arXiv subjects

Rajib Sarkar

Publications and source records attributed to Rajib Sarkar.

33 records · Page 2Linked to original sources

arXiv2021

Quartic metal: Spontaneous breaking of time-reversal symmetry due to four-fermion correlations in Ba$_{1-x}$K$_x$Fe$_2$As$_2$

Discoveries of ordered quantum states of matter are of great fundamental interest, and often lead to unique applications. The most well known example -- superconductivity -- is caused by the formation and condensation of pairs of electrons. A key property of superconductors is diamagnetism: magnetic fields are screened by dissipationless currents. Fundamentally, what distinguishes superconducting states from normal states is a spontaneously broken symmetry corresponding to long-range coherence of fermion pairs. Here we report a set of experimental observations in hole doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ which are not consistent with conventional superconducting behavior. Our specific-heat measurements indicate the formation of fermionic bound states when the temperature is lowered from the normal state. However, for $x \sim 0.8$, instead of the standard for superconductors, zero resistance and diamagnetic screening, for a range of temperatures, we observe the opposite effect: the generation of self-induced magnetic fields measured by spontaneous Nernst effect and muon spin rotation experiments. The finite resistance and the lack of any detectable diamagnetic screening in this state exclude the spontaneously broken symmetry associated with superconducting two-fermion correlations. Instead, combined evidence from transport and thermodynamic measurements indicates that the formation of fermionic bound states leads to spontaneous breaking of time-reversal symmetry above the superconducting transition temperature. These results demonstrate the existence of a broken-time-reversal-symmetry bosonic metal state. In the framework of a multiband theory, such a state is characterized by quartic correlations: the long-range order exists only for {\it pairs} of fermion pairs.

cond-mat.supr-con↗

arXiv2021

Language Independent Speech Emotion and Non-invasive Early Detection of Neurocognitive Disorder

Emotions(like fear,anger,sadness,happiness etc.) are the fundamental features of human behavior and governs his/her mental health. The subtlety of emotional fluctuations can be examined through perturbation in conversations or speech. Analysis of emotional state of a person from acoustical features of speech signal leads to discovery of vital cues determining his or her mental health. Hence, it's an important field of research in the area of Human Computer Interaction(HCI). In a recent work we have shown that how the contrast in Hurst-Exponent calculated from the non-stationary and nonlinear aspects of "angry" and "sad" speech(spoken in English language) recordings in the Toronto-Emotional-Speech-Set(TESS) can be used for early detection and diagnosis of Alzheimer's Disease. In this work we have extended the work and extracted Hurst-exponent for the speech-signals of similar emotions but spoken in German language. It has been observed that the Hurst-exponent efficiently segregates the contrasting emotions of "anger" and "sadness" in the speech spoken in German language, in similar fashion it has been doing for English speech. Hence it can be concluded that the Hurst-exponent can differentiate among speech spoken out of different emotions in language-independent manner. We propose algorithm for a language-independent application for early non-invasive detection of various severe neurocognitive-disorders like Alzheimer's Disease, MND(motor-neuron-disorder), ASD(autism-spectrum-disorder), depression, suicidal-tendency etc. which is not possible with the state of the art medical science.

cs.SD↗

arXiv2021

Symbolic powers of certain cover ideals of graphs

In this paper, we compute the regularity and Hilbert series of symbolic powers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover ideals in terms of the number of edges.

math.AC↗

arXiv2020

Bound for the regularity of binomial edge ideals of cactus graphs

In this article, we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique. As a consequence, we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph. We also identify certain subclass attaining the upper bound.

math.AC↗

arXiv2020

Almost complete intersection binomial edge ideals and their Rees algebras

Let $G$ be a simple graph on $n$ vertices and $J_G$ denote the binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the second graded Betti numbers of $J_G$, and we obtain a minimal presentation of it when $G$ is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a $d$-sequence and that the Rees algebra of their binomial edge ideal is Cohen-Macaulay. We also obtain an explicit description of the defining ideal of the Rees algebra of those binomial edge ideals.

math.AC↗

arXiv2020

Regularity of powers of quadratic sequences with applications to binomial ideals

In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms of the regularity of its related ideals and degrees of its generators. As a consequence, we compute upper bounds for the regularity of powers of several binomial ideals. We generalize a result of Matsuda and Murai to show that the regularity of $J^s_G$ is bounded below by $2s+\ell(G)-1$ for all $s \geq 1$, where $J_G$ denotes the binomial edge ideal of a graph $G$ and $\ell(G)$ is the length of a longest induced path in $G$. We compute the regularity of powers of binomial edge ideals of cycle graphs, star graphs, and balloon graphs explicitly. Also, we give sharp bounds for the regularity of powers of almost complete intersection binomial edge ideals and parity binomial edge ideals.

math.AC↗

arXiv2020

Certain Algebraic Invariants of Edge Ideals of Join of Graphs

Let $G$ be a simple graph and $I(G)$ be its edge ideal. In this article, we study the Castelnuovo-Mumford regularity of symbolic powers of edge ideals of join of graphs. As a consequence, we prove Minh's conjecture for wheel graphs, complete multipartite graphs, and a subclass of co-chordal graphs. We obtain a class of graphs whose edge ideals have regularity three. By constructing graphs, we prove that the multiplicity of edge ideals of graphs is independent from the depth, dimension, regularity, and degree of $h$-polynomial. Also, we demonstrate that the depth of edge ideals of graphs is independent from the regularity and degree of $h$-polynomial by constructing graphs.

math.AC↗

arXiv2020

Split superconducting and time-reversal symmetry-breaking transitions, and magnetic order in Sr$_2$RuO$_4$ under uniaxial stress

Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$μ$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2019

Depth and Extremal Betti Number of Binomial Edge Ideals

Let $G$ be a simple graph on the vertex set $[n]$ and $J_G$ be the corresponding binomial edge ideal. Let $G=v*H$ be the cone of $v$ on $H$. In this article, we compute all the Betti numbers of $J_G$ in terms of Betti number of $J_H$ and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen-Macaulay defect of $S/J_G$ in terms of Cohen-Macaulay defect of $S_H/J_H$ and using this we construct a graph with Cohen-Macaulay defect $q$ for any $q\geq 1$. We obtain the depth of binomial edge ideal of join of graphs. Also, we prove that for any pair $(r,b)$ of positive integers with $1\leq b< r$, there exists a connected graph $G$ such that $reg(S/J_G)=r$ and the number of extremal Betti number of $S/J_G$ is $b$.

math.AC↗

arXiv2019

Hilbert Series Of Binomial Edge Ideals

Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge ideal of decomposable graphs in terms of Hilbert series of its indecomposable subgraphs. Also, we compute the Hilbert series of binomial edge ideal of join of two graphs and as a consequence we obtain the Hilbert series of complete $k$-partite graph, fan graph, multi-fan graph and wheel graph.

math.AC↗

arXiv2018

New Classes of Infinite Image Partition Regular Matrices Near Zero

Image partition regular matrices near zero generalizes many classical results of Ram- sey Theory. There are several characterizations of finite image partition regular matrices near zero. Contrast to the finite cases there are only few classes of matri- ces that are known to be infinite image partition regular near zero. In this present work we have produced several new examples of such classes.

math.CO↗

arXiv2015

Microscopic coexistence of superconductivity and magnetism in Ca1-xNaxFe2As2

We present a detailed investigation of the magnetic and superconducting properties of Ca1-xNaxFe2As2 single crystals with x = 0.00, 0.35, 0.50, and 0.67 by means of the local probe techniques Moessbauer spectroscopy and muon spin relaxation experiments. With increasing Na substitution level, the magnetic order parameter as well as the magneto-structural phase transition are suppressed. For x = 0.50 we find a microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature Tc. A systematic comparison with other 122 pnictides reveals a square-root correlation between the reduction of the magnetic order parameter and the ratio of the transition temperatures, Tc/TN, which can be understood in the framework of a Landau theory. In the optimally doped sample with Tc = 34 K, diluted magnetism is found and the temperature dependence of the penetration depth and superfluid density are obtained, proving the presence of two superconducting s-wave gaps

cond-mat.supr-con↗

arXiv2014

Coexistence of 3d-ferromagnetism and superconductivity in [(Li(1-x)Fex)OH](Fe(1-y)Liy)Se

Superconducting [(Li(1-x)Fex)OH](Fe(1-y)Liy)Se (x ~ 0.2, y ~ 0.08) was synthesized by hydrothermal methods and structurally characterized by single crystal X-ray diffraction. The crystal structure contains anti-PbO type (Fe(1-y)Liy)Se layers separated by layers of (Li(1-x)Fex)OH. Electrical resistivity and magnetic susceptibility measurements reveal superconductivity at 43 K. An anomaly in the diamagnetic shielding indicates ferromagnetic ordering near 10 K while superconductivity is retained. The ferromagnetism emerges from the iron atoms in the (Li(1-x)Fex)OH layer. Isothermal magnetization measurements confirm the superposition of ferromagnetic with superconducting hysteresis. The internal ferromagnetic field is larger than the lower, but smaller than the upper critical field of the superconductor, which gives evidence for a spontaneous vortex phase where both orders coexist. 57Fe-Mössbauer spectra, 7Li-NMR spectra, and muSR experiments consistently support this rare situation, especially in a bulk material where magnetism emerges from a 3d-element.

cond-mat.supr-con↗

arXiv2014

Interplay of magnetism and superconductivity in EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals probed by muon spin rotation and ${}^{57}$Fe Mössbauer spectroscopy

We present our results of a local probe study on EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals with $x$=0.13, 0.19 and 0.28 by means of muon spin rotation and ${}^{57}$Fe Mössbauer spectroscopy. We focus our discussion on the sample with $x$=0.19 viz. at the optimal substitution level, where bulk superconductivity ($T_{\text{SC}}=28$ K) sets in above static europium order ($T^{\text{Eu}}=20$K) but well below the onset of the iron antiferromagnetic (AFM) transition ($\sim$100 K). We find enhanced spin dynamics in the Fe sublattice closely above $T_{\text{SC}}$ and propose that these are related to enhanced Eu fluctuations due to the evident coupling of both sublattices observed in our experiments.

cond-mat.supr-con↗

arXiv2010

Interplay between Co-3d and Ce-4f magnetism in CeCoAsO

We have investigated the ground state properties of polycrystalline CeCoAsO by means of magnetization, specific heat and solid state NMR. Susceptibility and specific-heat measurements suggest a ferromagnetic order at about, $T_\mathrm{C}$=75 K. No further transitions are found down to 2 K. At 6.5 K a complex Schottky type of anomaly shows up in the specific heat results. The interplay between Ce-4f and Co-3d magnetism being responsible for that anomaly is discussed. Furthermore $^{75}$As NMR investigations have been performed to probe the magnetism on a microscopic scale. As-NMR spectra are analysed in terms of first and second order quadrupolar interaction. The anisotropic shift component $K_{\mathrm{ab}}$ and $K_{\mathrm{c}}$ could be derived from the $^{75}$As powder spectra. Towards lower temperature a strong shift anisotropy was found. Nonetheless $K_{\mathrm{iso}}$ tracks the bulk susceptibility down to $T=$50 K very well. Furthermore the presence of weak correlations among the Ce ions in the ferromagnetic state is discussed. The observed increase of $C/T$ towards lower temperatures supports this interpretation.

cond-mat.str-el↗