Searcharxiv⌕ Search

arXiv subjects

Sahana Das

Publications and source records attributed to Sahana Das.

8 recordsLinked to original sources
arXiv2026

Three-dimensional Foliated Fractional Quantum Hall Phases

Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $\nu=1/3$ of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to 10 layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the 9-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures.

cond-mat.str-el↗
arXiv2025

Fractional topological insulators at odd-integer filling: Phase diagram of two-valley quantum Hall model

The fractional quantum Hall effect has recently been shown to exist in heterostructures of van der Waals materials without an externally applied magnetic field, e.g. in twisted bilayers of MoTe$_2$. These fractional Chern insulators break time-reversal symmetry spontaneously through polarization of the electron spins in a quantum spin Hall insulator band structure with flat bands. This prompts the question, which states could be realized if the spins remain unpolarized or polarize partially. Specifically, the possibility of time-reversal symmetric topological order arises. Here, we study this problem for odd integer filling of the bands, specifically focusing on vanishing and half valley polarization. Short of reliable microscopic models for small twist angles around $2.1^\circ$, we study the idealized situation of two Landau levels with opposite chirality, the two-valley quantum Hall model. Using exact diagonalization, we identify different phases arising in this model by tuning the interaction. In the physically relevant regime, the system initially exhibits phase-separated or valley-polarized states, which eventually transition into paired states by reducing onsite Coulomb repulsion.

cond-mat.str-el↗
arXiv2024

Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State

Observation of filling factor 6/13 is one of the surprising fractional quantum Hall states in the second Landau level because, in contrast to the standard wisdom, the fractions ($\nu < 1/2$) with lower numerators, namely 4 and 5, have not yet been observed. We find that a state indeed forms at $\nu=6/13$ as an intermittent topological state between two prominent states at $\nu =1/2$ and $\nu = 2/5$ with lower numerators. Also, we predict that a state forms at $\nu=5/13$ as an intermittent to $\nu = 2/5$ and $\nu =3/8$. Our proposed wave functions for $\nu =6/13$ and $5/13$ have excellent overlaps with the corresponding exact ground state wave functions. The Chern-Simons coupling matrices deduced from the form of these wave functions are analyzed to predict the topological properties, which may be experimentally verified.

cond-mat.mes-hall↗
arXiv2024

Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level

A proposal of the existence of an {\em Anomalous} phase ($\mathcal{A}$ phase) [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.056202 Das et al., Phys. Rev. Lett. 131, 056202 (2023)] at the experimental range of moderate Landau-level-mixing strength has recently been made for $5/2$ state. We here report that the gapped $\mathcal{A}$ phase is generic to the sequence of spin-polarized fractional quantum Hall states with filling fractions $ν= n/(nm-1)$ and $ν= 1-n/(nm-1)$, $(n \geqslant 1,\,m\geqslant 3)$, that exhausts almost all the observed states and also predicts some states in the second Landau level for GaAs systems. Our proposed trial wavefunctions for all these states have remarkably high overlaps with the corresponding exact ground states and can support non-Abelian quasiparticle excitations with charge $e/[2(nm-1)]$. By analyzing edge modes, we predict experimentally verifiable thermal Hall conductance $2.5(π^2 k_B^2T/3h)$ for all the states in these sequences.

cond-mat.mes-hall↗
arXiv2022

An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength

A successful probing of neutral Majorana mode in recent thermal Hall conductivity measurements opines in favor of the particle-hole symmetric Pfaffian (PH-Pf) topological order, contrasting the theoretical predictions of Pfaffian or anti-Pfaffian phases. Here we report a reentrant anomalous quantized phase which is found to be gapped in the thermodynamic limit, distinct from the conventional Pfaffian, anti-Pfaffian, or PH-Pf phases, at an intermediate strength of Landau level mixing. Our proposed wave function consistent with the PH-Pf shift in spherical geometry rightly captures the topological order of this phase, as its overlap with the exact ground state is very high and it reproduces low-lying entanglement spectra. A unique topological order, irrespective of the flux shifts, found for this phase possibly corroborates the experimentally found topological order.

cond-mat.mes-hall↗
arXiv2021

From the Gaffnian critical point to the incompressible 2/5 quantum Hall state

Despite the high overlap with the exact Coulomb ground state, the so-called Gaffnian state fails to describe the incompressibility at the 2/5 quantum Hall filling factor and consequently it was conjectured to be a quantum critical state. To achieve a gapped state starting from the Gaffnian wavefunction, which we interpret as the inter-flavor pairing of the composite fermions, we propose a minimally `modified Gaffnian' wavefunction keeping the pairing intact. We find that a suitable hybridization of these two wavefunctions is an excellent description of the 2/5 quantum Hall state. It has a very high overlap with the exact Coulomb state and their entanglement spectra match up to reasonably higher levels. Interestingly, this hybridized wavefunction being a representative of a paired state suggests an exotic possibility of non-Abelian quasiparticle excitations at 2/5 filling.

cond-mat.mes-hall↗
arXiv2021

Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function

The ground state at 4/11 filling factor is very well understood [Phys. Rev. Lett. 112, 016801 (2014)] in terms of the 1/3 filled second effective Landau level of the composite fermions whose correlations resemble with that of electrons in the ground state of two-body Haldane pseudo-potential of relative angular momentum 3, $V_3$. We here propose a closed-form ground state wave function for $V_3$ at 1/3 filling factor. We successfully compare it with the exact wave function for the systems with a few electrons, by calculating their mutual overlap, pair-correlation function, and entanglement spectra. By numerical exact diagonalization for a few electron systems, we find a window of nonzero $V_3$ is essential together with $V_1$ for being 4/11 state incompressible. The constructed wave function for 4/11 state using this proposed wave function has satisfactorily high overlap with the previously studied composite-fermion-diagonalized ground state wave function.

cond-mat.mes-hall↗