arXiv subjects

Ajit C. Balram

Publications and source records attributed to Ajit C. Balram.

At least 55 records · Page 3Linked to original sources

arXiv2022

Fractional quantum Hall effect with unconventional pairing in monolayer graphene

Motivated by the observation of even denominator fractional quantum Hall effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\textit{et al.}$, Nature Physics $\textbf{15}$, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an $f$-wave pairing. Analogous calculation suggests the possibility of a $p$-wave pairing of composite fermions at half filling in the $n=2$ graphene Landau level, whereas no pairing instability is found at half filling in the $n=0$ and $1$ graphene Landau levels. The relevance of these results to experiments is discussed.

cond-mat.str-el↗

arXiv2022

Local density of states and particle entanglement in topological quantum fluids

The understanding of particle entanglement is an important goal in the studies of correlated quantum matter. The widely-used method of scanning tunneling spectroscopy -- which measures the local density of states (LDOS) of a many-body system by injecting or removing an electron from it -- is expected to be sensitive to particle entanglement. In this paper, we systematically investigate the relation between the particle entanglement spectrum (PES) and the LDOS of fractional quantum Hall (FQH) states, the paradigmatic strongly-correlated phases of electrons with topological order. Using exact diagonalization, we show that the counting of levels in both the LDOS and PES in the Jain sequence of FQH states can be predicted from the composite fermion theory. We point out the differences between LDOS and PES characterization of the bulk quasihole excitations, and we discuss the conditions under which the LDOS counting can be mapped to that of PES. Our results affirm that tunneling spectroscopy is a sensitive tool for identifying the nature of FQH states.

cond-mat.str-el↗

arXiv2022

Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene

Extensive fractional quantum Hall effect (FQHE) has been observed in graphene-based materials. Some of the observed fractions are anomalous in that FQHE has not been established at these fractions in conventional GaAs systems. One such fraction is $4/13$, where incompressibility has recently been reported in graphene [Kumar et al., Nat. Comm. 9, 2776 (2018)]. We propose a partonic wave function at $4/13$ and show it to be a viable candidate to describe the Coulomb ground state. Using the effective edge theory, we make predictions for experimentally measurable properties of the state.

cond-mat.str-el↗

arXiv2022

Revisiting excitation gaps in the fractional quantum Hall effect

Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples [Villegas Rosales {\it et al.}, Phys. Rev. Lett. {\bf 127}, 056801 (2021)] open the possibility of a better quantitative understanding of this important issue. We present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the $n/(2n\pm 1)$ states as $Δ_{n/(2n\pm 1)} = Ce^2/[(2n\pm 1)\varepsilon l]-Γ$, where $\varepsilon$ is the dielectric constant of the background semiconductor and $l$ is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and $Γ$ as a disorder-induced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that $Γ$ can be nonzero even in the absence of disorder.

cond-mat.str-el↗

arXiv2022

Prethermalization and entanglement dynamics in interacting topological pumps

We investigate the formation of quasisteady states in one-dimensional pumps of interacting fermions at non-integer filling fraction, in the regime where the driving frequency and interaction strength are small compared to the instantaneous single-particle band gap throughout the driving cycle. The system rapidly absorbs energy from the driving field, and approaches a quasisteady state that locally resembles a maximal entropy state subject to the constraint of fixed particle number in each of the system's single-particle Floquet bands. We explore the nature of this quasisteady state through one-body observables including the pumped current and natural orbital occupations, as well as the (many-body) entanglement spectrum and entropy. Potential disorder significantly reduces the amplitude of fluctuations of the quasisteady state current around its universal value, while the lifetime of the quasisteady state remains nearly unaffected for disorder strengths up to the scale of the single-particle band gap. Interestingly, the natural orbital occupations and entanglement entropy display patterns signifying the periodic entangling and disentangling of the system's degrees of freedom over each driving cycle. Moreover, prominent features in the system's time-dependent entanglement spectrum reveal the emergence of new long timescales associated with the equilibration of many-particle correlations.

cond-mat.quant-gas↗

arXiv2022

Fractional quantum Hall effect in semiconductor systems

The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems, topology and quantum mechanics conspire to give rise to exotic physics that manifests via robust quantization of the Hall resistance. In this chapter, we provide an overview of the experimental phenomenology of the FQH effect in GaAs-based semiconductor materials and present its theoretical interpretations in terms of trial wave functions, composite fermion quasiparticles, and enigmatic non-Abelian states. We also highlight some recent developments, including the parton theory and the Dirac composite fermion field theory of FQH states, the role of anisotropy and geometrical degrees of freedom, and quantum entanglement in FQH fluids.

cond-mat.mes-hall↗

arXiv2022

Very high-energy collective states of partons in fractional quantum Hall liquids

The low energy physics of fractional quantum Hall (FQH) states -- a paradigm of strongly correlated topological phases of matter -- to a large extent is captured by weakly interacting quasiparticles known as composite fermions (CFs). In this paper, based on numerical simulations and effective field theory, we argue that some \emph{high energy} states in the FQH spectra necessitate a different description based on \emph{parton} quasiparticles. We show that Jain states at filling factor $ν{=}n/(2pn\pm1)$ with integers $n,p{\geq}2$, support two kinds of collective modes: in addition to the well-known Girvin-MacDonald-Platzman (GMP) mode, they host a high energy collective mode, which is interpreted as the GMP mode of partons. We elucidate observable signatures of the parton mode in the dynamics following a geometric quench. We construct a microscopic wave function for the parton mode, and demonstrate agreement between its variational energy and exact diagonalization. Using the parton construction, we derive a field theory of the Jain states and show that the previously proposed effective theories follow from our approach. Our results point to partons being "real" quasiparticles which, in a way reminiscent of quarks, only become observable at sufficiently high energies.

cond-mat.str-el↗

arXiv2022

A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even denominator fraction, namely $ν=2+3/8$, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the "$\bar{3}\bar{2}^{2}1^{4}$" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at $ν=2+3/8$. We make predictions for experimentally measurable properties of the $\bar{3}\bar{2}^{2}1^{4}$ state that can reveal its underlying topological structure.

cond-mat.str-el↗

arXiv2022

Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene

The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is dominated by the non-relativistic second Landau level wave function, by tuning the magnetic field a topological quantum phase transition from an Abelian composite fermion to a non-Abelian parton fractional quantum Hall state can be induced at filling factors $1/2, ~2/5$ and $3/7$. The parton states host exotic anyons that can potentially be utilized to store and process quantum information. Intriguingly, some of these transitions may have been observed in a recent experiment [Huang \emph{et al.} arXiv:2105.07058].

cond-mat.str-el↗

arXiv2021

Parton wave function for the fractional quantum Hall effect at $ν=6/17$

We consider the fractional quantum Hall effect at the filling $ν=6/17$, where experiments have observed features of incompressibility in the form of a minimum in the longitudinal resistance. We propose a parton state denoted as "$3\bar{2}1^{3}$" and show it to be a feasible candidate to capture the ground state at $ν=6/17$. We work out the low-energy effective theory of the $3\bar{2}1^{3}$ edge and make several predictions for experimentally measurable properties of the state which can help detect its underlying topological order. Intriguingly, we find that the $3\bar{2}1^{3}$ state likely lies in the same universality class as the state obtained from composite-fermionizing the 1+1/5 Laughlin state.

cond-mat.str-el↗

arXiv2021

Abelian parton state for the $ν=4/11$ fractional quantum Hall effect

We consider the fractional quantum Hall effect at the filling factor $ν=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the "$4\bar{2}1^{3}$" parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $ν=4/11$. We work out the low-energy effective theory of the $4\bar{2}1^{3}$ edge and make predictions for experimentally measurable properties of the state.

cond-mat.str-el↗

arXiv2021

Origin of the $ν=1/2$ fractional quantum Hall effect in wide quantum wells

The nature of the fractional quantum Hall effect at $ν=1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.

cond-mat.str-el↗

arXiv2020

Unconventional $\mathbb{Z}_{n}$ parton states at $ν= 7/3$: The role of finite width

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. ${\bf 2}$, 013349 (2020)] has suggested that an unconventional state describing $\mathbb{Z}_{n}$ superconductivity of composite bosons, which supports excitations with charge $1/(3n)$ of the electron charge, is energetically better than the Laughlin wave function at $ν=7/3$ in GaAs systems. All experiments to date, however, are consistent with the latter. To address this discrepancy, we study the effect of finite width on the ground state and predict a phase transition from an unconventional $\mathbb{Z}_{n}$ state at small widths to the Laughlin state for widths exceeding $\sim$ 1.5 magnetic lengths. We also determine the parameter region where an unconventional state is stabilized in the one third filled zeroth Landau level in bilayer graphene. The roles of Landau level mixing and spin are also considered.

cond-mat.str-el↗

arXiv2020

Quench dynamics of collective modes in fractional quantum Hall bilayers

We introduce different types of quenches to probe the non-equilibrium dynamics and multiple collective modes of bilayer fractional quantum Hall states. We show that applying an electric field in one layer induces oscillations of a spin-1 degree of freedom, whose frequency matches the long-wavelength limit of the dipole mode. On the other hand, oscillations of the long-wavelength limit of the quadrupole mode, i.e., the spin-2 graviton, as well as the combination of two spin-1 states, can be activated by a sudden change of band mass anisotropy. We construct an effective field theory to describe the quench dynamics of these collective modes. In particular, we derive the dynamics for both the spin-2 and the spin-1 states and demonstrate their excellent agreement with numerics.

cond-mat.mes-hall↗

arXiv2020

Interplay between fractional quantum Hall liquid and crystal phases at low filling

The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ν\lesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ν=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ν=n/(6n\pm 1)$ and $ν=n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$ν$ states, specifically $ν=1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

cond-mat.str-el↗

arXiv2020

A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level

We consider a non-Abelian candidate state at filling factor $ν=3/7$ state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e. at filling factor $ν=2+3/7$), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that \emph{if} a fractional quantum Hall effect is observed at $ν=3/7$ in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.

cond-mat.str-el↗

arXiv2020

Fractional Quantum Hall Effect at $ν=2+4/9$

Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $ν=2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown quantum liquid, we propose that this state likely belongs in a parton sequence, put forth recently to understand the emergence of FQHE at $ν=2+6/13$. While the $ν=2+4/9$ state proposed here directly follows three simpler parton states, all known to occur in the second LL, it is topologically distinct from the Jain composite fermion (CF) state which occurs at the same $ν=4/9$ filling of the lowest LL. We predict experimentally measurable properties of the $4/9$ parton state that can reveal its underlying topological structure and definitively distinguish it from the $4/9$ Jain CF state.

cond-mat.str-el↗

arXiv2020

$\mathbb{Z}_{n}$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect

The topological $p$-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. Motivated by the parton theory of the FQHE, we consider the possibility of a new kind of emergent "superconductivity" in the 1/3 FQHE, which involves condensation of clusters of $n$ composite bosons. From a microscopic perspective, the state is described by the $n\bar{n}111$ parton wave function ${\cal P}_{\rm LLL} Φ_nΦ_n^*Φ_1^3$, where $Φ_n$ is the wave function of the integer quantum Hall state with $n$ filled Landau levels and ${\cal P}_{\rm LLL}$ is the lowest-Landau-level projection operator. It represents a $\mathbb{Z}_{n}$ superconductor of composite bosons, because the factor $Φ_1^3\sim \prod_{j<k}(z_j-z_k)^3$, where $z_j=x_j-iy_j$ is the coordinate of the $j$th electron, binds three vortices to electrons to convert them into composite bosons, which then condense into the $\mathbb{Z}_{n}$ superconducting state $|Φ_n|^2$. From a field theoretical perspective, this state can be understood by starting with the usual Laughlin theory and gauging a $\mathbb{Z}_n$ subgroup of the $U(1)$ charge conservation symmetry. We find from detailed quantitative calculations that the $2\bar{2}111$ and $3\bar{3}111$ states are at least as plausible as the Laughlin wave function for the exact Coulomb ground state at filling $ν=7/3$, suggesting that this physics is possibly relevant for the 7/3 FQHE. The $\mathbb{Z}_{n}$ order leads to several observable consequences, including quasiparticles with fractionally quantized charges of magnitude $e/(3n)$ and the existence of multiple neutral collective modes. It is interesting that the FQHE may be a promising venue for the realization of exotic $\mathbb{Z}_{n}$ superconductivity.

cond-mat.str-el↗