arXiv subjects

Navketan Batra

Publications and source records attributed to Navketan Batra.

11 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

Anyonic analogue of optical Mach-Zehnder interferometer

Anyonic interferometry is a direct probe of fractional statistics. We propose an interferometry geometry that parallels an optical Mach-Zehnder interferometer and offers several advantages over existing interferometry schemes. In contrast to the currently studied electronic Mach-Zehnder interferometer, our setup has no drain inside the device so that the trapped topological charge is time-independent. In contrast to electronic Fabry-P\'erot interferometry, anyons cannot go around the device more than once. Thus, the interference signal has a straightforward interpretation in terms of anyonic statistical phases. The proposed geometry suppresses the undesirable effects of bulk-edge coupling. Moreover, the setup allows for simple exact solutions for the electric current and noise for an arbitrary quasiparticle tunneling strength in a broad range of conditions. The structure of the solutions is similar to that for non-interacting electrons but reflects fractional charge and statistics. We present results for electric current and noise in Jain states and address thermal interferometry at zero voltage bias.

cond-mat.mes-hall↗

arXiv2024

Excitons in the Fractional Quantum Hall Effect

Excitons, Coulomb-driven bound states of electrons and holes, are typically composed of integer charges. However, in bilayer systems influenced by charge fractionalization, a more exotic form of interlayer exciton can emerge, where pairing occurs between constituents that carry fractional charges. Despite numerous theoretical predictions for such fractional excitons, their experimental observation has remained elusive. Here, we report transport signatures of excitonic pairing within fractional quantum Hall effect states. By probing the composition of these excitons and their impact on the underlying wavefunction, we uncover two novel quantum phases of matter. One of these orders can be viewed as the fractional counterpart of the exciton condensate at a total filling of one, while the other involves a more unusual type of exciton that obeys fermionic and anyonic quantum statistics, challenging the standard paradigm of bosonic excitons.

cond-mat.mes-hall↗

arXiv2024

A Bound on Topological Gap from Newton's Laws

A striking general bound on the energy gap in topological matter was recently discovered in Ref. [Onishi and Fu, Phys. Rev. X {\bf 14}, 011052 (2024)]. A non-trivial indirect derivation builds on the properties of optical conductivity at an arbitrary frequency. We propose a simpler derivation, allowing multiple generalizations, such as a universal bound on a gap in anisotropic systems, systems with multiple charge carrier types, and topological systems with zero Hall conductance. The derivation builds on the observation that the bound equals $\hbar$ times the ratio of the force by the external electric field on the charge carriers and their total kinematic momentum in the direction perpendicular to the force.

cond-mat.mes-hall↗

arXiv2023

Anyonic Mach-Zehnder interferometer on a single edge of a 2D electron gas

Anyonic Fabry-P\'erot and Mach-Zehnder interferometers have been proposed theoretically and implemented experimentally as tools to probe electric charges and statistics of anyons. The experimentally observed visibility of Aharonov-Bohm oscillations is maximal at a high transmission through an interferometer but simple theoretical expressions for the electric currents and noises are only available at low visibility. We consider an alternative version of a Mach-Zehnder interferometer, in which anyons tunnel between co-propagating chiral channels on the edges of quantum Hall liquids at the filling factors $n/(2n+1)$. We find simple exact solutions for any transmission. The solutions allow a straight-forward interpretation in terms of fractional charges and statistics.

cond-mat.mes-hall↗

arXiv2023

Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes

Fractional charges of anyons can be extracted from shot noise in two ways. One can use either the auto-correlation noise of the current in one drain or the cross-correlation noise between two drains on the two sides of the device. The former approach typically overestimates the charge. This may happen due to upstream edge modes. We propose a mechanism for the excess auto-correlation noise without upstream modes. It applies to systems with multiple co-propagating edge modes and assumes that the noise is measured at a low but non-zero frequency.

cond-mat.mes-hall↗

arXiv2023

Thermal interferometry of anyons

Anyonic interferometry probes the braiding phases of excitations in topologically ordered matter. This technique is well established for charged quasiparticles in the fractional quantum Hall effect. We propose to extend it to neutral anyons, such as Ising anyons in Kitaev magnets and quasiparticles in other neutral spin liquids. We find that the thermal current through an interferometer is sensitive to the statistics of tunneling quasiparticles. We present a systematic investigation of signatures of various Abelian and non-Abelian topological orders in Fabry-Pérot and Mach-Zehnder interferometers. The heat current through a Fabry-Pérot device is different for different topological orders and depends on the topological charge inside the interferometer. A Mach-Zehnder device shows interference in topologically trivial systems only. For a non-trivial statistics, the heat current reduces to the sum of the contributions from two constrictions in the interferometer. Furthermore, we identify another probe of topological order that involves the scaling of the thermal current through a single tunneling contact at low temperatures. The current shows a universal temperature dependence, sensitive to the topological order in the system.

cond-mat.mes-hall↗

arXiv2021

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the extended attractive Hubbard model (EAHM) exhibits rich ground state phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree-Fock- Bogoliubov-de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

cond-mat.supr-con↗

arXiv2021

Quantum theory of statistical radiation pressure in free space

Light is known to exert radiation pressure on any surface it is incident upon, via the transfer of momentum from the light to the surface. In general, this force is assumed to be pushing or repulsive in nature. In this paper, we present a complete quantum treatment of radiation pressure. We show that the interaction of an atom with light can lead to both repulsive and attractive forces due to the absorption and emission of photons, respectively. An atom prepared in the excited state initially will experience a pulling force when interacting with light. On the other hand, if the atom is prepared in the ground state then the force will be repulsive while having the same magnitude as in the earlier case. Therefore, for an ensemble of atoms, the direction of the net force will be decided by the excited and ground state populations. In the semi-classical treatment of light-matter interaction, the absorption and emission processes have the same probability. Therefore the magnitudes of the force in the two processes turn out to be the same. We obtain the effective emission profile for an excited atom interacting with a quantum electromagnetic field, and show that in the quantum treatment, despite these probabilities being different, the magnitudes of the two statistical forces remain the same. This can be explained by noting that the extra contribution in the emission process is due to the interaction of the atom with the vacuum modes of the electromagnetic field, which results in a symmetric emission profile, contributing to a net zero force on the atoms in an ensemble. We further identify the set of states of electromagnetic field which give rise to non-zero momentum transfer to the atom.

quant-ph↗

arXiv2019

Understanding Basic Concepts of Topological Insulators Through Su-Schrieffer-Heeger (SSH) Model

Topological insulators are a new class of materials that have attracted significant attention in contemporary condensed matter physics. They are different from the regular insulators and they display novel quantum properties that also involve the idea of `topology', an area of mathematics. Some of the fundamental ideas behind the topological insulators, particularly in low-dimensional condensed matter systems such as poly-acetylene chains, can be understood using a simple one-dimensional toy model popularly known as the Su-Schrieffer-Heeger model or the SSH model. This model can also be used as an introduction to the topological insulators of higher dimensions. Here we give a concise description of the SSH model along with a brief review of the background physics and attempt to understand the ideas of topological invariants, edge states, and bulk-boundary correspondence using the model.

cond-mat.mes-hall↗

arXiv2019

Topological Transitions in a Model for Proximity Induced Superconductivity

Using a prototype model for proximity induced superconductivity on a bilayer square lattice, we show that interlayer tunneling can drive change in topology of the Bogoliubov quasiparticle bands. Starting with topologically trivial superconductors, transitions to a non-trivial $p_x + {\rm i} p_y$ state and back to another trivial state are discovered. We characterize these phases in terms of edge-state spectra and Chern indices. We show that these transitions can also be controlled by experimentally viable control parameters, the bandwidth of the metallic layer and the gate potential. Insights from our results on a simple model for proximity induced superconductivity may open up a new route to discover topological superconductors.

cond-mat.supr-con↗