arXiv subjects

Ankur Das

Publications and source records attributed to Ankur Das.

At least 19 recordsLinked to original sources

arXiv2026

Mixed Floquet Lattice model for gapless topology

We investigate the realization of a time-reversal-broken Weyl semimetal in Floquet synthetic dimensions generated by two incommensurate drives, in the spirit of topological frequency conversion in driven synthetic lattices PRX 7, 041008 (2017). The system is described by a one-dimensional lattice model in a mixed $(1~\mathrm{real}+2~\mathrm{synthetic})$-dimensional setting, where the driving phases act as synthetic momenta and generate Weyl points in the mixed Floquet band structure. Using the topology associated with these band degeneracies, we analyze the energy transfer between the two drives. We find that the mixed Floquet lattice captures the Weyl-semimetal topology only in a momentum-resolved sense: for fixed real momentum $k_x$, the power transfer measures the $k_x$-resolved Chern number and detects the separation of the Weyl nodes. However, the full real-space response is qualitatively different. The total power transfer does not reproduce the static Weyl-semimetal phase diagram, but instead follows an effective Rice-Mele-type pumping structure. Thus, in contrast to fully gapped topological insulators, gapless semimetallic phases do not straightforwardly translate to Floquet synthetic dimensions. Our results reveal a distinct dynamical phase structure of driven Weyl systems and establish mixed Floquet lattices as a platform for exploring non-equilibrium gapless topology.

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arXiv2026

Local Magnetometry from Measurement-Induced Dissipation

Magnetic phases are commonly identified through macroscopic magnetization, yet many ordered states, including antiferromagnets and altermagnets, possess a vanishing net moment despite distinct local spin structure. We show that such an order can be accessed through the measurement-induced steady state of a single primary qubit locally coupled to a spin lattice. Using a controlled primary-ancillary qubit protocol, we derive analytically that the steady state \emph{encodes} a locally weighted exchange field in a signed observable that is linear in the weak-coupling regime. Numerical simulations demonstrate lattice-scale resolution of antiferromagnetic and altermagnetic textures and robustness against short-correlated noise. Our results establish measurement-induced dissipation as a resource for detecting magnetic order through microscopic structure rather than through global moments.

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arXiv2025

Half-integer thermal conductance in the absence of Majorana mode

Considering a range of candidate quantum phases of matter, half-integer thermal conductance ($\kappa_{\text{th}}$) is believed to be an unambiguous evidence of non-Abelian states. It has been long known that such half-integer values arise due to the presence of Majorana edge modes, representing a significant step towards topological quantum computing platforms. Here, we challenge this prevailing notion by presenting a comprehensive theoretical and experimental study where half-integer two-terminal thermal conductance plateau is realized employing Abelian phases. Our proposed setup features a confined geometry of bilayer graphene, interfacing distinct particle-like and hole-like integer quantum Hall states. Each segment of the device exhibits full charge and thermal equilibration. Our approach is amenable to generalization to other quantum Hall platforms, and may give rise to other values of fractional (electrical and thermal) quantized transport. Our study demonstrates that the observation of robust non-integer values of thermal conductance can arise as a manifestation of mundane equilibration dynamics as opposed to underlying non-trivial topology.

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arXiv2025

Shot noise signatures of candidate states for the fractional quantum Hall $\nu = 12/5$ state

Fractional quantum Hall (FQH) states are highly sought after because of their ability to host non-abelian anyons, whose braiding statistics make them excellent candidates for qubits in topological quantum computing. Multiple theoretical studies on the $\nu=\frac{12}{5}$ FQH state predict various quasi-particle states hosted by the $\frac{12}{5}$ plateau, which include $\mathbb Z_3$ parafermions and Majorana modes. In this work, we provide a systematic protocol to distinguish among four possible candidate wavefunctions of the $\frac{12}{5}$ plateau using zero-frequency shot noise experiments on a filter-geometry. Qualitative comparisons of Fano-Factors provide a robust way to predict the candidate state across both the full and partial thermal equilibration regimes without prior knowledge of the experimental information, like thermal equilibration length, to allow for more realistic experiments.

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arXiv2024

Half-quantized Hall Plateaus in the Confined Geometry of Graphene

Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite fermion framework used to explain fractional quantum Hall states (such as Laughlin states). Crucially, they hold promise for hosting non-Abelian excitations, which are essential for developing topological qubits - key components for fault-tolerant quantum computing. In this work, we show that these coveted half-quantized plateaus can appear in more than one unexpected way. We report the observation of fractional states with conductance quantization at $\nu_H = 5/2$ arising due to charge equilibration in the confined region of a quantum point contact in monolayer graphene.

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arXiv2024

Fractional Quantum Hall phases of graphene beyond ultra-short range intervalley-anisotropic interaction

Recent experimental and theoretical development in the Quantum Hall effect in monolayer graphene showed that the previous model of the valley-anisotropy interaction is incomplete, as it was assumed to be ultra-short range (USR). In this work, we use exact diagonalization to go beyond the ultra-short range to find the different phases for $\nu=2/3$. We model the interaction as Yukawa so that we can control the range as a proof of concept. Even in this simple setting, we discovered how dropping the USR condition shifts the transition borders in favour of certain phases, leads to a new bond-ordered phase appearing, and breaks the ferromagnetic phase in two competing states as a result of lifting the USR-driven degeneracy.

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arXiv2023

Topological nodal line semimetals with chiral symmetry

Topological semimetals in three dimensions display band-touchings at points (Weyl or Dirac semimetals) or nodal lines in the Brillouin zone. Weyl semimetals can occur with internal symmetries only (time-reversal ${\cal T}$, charge conjugation ${\cal C}$, and a product of the two, called chiral/sublattice symmetry ${\cal S}={\cal T}{\cal C}$). Nodal line semimetals possessing solely internal symmetries have only been classified abstractly, while those with SU(2) spin rotation or crystalline symmetries are known more explicitly. We show that chiral symmetry classes that are topologically nontrivial in three dimensions (namely class AIII, CII, CI, and DIII) always have a stable gapless phase, which is a topological nodal line semimetal. Our classification differs from previous approaches and has direct implications for gapless surface states.

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arXiv2023

Stable nodal line semimetals in the chiral classes in three dimensions

It has been realized over the past two decades that topological nontriviality can be present not only in insulators but also in gapless semimetals, the most prominent example being Weyl semimetals in three dimensions. Key to topological classification schemes are the three ``internal" symmetries, time reversal ${\cal T}$, charge conjugation ${\cal C}$, and their product, called chiral symmetry ${\cal S}={\cal T}{\cal C}$. In this work, we show that robust topological nodal line semimetal phases occur in $d=3$ in systems whose internal symmetries include ${\cal S}$, without invoking crystalline symmetries other than translations. Since the nodal loop semimetal naturally appears as an intermediate gapless phase between the topological and the trivial insulators, a sufficient condition for the nodal loop phase to exist is that the symmetry class must have a nontrivial topological insulator in $d=3$. Our classification uses the winding number on a loop that links the nodal line. A nonzero winding number on a nodal loop implies robust gapless drumhead states on the surface Brillouin zone. We demonstrate how our classification works in all the nontrivial chiral classes and how it differs from the previous understanding of topologically protected nodal line semimetals.

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arXiv2023

Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise

The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady-state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations \emph{(electrical shot noise)} in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs.\ partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.

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arXiv2023

Experimentally Motivated Order of Length Scales Affect Shot Noise

Shot noise at a conductance plateau in a quantum point contact (QPC) can be explained by considering equilibrations at the quantum Hall edges. The indication from recent experiments is that the charge equilibration length is much shorter than the thermal equilibration length. We discuss how this discovery gives rise to different thermal equilibration regimes in the presence of full charge equilibration. In this work, we classify these distinct regimes via dc current-current correlations (electrical shot noise) at definite experimentally found (or possible) QPC conductance plateaus for the edges of integer, particle-like, and hole-like filling fractions in a two dimensional electron gas. Our analyses show that distinct universal features arise among the different thermal equilibration regimes for the edges of particle-like and hole-like states.

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arXiv2023

Shot noise as a diagnostic in the $\nu=2/3$ fractional quantum Hall edge zoo

The $\nu = 2/3$ filling is the simplest paradigmatic example of a fractional quantum Hall state, which contains counter-propagating edge modes. These modes can be either in the unequilibrated regime or equilibrated to different extents, on top of a possible edge reconstruction. In the unequilibrated regime, two distinct renormalization group fixed points have been previously proposed, namely Kane-Fischer-Polchinski and Wang-Meir-Gefen. In the equilibration regime, different degree of thermal equilibration may occur, while charge is fully equilibrated. Here, we show that this rich variety of models can give rise to three possible conductance plateaus at $e^2/2h$ (recently observed in experiments), $5e^2/9h$ (predicted here), and $e^2/3h$ (observed earlier in experiments) in a quantum point contact geometry. We identify different mechanisms for \emph{electrical shot noise} generation at these plateaus, which provides an experimentally accessible venue for distinguishing among the distinct models.

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arXiv2023

Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States

Two-terminal conductance quantization in the context of quantum Hall (QH) physics is intimately related to the current carried by a discrete number of chiral edge modes. Upon pinching off a QH bar, one may engineer setups where some modes are fully transmitted (while the others are fully reflected), giving rise to the orthodox theory of quantized conductance plateaus. Here, we note that the observation of quantized plateaus \emph{does not} uniquely indicate the underlying mechanism. Our study demonstrates explicitly that (i) such plateaus may be the manifestations of entirely different mechanisms; (ii) conductance measurements alone will not suffice to distinguish one from the other. We further show that measurements of shot noise (auto- and cross-correlation) at the plateau may discriminate among different mechanisms. While our observations apply to a broad class of QH states, we demonstrate their applicability employing a prototypical example: the bulk state of filling factor $\nu=2/3$. We present distinctly different scenarios that lead to a conductance plateau $G_{2-\text{terminal}} = e^2/3h$ (observed previously), and likewise qualitatively different mechanisms leading to $e^2/2h$ (recently observed). We also predict the possibility of a new conductance plateau at $5e^2/9h$, following a non-orthodox scenario.

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arXiv2023

Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekulé bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekulé order exists in the region of the phase diagram believed to correspond to real samples. In this work, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $ν=0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

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arXiv2022

Punctured-Chern topological invariants for semi-metallic bandstructures

Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We construct a general wavefunction-based ``punctured-Chern" invariant to capture such topology. To show its general applicability, we analyze two systems with disparate gapless topology: 1) a recent two-dimensional fragile topological model to capture the various band-topological transitions and 2) a three-dimensional model with a triple-point nodal defect to characterize its semi-metallic topology with \emph{half-integers} that govern physical observables such as anomalous transport. This invariant also gives the classification for Nexus triple-points ($\mathbb{Z}\times\mathbb{Z}$) with certain symmetry restrictions, which is re-confirmed by abstract algebra.

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arXiv2022

Dc Electrical Current Generated by Upstream Neutral Modes

Quantum Hall phases are gapped in the bulk but support chiral edge modes, both charged and neutral. Here we consider a circuit where the path from the source of electric current to the drain necessarily passes through a segment consisting solely of neutral modes. We find that upon biasing the source, a dc electric current is detected at the drain, provided there is backscattering between counter-propagating modes under the contacts placed in certain locations. Thus, neutral modes carry information that can be used to nonlocally reconstruct a dc charge current. Our protocol can be used to detect any neutral mode that counterpropagates with respect to all charge modes. Our protocol applies not only to the edge modes of a quantum Hall system, but also to systems that have neutral modes of non-quantum Hall origin. We conclude with a possible experimental realization of this phenomenon.

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arXiv2022

Time-reversal-broken Weyl semimetal in the Hofstadter regime

We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p \le q-1$), with minimal crystalline symmetry. We find several interesting phases: (i) WSM phases with $2q$, $4q$, $6q$, and $8q$ Weyl nodes and corresponding surface Fermi arcs, (ii) a layered Chern insulating (LCI) phase, gapped in the bulk, but with gapless surface states, (iii) a phase in which some bulk bands are gapless with Weyl nodes, coexisting with others that are gapped but topologically nontrivial, adiabatically connected to an LCI phase, (iv) a new gapped trivially insulating phase (I$'$) with (non-topological) counter-propagating surface states, which could be gapped out in the absence of crystal symmetries. Importantly, we are able to obtain the phase boundaries analytically for all $p,q$. Analyzing the gaps for $p=1$ and very large $q$ enables us to smoothly take the zero-field limit, even though the phase diagrams look ostensibly very different for $q=1, B=0$, and $q\to\infty, B\to 0$.

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arXiv2021

Does shot noise always provide the quasiparticle charge?

The fractional charge of quasiparticles is a fundamental feature of quantum Hall effect (QHE) States. The charge has long been measured via shot-noise at moderate temperatures ($T$>30mK), with the Fano factor $F=e^*/e$ revealing the charge $e^*$ of the quasiparticles. However, at sufficiently low temperatures ($T\approx$10mK), we consistently find $F$ being equal to the bulk filling factor, $ν_b$. Surprisingly, noise with $F=ν_b$ is also observed on intermediate conductance plateaus in the transmission of the quantum point contact (QPC), where shot noise is not expected. We attribute the unexpected Fano factor to upstream neutral modes, which proliferate at the lowest spinless Landau level. The universality of the Fano factor is also confirmed when the edge modes do not conform to the bulk. For this, the ubiquitous edge modes at the periphery of the sample are replaced by artificially constructed 'interface modes', propagating at the interface between two adjoined QHE states: the tested state and a different state. We present a new theoretical paradigm based on an interplay between charge and neutral modes, explaining the origin of the universal Fano factor.

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arXiv2021

Layer Coherent Phase in Double Layer graphene at $ν^{}_1=ν^{}_2=0$

In the recent advancement in graphene heterostructures, it is possible to create a double layer tunnel decoupled graphene system that has a strong interlayer electronic interaction. In this work, we restrict the parameters in the low energy effective Hamiltonian using simple symmetry arguments. Then, we study the ground state of this system in the Hartree-Fock approximation at $ν^{}_1=ν^{}_2=0$. In addition to the phases found in monolayer graphene, we found an existence of layer coherent phase which breaks the layer $U(1)$ symmetry. At non-zero Zeeman coupling strength ($E^{}_z$), this layer coherent state has a small magnetization, that vanishes when $E^{}_z$ tends to zero. We discuss the bulk gapless modes using the Goldstone theorem. We also comment on the edge structure for the layer coherent phase.

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