arXiv subjects

Abhishek Banerjee

Publications and source records attributed to Abhishek Banerjee.

At least 73 records · Page 4Linked to original sources

arXiv2020

Probing the Relaxed Relaxion at the Luminosity and Precision Frontiers

Cosmological relaxation of the electroweak scale is an attractive scenario addressing the gauge hierarchy problem. Its main actor, the relaxion, is a light spin-zero field which dynamically relaxes the Higgs mass with respect to its natural large value. We show that the relaxion is generically stabilized at a special position in the field space, which leads to suppression of its mass and potentially unnatural values for the model's effective low-energy couplings. In particular, we find that the relaxion mixing with the Higgs can be several orders of magnitude above its naive naturalness bound. Low energy observers may thus find the relaxion theory being fine-tuned although the relaxion scenario itself is constructed in a technically natural way. More generally, we identify the lower and upper bounds on the mixing angle. We examine the experimental implications of the above observations at the luminosity and precision frontiers. A particular attention is given to the impressive ability of future nuclear clocks to search for rapidly oscillating scalar ultra-light dark matter, where the future projected sensitivity is presented.

hep-ph↗

arXiv2020

Cycles over DGH-semicategories and pairings in categorical Hopf-cyclic cohomology

Let $H$ be a Hopf algebra and let $\mathcal D_H$ be a Hopf-module category. We describe the cocycles and coboundaries for the Hopf cyclic cohomology of $\mathcal D_H$, which correspond respectively to categorified cycles and vanishing cycles over $\mathcal D_H$. An important role in our work is played by semicategories, which are categories that may not contain identity maps. In particular, a cycle over $\mathcal D_H$ consists of a differential graded $H$-module semicategory equipped with a trace on endomorphism groups satisfying some conditions. Using a pairing on cycles, we obtain a pairing $HC^p(\mathcal{C}) \otimes HC^q(\mathcal{C}') \longrightarrow HC^{p+q}(\mathcal{C} \otimes \mathcal{C}')$ on cyclic cohomology groups for small $k$-linear categories $\mathcal C$ and $\mathcal C'$.

math.CT↗

arXiv2020

Cyclic cohomology of entwining structures

In this paper, we introduce and study a cyclic cohomology theory $H^\bullet_λ(A,C,ψ)$ for an entwining structure $(A,C,ψ)$ over a field $k$. We then provide a complete description of the cocycles and the coboundaries in this theory using entwined traces applied to dg-entwining structures over $(A,C,ψ)$. We then apply these descriptions to construct a pairing $ H^m_λ(A,C,ψ) \otimes H^n_λ(A',C',ψ') \longrightarrow H^{m+n}_λ(A \otimes A', C \otimes C', ψ\otimes ψ') $, where $(A,C,ψ)$ and $(A',C',ψ')$ are entwining structures.

math.RA↗

arXiv2020

On measurings of algebras over operads and homology theories

The notion of a coalgebra measuring, introduced by Sweedler, is a kind of generalized ring map between algebras. We begin by studying maps on Hochschild homology induced by coalgebra measurings. We then introduce a notion of coalgebra measuring between Lie algebras and use it to obtain maps on Lie algebra homology. Further, these measurings between Lie algebras satisfy nice adjoint like properties with respect to universal enveloping algebras. More generally, we introduce and undertake a detailed study of the notion of coalgebra measuring between algebras over any operad $\mathcal O$. In case $\mathcal O$ is a binary and quadratic operad, we show that a measuring of $\mathcal O$-algebras leads to maps on operadic homology. In general, for any operad $\mathcal O$, we construct universal measuring coalgebras to show that the category of $\mathcal O$-algebras is enriched over coalgebras. We develop measuring comodules and universal measuring comodules for this theory. We also relate these to measurings of the universal enveloping algebra $U_{\mathcal O}(\mathscr A)$ of an $\mathcal O$-algebra $\mathscr A$ and the modules over it. Finally, we construct the Sweedler product $C\rhd \mathscr A$ of a coalgebra $C$ and an $\mathcal O$-algebra $\mathscr A$. The object $C\rhd \mathscr A$ is universal among $\mathcal O$-algebras that arise as targets of $C$-measurings starting from $\mathscr A$.

math.CT↗

arXiv2020

$FI$-modules over preadditive categories and torsion theories

We work with $FI$-modules over a small preadditive category $\mathcal R$, viewed as a ring with several objects. Our aim is to study torsion theories for $FI$-modules. We are especially interested in torsion theories on finitely generated $FI$-modules and the category of what we call "shift finitely generated" $FI$-modules. We also apply these methods to study inductive descriptions of $FI$-modules over $\mathcal R$.

math.CT↗

arXiv2020

BV-operators and secondary Hochschild complex

We introduce the notion of a BV-operator $Δ=\{Δ^n:V^n\longrightarrow V^{n-1}\}_{n\geq 0}$ on a homotopy $G$-algebra $V^\bullet$ such that the Gerstenhaber bracket on $H(V^\bullet)$ is determined by $Δ$ in a manner similar to the BV-formalism. As an application, we produce a BV-operator on the cochain complex defining the secondary Hochschild cohomology of a symmetric algebra $A$ over a commutative algebra $B$.

math.RA↗

arXiv2019

Categorified Fredholm Modules and Chern Characters

In this paper, we continue our program of systematic categorification of the Noncommutative Differential Geometry of Connes. We replace a ring with a small $\mathbb C$-linear category, seen as a ring with several objects in the sense of Mitchell. We introduced Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of $\mathcal C$. We show that this categorified Chern character depends only on the homotopy class of the Fredholm module and is well-behaved with respect to the periodicity operator in cyclic cohomology.

math.CT↗

arXiv2019

Relaxion Stars and their detection via Atomic Physics

The cosmological relaxion can address the hierarchy problem, while its coherent oscillations can constitute dark matter in the present universe. We consider the possibility that the relaxion forms gravitationally bound objects that we denote as relaxion stars. The density of these stars would be higher than that of the local dark matter density, resulting in enhanced signals in table-top detectors, among others. Furthermore, we raise the possibility that these objects may be trapped by an external gravitational potential, such as that of the Earth or the Sun. This leads to formation of relaxion halos of even greater density. We discuss several interesting implications of relaxion halos, as well as detection strategies to probe them.

hep-ph↗

arXiv2019

Coherent relaxion dark matter

We show that relaxion, that addresses the hierarchy problem, can account for the observed dark matter (DM) relic density. The setup is similar to the case of axion DM models topped with a dynamical misalignment mechanism. After the reheating, when the temperature is well above the electroweak scale, the backreaction potential disappears and the relaxion is displaced from its vacuum. When the "wiggles" reappear the relaxion coherently oscillates around its minimum as in the case of vanilla axion DM models. We identify the parameter space such that the relaxion is retrapped leading to the standard cosmology. When the relaxion is lighter than $10^{-7}\,$eV, Hubble friction during radiation-domination is sufficiently strong for retrapping, and even minimal models are found to be viable. It also leads to a new constraint on relaxion models, as a certain region of their parameter space could lead to overabundant relaxion DM. Alternatively, even a larger parameter space exists when additional friction is obtained by particle production from additional coupling to an additional dark photon field. The phenomenology of this class of models is quite unique, as it implies that we are surrounded by a time-dependent axion-like field that due to relaxion-Higgs mixing implies time-dependent Higgs vacuum-expectation-value that lead to time-variation of all coupling constants of nature.

hep-ph↗

arXiv2019

Signatures of Topological Superconductivity in Bulk Insulating Topological Insulator BiSbTe$_{1.25}$Se$_{1.75}$ in Proximity with Superconducting NbSe$_2$

The combination of superconductivity and spin-momentum locking at the interface between an s-wave superconductor and a three-dimensional topological insulator (3D-TI) is predicted to generate exotic p-wave topological superconducting phases that can host Majorana fermions. However, large bulk conductivities of previously investigated 3D-TI samples and Fermi level mismatches between 3D bulk superconductors and 2D topological surface states have thwarted significant progress. Here we employ bulk insulating topological insulators in proximity with two-dimensional superconductor NbSe$_2$ assembled via Van der Waals epitaxy. Experimentally measured differential conductance yields unusual features including a double-gap spectrum, an intrinsic asymmetry that vanishes with small in-plane magnetic fields and differential conductance ripples at biases significantly larger than the superconducting gap. We explain our results on the basis of proximity induced superconductivity of topological surface states, while also considering possibilities of topologically trivial superconductivity arising from Rashba-type surface states. Our work demonstrates the possibility of obtaining p-wave superconductors by proximity effects on bulk insulating TIs.

cond-mat.mes-hall↗

arXiv2019

Cohomology of modules over $H$-categories and co-$H$-categories

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the $H$-locally finite cohomologies of these objects. We also introduce relative $(\mathcal D,H)$-Hopf modules over a Hopf comodule category $\mathcal D$. These generalize relative $(A,H)$-Hopf modules over an $H$-comodule algebra $A$. We construct Grothendieck spectral sequences for their cohomologies by using their rational $Hom$ objects and higher derived functors of coinvariants.

math.RA↗

arXiv2019

Entwined modules over linear categories and Galois extensions

In this paper, we study modules over quotient spaces of certain categorified fiber bundles. These are understood as modules over entwining structures involving a small $K$-linear category $\mathcal D$ and a $K$-coalgebra $C$. We obtain Frobenius and separability conditions for functors on entwined modules. We also introduce the notion of a $C$-Galois extension $\mathcal E\subseteq \mathcal D$ of categories. Under suitable conditions, we show that entwined modules over a $C$-Galois extension may be described as modules over the subcategory $\mathcal E$ of $C$-coinvariants of $\mathcal D$.

math.CT↗

arXiv2018

Spatially varying electronic dephasing in three dimensional topological insulators

Information processing devices operating in the quantum mechanical regime strongly rely on the quantum coherence of charge carriers. Studies of electronic dephasing in conventional metallic and semiconductor systems have not only paved the way towards high coherence quantum electronics, but also led to fundamental new insights in condensed matter physics. In this work, we perform a spatially resolved study of electronic dephasing in three dimensional topological insulators by exploiting an edge versus surface contacted measurement scheme. Unlike conventional two dimensional systems that are characterized by a single dephasing mechanism, we find that dephasing in our samples evolves from a variable-range-hopping type mechanism on the sample surface to a Nyquist type electron-electron interaction mechanism in the sub-surface layers. This is confirmed independently by the temperature and chemical potential dependence of the dephasing length, and gate dependent suppression/enhancement of the weak anti-localization effect. Our devices are fabricated using bulk insulating topological insulator BiSbTe$_{1.25}$Se$_{1.75}$ capped with hexagonal-Boron Nitride in an inert environment, ruling out any extrinsic effects and confirming the topological surface state origin of our results. Our work introduces the idea of spatially resolved electronic dephasing and reveals a new regime of coherent transport in perhaps the most important topological insulator discovered so far. Our edge-vs-surface scheme may be applied to dephasing studies in a wide class of 2D materials.

cond-mat.mes-hall↗

arXiv2018

Enhanced coherence and decoupled surface states in topological insulators through structural disorder

To harness the true potential of topological insulators as quantum materials for information processing, it is imperative to maximise topological surface state conduction, while simulateneously improving their quantum coherence. However, these goals have turned out to be contradictory. Surface dominated transport in topological insulators has been achieved primarily through compensation doping of bulk carriers that introduces tremendous electronic disorder and drastically deteriorates electronic coherence. In this work, we use structural disorder instead of electronic disorder to manipulate electrical properties of thin films of topological insulator Bi$_2$Se$_3$. We achieve decoupled surface state transport in our samples and observe significantly suppressed carrier dephasing rates in the coupled surface state regime. As the film thickness is decreased, the dephasing rate evolves from a linear to a super-linear temperature dependence. While the former is consistent with Nyquist electron-electron interactions, the latter leads to significantly enhanced coherence at low temperatures and is indicative of energy exchange due to frictional drag between the two surface states. Our work opens up the way to harness topological surface states, without being afflicted by the deleterious effects of compensation doping.

cond-mat.mes-hall↗

arXiv2018

Quantized transport in topological insulator n-p-n junctions

Electrical transport in three dimensional topological insulators(TIs) occurs through spin-momentum locked topological surface states that enclose an insulating bulk. In the presence of a magnetic field, surface states get quantized into Landau levels giving rise to chiral edge states that are naturally spin-polarized due to spin momentum locking. It has been proposed that p-n junctions of TIs in the quantum Hall regime can manifest unique spin dependent effects, apart from forming basic building blocks for highly functional spintronic devices. Here, for the first time we study electrostatically defined n-p-n junctions of bulk insulating topological insulator BiSbTe$_{1.25}$Se$_{1.75}$ in the quantum Hall regime. We reveal the remarkable quantization of longitudinal resistance into plateaus at 3/2 and 2/3 h/e$^2$, apart from several partially developed fractional plateaus. Theoretical modeling combining the electrostatics of the dual gated TI n-p-n junction with Landauer Buttiker formalism for transport through a network of chiral edge states explains our experimental data, while revealing remarkable differences from p-n junctions of graphene and two-dimensional electron gas systems. Our work not only opens up a route towards exotic spintronic devices but also provides a test bed for investigating the unique signatures of quantum Hall effects in topological insulators.

cond-mat.mes-hall↗

arXiv2016

On some spectral spaces associated to tensor triangulated categories

We consider a closure operator $c$ of finite type on the space $SMod(\mathcal M)$ of thick $\mathcal K$-submodules of a triangulated category $\mathcal M$ that is a module over a tensor triangulated category $(\mathcal K,\otimes,1)$. Our purpose is to show that the space $SMod^c(\mathcal M)$ of fixed points of the operator $c$ is a spectral space that also carries the structure of a topological monoid.

math.AG↗

arXiv2016

Pure resolutions of unbounded complexes of modules

Let $R$ be a commutative ring. We show that pure injective resolutions and pure projective resolutions can be constructed for unbounded complexes of $R$-modules. We use these to obtain a closed symmetric monoidal structure on the unbounded pure derived category.

math.RA↗

arXiv2016

On integral schemes over symmetric monoidal categories

We propose notions of "Noetherian" and "integral" for schemes over an abelian symmetric monoidal category $(\mathcal C,\otimes,1)$. For Noetherian integral schemes, we construct a "function field" that is a commutative monoid object of $(\mathcal C,\otimes,1)$. Under certain conditions, we show that a Noetherian scheme over $(\mathcal C,\otimes,1)$ is integral if and only if it is reduced and irreducible.

math.AG↗