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Koushik Pal

Publications and source records attributed to Koushik Pal.

29 records · Page 2Linked to original sources
arXiv2017

Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and Theory

We report high pressure Raman experiments of Black phosphorus up to 24 GPa. The line widths of first order Raman modes A$^1_g$, B$_{2g}$ and A$^2_g$ of the orthorhombic phase show a minimum at 1.1 GPa. Our first-principles density functional analysis reveals that this is associated with the anomalies in electron-phonon coupling at the semiconductor to topological insulator transition through inversion of valence and conduction bands marking a change from trivial to nontrivial electronic topology. The frequencies of B$_{2g}$ and A$^2_g$ modes become anomalous in the rhombohedral phase at 7.4 GPa, and new modes appearing in the rhombohedral phase show anomalous softening with pressure. This is shown to originate from unusual structural evolution of black phosphorous with pressure, based on first-principles theoretical analysis.

cond-mat.str-el↗
arXiv2016

Emergence of a weak topological insulator from the Bi$_x$Se$_y$ family and the observation of weak anti-localization

The discovery of strong topological insulators led to enormous activity in condensed matter physics and the discovery of new types of topological materials. Bisumth based chalcogenides are exemplary strong three dimensional topological insulators that host an odd number of massless Dirac fermionic states on all surfaces. A departure from this notion is the idea of a weak topological insulator, wherein only certain surface terminations host surface states characterized by an even number of Dirac cones leading to exciting new physics. Experimentally however, weak topological insulators have proven to be elusive. Here, we report a discovery of a weak topological insulator (WTI), BiSe, of the Bi-chalcogenide family with an indirect band gap of 42 meV. Its structural unit consists of bismuth bilayer (Bi$_2$), a known quantum spin hall insulator sandwiched between two units of Bi$_2$Se$_3$ which are three dimensional strong topological insulators. Angle resolved photo-emission spectroscopy (ARPES) measurements on cleaved single crystal flakes along with density fucntional theory (DFT) calculations confirm the existence of weak topological insulating state of BiSe. Additionally, we have carried out magneto-transport measurements on single crystal flakes as well as thin films of BiSe, which exhibit clear signatures of weak anti-localization at low temperatures, consistent with the properties of topological insulators.

cond-mat.mtrl-sci↗
arXiv2016

Pressure-induced phase transition in Bi$_2$Se$_3$ at 3 GPa: electronic topological transition or not?

In recent years, a low pressure transition around P $\sim$ 3 GPa exhibited by the A$_2$B$_3$-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi$_2$Se$_3$) using Raman spectroscopy at pressure upto 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P $\sim$ 2.4 GPa followed by structural transitions at $\sim$ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P $\sim$ 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated $\mathbb{Z}_2$ invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.

cond-mat.mtrl-sci↗
arXiv2015

Partial metric spaces with negative distances and fixed point theorems

In this paper we consider partial metric spaces in the sense of O'Neill. We introduce the notions of strong partial metric spaces and Cauchy functions. We prove a fixed point theorem for such spaces and functions that improves Matthews' contraction mapping theorem in two ways. First, the existence of fixed points now holds for a wider class of functions and spaces. Second, our theorem also allows for fixed points with nonzero self-distances. We also prove fixed point theorems for orbitally $r$-contractive and orbitally $ϕ_r$-contractive maps. We then apply our results to give alternative proofs of some of the other known fixed point theorems in the context of partial metric spaces.

math.GN↗
arXiv2015

The model theory of separably tame valued fields

A henselian valued field $K$ is called separably tame if its separable-algebraic closure $K^{\operatorname{sep}}$ is a tame extension, that is, the ramification field of the normal extension $K^{\operatorname{sep}}|K$ is separable-algebraically closed. Every separable-algebraically maximal Kaplansky field is a separably tame field, but not conversely. In this paper, we prove Ax-Kochen-Ershov Principles for separably tame fields. This leads to model completeness and completeness results relative to the value group and residue field. As the maximal immediate extensions of separably tame fields are in general not unique, the proofs have to use much deeper valuation theoretical results than those for other classes of valued fields which have already been shown to satisfy Ax-Kochen-Ershov Principles. Our approach also yields alternate proofs of known results for separably closed valued fields.

math.LO↗
arXiv2015

Partial n-metric spaces and fixed point theorems

In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said structures, and also generalize the notions of $G$-metric and $G_p$-metric spaces to arbitrary finite dimension. We prove Cauchy mapping theorems and other fixed point theorems for such spaces.

math.GN↗
arXiv2014

Strain induced $\mathbb{Z}_2$ topological insulating state of $β$-As$_2$Te$_3$

Topological insulators are non-trivial quantum states of matter which exhibit a gap in the electronic structure of their bulk form, but a gapless metallic electronic spectrum at the surface. Here, we predict a uniaxial strain induced electronic topological transition (ETT) from a band to topological insulating state in the rhombohedral phase (space group: R$\bar{3}$m) of As$_2$Te$_3$ ($β$-As$_2$Te$_3$) through \textit{first-principles} calculations including spin-orbit coupling within density functional theory. The ETT in $β$-As$_2$Te$_3$ is shown to occur at the uniaxial strain $ε_{zz}$ = -0.05 ($σ_{zz}$=1.77 GPa), passing through a Weyl metallic state with a single Dirac cone in its electronic structure at the $Γ$ point. We demonstrate the ETT through band inversion and reversal of parity of the top of the valence and bottom of the conduction bands leading to change in the $\mathbb{Z}_2$ topological invariant $ν_0$ from 0 to 1 across the transition. Based on its electronic structure and phonon dispersion, we propose ultra-thin films of As$_2$Te$_3$ to be promising for use in ultra-thin stress sensors, charge pumps and thermoelectrics.

cond-mat.mtrl-sci↗
arXiv2013

Model companion of ordered theories with an automorphism

Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal{L}$, then in the expanded language $\mathcal{L}_σ:= \mathcal{L}\cup\{σ\}$ with a new unary function symbol $σ$, the bigger theory $T_σ:= T\cup\{``σ\mbox{is an} \mathcal{L}\mbox{-automorphism''}\}$ does not have a model companion. We show in this paper that if, however, we restrict the automorphism and consider the theory $T_σ$ as the base theory $T$ together with a ``restricted'' class of automorphisms, then $T_σ$ can have a model companion in $\mathcal{L}_σ$. We show this in the context of linear orders and ordered abelian groups.

math.LO↗
arXiv2013

Sharp Raman Anomalies and Broken Adiabaticity at a Pressure Induced Transition from Band to Topological Insulator in Sb2Se3

The nontrivial electronic topology of a topological insulator is thus far known to display signatures in a robust metallic state at the surface. Here, we establish vibrational anomalies in Raman spectra of the bulk that signify changes in electronic topology: an E2 g phonon softens unusually and its linewidth exhibits an asymmetric peak at the pressure induced electronic topological transition (ETT) in Sb2Se3 crystal. Our first-principles calculations confirm the electronic transition from band to topological insulating state with reversal of parity of electronic bands passing through a metallic state at the ETT, but do not capture the phonon anomalies which involve breakdown of adiabatic approximation due to strongly coupled dynamics of phonons and electrons. Treating this within a four-band model of topological insulators, we elucidate how nonadiabatic renormalization of phonons constitutes readily measurable bulk signatures of an ETT, which will facilitate efforts to develop topological insulators by modifying a band insulator.

cond-mat.mtrl-sci↗
arXiv2010

Multiplicative Valued Difference Fields

The theory of valued difference fields $(K, σ, v)$ depends on how the valuation $v$ interacts with the automorphism $σ$. Two special cases have already been worked out - the isometric case, where $v(σ(x)) = v(x)$ for all $x\in K$, has been worked out by Luc Belair, Angus Macintyre and Thomas Scanlon; and the contractive case, where $v(σ(x)) > n\cdot v(x)$ for all $n\in\mathbb{N}$ and $x\in K^\times$ with $v(x) > 0$, has been worked out by Salih Azgin. In this paper we deal with a more general version, called the multiplicative case, where $v(σ(x)) = ρ\cdot v(x)$, where $ρ(> 0)$ is interpreted as an element of a real-closed field. We give an axiomatization and prove a relative quantifier elimination theorem for such a theory.

math.LO↗