landau level (SLL) likely stabilizes non-Abelian topological orders. Recently, a parton sequence has been proposed to capture many of the fractions observed in the SLL [Ajit C. Balram, SciPost Phys. {\bf 10}, 083 (2021)]. We consider the first member of this sequence which has not yet been studied, which is a non-Abelian state that occurs at $4/11$. As yet FQHE in the SLL at this fraction has not been observed in experiments. Nevertheless, by studying its competition with other candidate FQHE states in the SLL we show that this parton state might be viable. We also make predictions for experimentally measurable properties of the parton state which can distinguish it from other topological orders.

cond-mat.str-el↗

arXiv2023

Signatures of Supersymmetry in the $ν{=}5/2$ Fractional Quantum Hall Effect

The Moore-Read state, one of the leading candidates for describing the fractional quantum Hall effect at filling factor $ν{=}5/2$, is a paradigmatic $p$-wave superconductor with non-Abelian topological order. Among its many exotic properties, the state hosts two collective modes: a bosonic density wave and a neutral fermion mode that arises from an unpaired electron in the condensate. It has recently been proposed that the descriptions of the two modes can be unified by postulating supersymmetry (SUSY) that relates them in the long-wavelength limit. Here we extend the SUSY description to construct wave functions of the two modes on closed surfaces, such as the sphere and torus, and we test the resulting states in large-scale numerical simulations. We demonstrate the equivalence in the long-wavelength limit between SUSY wave functions and previous descriptions of collective modes based on the Girvin-MacDonald-Platzman ansatz, Jack polynomials, and bipartite composite fermions. Leveraging the first-quantized form of the SUSY wave functions, we study their energies using the Monte Carlo method and show that realistic $ν{=}5/2$ systems are close to the putative SUSY point, where the two collective modes become degenerate in energy.

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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.

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arXiv2023

Real-space entanglement spectra of parton states in fractional quantum Hall systems

Real-space entanglement spectra (RSES) capture characteristic features of the topological order encoded in the fractional quantum Hall (FQH) states. In this work, we numerically compute, using Monte Carlo methods, the RSES and the counting of edge excitations of non-Abelian FQH states constructed using the parton theory. Efficient numerical computation of RSES of parton states is possible, thanks to their product-of-Slater-determinant structure, allowing us to compute the spectra in systems of up to 80 particles. Specifically, we compute the RSES of the parton states $ϕ_2^2$, $ϕ_2^3$, and $ϕ_3^2$, where $ϕ_n$ is the wave function of $n$ filled Landau levels, in the ground state as well as in the presence of bulk quasihole states. We then explicitly demonstrate a one-to-one correspondence of RSES of the parton states with representations of the Kac-Moody algebras satisfied by their edge currents. We also show that for the lowest Landau level projected version of these parton states, the spectra match with that obtained from the edge current algebra. We also perform a computation of spectra of the overlap matrices corresponding to the edge excitations of the parton states with a constrained number of particles in the different parton Landau levels. Counting in these matches the individual branches present in RSES, providing insight about how different branches are formed.

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arXiv2023

Supergravity model of the Haldane-Rezayi fractional quantum Hall state

Supersymmetry and supergravity were invented in the 1970s to solve fundamental problems in high-energy physics. Even though neither of these ideas has yet been confirmed in high-energy and cosmology experiments, they have been beneficial in constructing numerous theoretical models, including superstring theory. Despite the absence of supersymmetry in particle physics, it can potentially emerge in exotic phases of strongly correlated condensed matter systems. In this paper, we propose a supergravity model that describes the low-energy physics of the Haldane-Rezayi state, a gapless quantum Hall state that occurs in a half-filled Landau level. We show that the corresponding edge modes of the Haldane-Rezayi state and the Girvin-MacDonald-Platzman algebra appear naturally in the supergravity model. Finally, we substantiate our theoretical findings with numerical exact diagonalization calculations that support the appearance of the emergent graviton and gravitino excitations in the Haldane-Rezayi state.

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arXiv2023

Robust quantum many-body scars in the one-dimensional spin-1 Kitaev model

Experimental observation of coherent oscillations in a Rydberg atom chain [Bernien et al., Nature 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBS) which is a new paradigm for ergodicity-breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the "PXP" model, which has been shown to host the Eigenstate Thermalization Hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this work, we study the QMBS that can arise in one such model, namely the spin-$1$ Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Research 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are robust and longer-lived than those in the PXP model.

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