1,720,981 research outputs found
Edge States and Effects of Disorder in Finite Graphene Sheets
No full textThe thesis endeavours to theoretically understand electronic properties of nite trapezoidal shaped graphene sheets, and understand zero energy edge states. The motivation for this thesis is recent experimental work at Low Temperature Nano-electronics Laboratory under Prof. Arindam Ghosh[ ?]. This work sys-tematically tries to understand graphene, a two dimensional material, and it's confinement in spacial dimensions. In Part I, we start with analytical study of bulk graphene with various hoppings in a tight-binding formulation and its band structure. Then we confine graphene in one-dimension to form semi-in finite graphene nanoribbons and numerically determine its energy spectra and wave-functions for sites along the finite direction.
In Part II, graphene is confined in both spacial dimensions and starting from simplest case of finite rectangular sheet, we move on to the two different ways in which graphene can be torn. Here, numerical studies were done to determine the density of states and local density of states.
Finally Parts III and IV are devoted to the study of disorders and how various kinds of disorders can be introduced in the system and their effect in localising the wave-functions along the edges
Quantum oscillation in band insulators and properties of non-equilibrium steady states in disordered insulators
No full textStarting with the experiment on Kondo insulator SmB6 , which shows 1/B-periodic oscillations despite the absence of gapless electronic excitations in bulk, the candidate insulators showing quantum oscillation (QO) are on the rise. But this is contrary to our conventional understanding that we need a Fermi surface to have QO. So an obvious question to ask is, ‘How can insulators show QO?’. If there is QO, then which physical quantities show QO, and what is the physical reason behind their origin? In the absence of a Fermi surface, what determines the frequency of these QO? In search of answers, we revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast with metals where all observables exhibit oscillations at the same frequency. The temperature dependence of the amplitudes of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well-known in metals.
The interplay of disorder and interactions in quantum systems can lead to several intriguing phenomena, amongst which many-body localization (MBL) has caught many physicists’ attention in recent times. In the second work, we investigate whether an MBL system undergoes a transition to a current-carrying non-equilibrium steady state under a drive and how the entanglement properties of the quantum states change across the transition. The drive is introduced by using a phenomenological non-Hermitian model. We also discuss the dynamics, entanglement growth, and long-time fate of a generic initial state under an appropriate time evolution of the system governed by the non-H ermitian Hamiltonian. Our study reveals rich entanglement structures of the eigenstates of the non-Hermitian Hamiltonian. We find the transition between current-carrying states with volume-law to area-law entanglement entropy as a function of disorder and the strength of the non-Hermitian term.
In the third work, we take two 1D systems, namely the 1D Anderson model and Aubry-André-Harper model, that show the localization of single particle eigenstates depending on the strength of disorder and study it under a chemical potential drive. The drive is induced by connecting baths at different chemical potentials to the two edges of the system. We calculate the Green functions of the systems on the Keldysh contour that we use to calculate physical quantities like current and occupation of the non-equilibrium steady state. Our results can distinguish between the localized and delocalized phases in the non-interacting limit. In the presence of interaction, our systems can show MBL to a thermal phase transition. We end with a discussion on the possibility of probing this thermal to MBL phase boundary using dynamical mean field theory
Many-body classical chaos: A case study across thermal phase transitions and connection to quantum measurements
No full textThere has been enormous interest in understanding the emergence of thermal behavior in systems isolated from the environment, be it classical or quantum. For classical systems, it has been argued that chaos plays a vital role in attaining the ‘ergodicity’ and ‘mixing,’ two essential ingredients behind thermalization. Therefore, it becomes indispensable to understand the chaos for many particles (or many-body) with interactions, where the role of chaos in thermalization has long been studied. In the first part of this thesis, we discuss our findings on the behavior of many-body chaos across thermal phase transitions in a classical spin system. We have studied a well-known paradigmatic model: a two-dimensional XXZ Model in two universality classes, namely the Kosterlitz-Thouless (KT) and Ising. After suitably defining a recently introduced classical out-of-time-ordered correlator (cOTOC) for our model, we calculate the Lyapunov exponent and butterfly velocity, diagnostics for a chaotic system, across the aforementioned phase transitions. We, thereafter, discuss how many-body chaos can be an additional tool to characterize different thermal phases. For quantum systems, in addition to a remarkable bound in chaos, there exists a phenomenological relation between short- or intermediate-time chaos and long-time hydrodynamic transport. We explore such a connection in classical systems where no such bound in chaos exists. After discussing the dynamical structure factor for conserved modes, we comment on the connection between chaos and transport across the KT and Ising phase transition in the same XXZ model. To extend our discussion further, we discuss the fate of many-body chaos when randomness (or noise) is added to the dynamics. As we see, using a modified cOTOC with noise, there exists a critical noise strength, after which a chaotic system becomes non-chaotic and vice versa. After suitably defining a chaotic model of coupled anharmonic oscillators, such transition in the classical systems can be liked with quantum measurement-induced transitions via a nontrivial Schwinger-Keldysh path-integral. Finally, we discuss the many-body chaotic behavior in a ‘frustrated’ spin system, where we can access a low-temperature classical spin-liquid phase. After introducing the two-dimensional Kagome Heisenberg anti-ferromagnetic model, We discuss the equilibration at low temperatures using Monte Carlo and show the results of the Lyapunov exponent and butterfly velocity across the crossover from the paramagnetic to the spin-liquid phase. We parallelly explore the connection between chaos and transport. In the end, I conclude with the future outlook
Transport, localization and entanglement in disordered and interacting systems: From real space to Fock space
No full textIn this thesis, we explore some of the exciting physics of condensed matter systems
manifested because of imperfection or disorder and interactions among the constituent
particles. In phenomena like transport, e.g., electrical current; localization, e.g.,
confinement of electrons only within a small part of a system; entanglement (a
correlation among the constituents particle); disorder and interaction play essential
roles. These three properties are our main focus in the thesis.
There are six chapters. In the first chapter, we introduce a few landmarks in the
field to set the stage and give an overview of the works presented in the thesis. In the
second chapter, we consider quasi-disordered or quasiperiodic systems in one, two, and
three dimensions, where the quasi-disorder is deterministic but non-repeating
throughout a lattice and considered from. Metal-insulator transitions in these systems
are probed by calculating conductances and their change with system size. More
specifically, we look at the systems from the perspective of single-parameter scaling
theory. In the third chapter, we consider both the disordered and quasi-disordered
systems with interactions. The systems show transitions from thermal to many-body
localized phases, and we study them in Fock space, which is a natural description for an
interacting system. We exploit the Fock space structure to calculate the propagator or
Green’s function in an iterative way to push the system size accessible in the exact
calculations. We define a length scale in Fock space, which can detect the phase transition
and distinguish between the disordered and the quasi-disordered systems. In the fourth
chapter, motivated by an experiment, we study the electrical current and noise therein in
a disordered quantum Hall system in the proximity of a superconductor. To our surprise,
the quantum Hall conductance plateau in the system comes with noise in the current as
also observed in the experiment, and the calculated quantities match pretty well with the
observed values. In the fifth chapter, we study the entanglement entropy of an interacting
fermionic system using a new saddle-point approximation similar to a mean-field
approximation. The approximation is based on a newly developed path integral approach
for calculating the entanglement entropy. In the last chapter, we conclude the thesis by
summarizing the important findings of our works presented in the thesis with some
future directions
Dynamics of glass forming liquids with emphasis on vibrational modes
No full textThe potential energy landscape (PEL) description is regarded as one of the fundamental landmarks in the theory of glass transition, which has found wide applications not only in the understanding of disordered materials but also in other frontiers of research, such as bio-molecules, catalysis, machine learning, and neural networks. In this context, the mechanically stable local minimum energy configurations of the PEL, which are known as inherent structures (ISs), have a major role to play in elucidating various dynamical and thermodynamic properties of the system in terms of its sojourn over the complex multi-dimensional potential energy surface (PES). However contrary to the crystals, disordered materials pose a greater challenge in understanding their properties. Due to their ordered structures, the normal modes of collective vibrational excitations in crystals can be described by plane waves, which are known as phonons, and they play a fundamental role in determining the kinetic and thermodynamic properties of crystalline solids. Notwithstanding the difficulties presented by the inherent disorder in glass-forming materials, collective excitations associated with small-amplitude vibrations of the system about their ISs can be defined. This thesis presents a study of the dynamics of glass-forming liquids with emphasis on the collective vibrational excitations of the underlying disordered solid.
The vibrational spectrum of disordered harmonic solids consists of a coexisting region of extended phonon modes that obey the Debye scaling law in their density of states, g(ω) ∼ ω^(d−1) in d dimensions, and quasi-localized modes that obey a universal g(ω) ∼ ω^4 law. These excess quasi-localized modes, appearing in the boson peak region of the vibrational spectrum, are found to be substantially different in nature as compared to the modes in other parts of the spectrum. The first part of the thesis describes an investigation of the dynamics of model glass-forming systems based on the measurement of thermal transport properties, with emphasis on the role of the vibrational modes in determining the thermal conductivity. Depending on the protocol of preparation of the glass, the system explores different parts of the PEL. The distinct ISs visited by the system in its exploration of the PEL impact the thermal transport characteristics of the low-temperature glassy states significantly. The observation of lower values of thermal conductivity with slower cooling or growing age of the glass former can be rationalized in terms of the system’s exploration of ISs with progressively lower energy. This in turn has been linked to the presence of more localized normal mode excitations associated with the ISs. Further, the energy diffusivity d(ω) that measures the ability of an excitation to transport thermal energy, has been found to obey a generic d(ω) ∼ 1/(ω^3) law for the quasi-localized normal modes. The diffusivity of low-frequency delocalized phonon modes in two dimensions, on the other hand, follows a d(ω) ∼ 1/(ω^2) law, and it is possible to transform these extended modes to acquire quasi-localized character by the introduction of quenched disorder, which can be achieved via pinning a fraction of the particles. Notably, the boson peak coincides with the well-known Ioffee-Regel limit for phonons, which signals the crossover in terms of d(ω), from a regime populated by delocalized modes to a regime of quasi-localized modes.
In the second part of the thesis, the low-temperature short-time dynamics of a model glass forming system in metabasins of the PEL has been examined. A metabasin is an assembly of strongly correlated basins of ISs in the PEL. Our analysis in terms of the complete vibrational spectrum reveals that the harmonic approximation is not adequate for describing the short-time dynamics at temperatures near the glass transition point. The mean-square displacements computed within the harmonic approximation deviates from that obtained from molecular dynamics simulation at a time shorter than the β-relaxation timescale (τ_β ). With the added contribution of the anharmonic terms in the Hamiltonian via an approximate scheme, the mean- square displacement obtained from the modified calculation shows an agreement with that from both molecular dynamics and metabasin dynamics to a time extending beyond τ_β . The short-time dynamics appears as a combination of the dynamics within the basins of individual ISs and the system’s exploration of different basins inside a metabasin. Moreover, our study shows that the manifestation of the low-frequency quasi-localized excitations in the dynamical quantities depends on the nature of the microscopic dynamics (Newtonian or Langevin) of the system. Our studies in the thesis thus highlight a few important features of the low-temperature dynamics of glass formers and their close connection with the system’s potential energy landscape via the collective vibrational excitations
Phenomenological Theory Of Superconductivity And Low-Energy Electronic Spectra In The High-Tc Cuprates
Full text linkCondensed matter physics is a rapidly evolving field of research enriched with the synthesis of new materials exhibiting a bewildering variety of phenomena and advances in experimental techniques. Over the years, discoveries and innovations in electronic systems have emphasized the crucial role played by correlations among electrons behind many of the observed unusual properties and have posed serious challenges to the physics community by exposing the lack of well-controlled theoretical methods to study the class of materials known as strongly correlated electronic systems. In these systems, known theoretical techniques typically fail to capture the essential features of the many-body ground state and finite temperature properties of the systems as typical electronic interaction energies are of order of or larger than the kinetic energies.
The study of strongly correlated electronic systems went through a revolution in the 1980s and 1990s after the discovery of superconductivity inorganic compounds, in heavy fermion systems and ultimately in copper oxides, referred to as cuprates, by Bednorz and Muller. In particular, the pursuit of understanding the mysterious origin of superconductivity in the cuprates and other associated strange phenomena has fascinated the condensed matter community over last two and half decades leading to most of the important unsolved, and probably interconnected, problems of quantum condensed matter physics such as the metal-insulator transition in low dimensions breakdown of Fermi liquid theory, the origin and behavior of unconventional superconductivity, quantum critical points, electronic in homogeneities and localization in interacting systems. This thesis is devoted to the study of some of the aspects of high-temperature superconductivity and associated phenomena in cuprates. In what follows, I give an overview of the organization of the thesis in to different chapters and their contents.
For setting up the stage, in Chapter 1, I give a brief account of some of the remarkable phenomena and properties observed in strongly correlated electronic matter and their salient features, that continue to draw much attention and excitement in current times. The peculiarity of the state of affairs in these systems is emphasized and motivated in the background of the paradigmatic Landau Fermi liquid theory and Hubbard model, the minimal model that is expected to capture the quintessence of electronic strong correlation.
In Chapter 2, starting with a brief historical account of the discovery of superconductivity in cuprates, the crystal structure of these materials, their chemical realities and basic electronic details are reviewed. This is followed by a survey of the phase diagram of cuprates, doped with, say, x number of holes per copper site, and a plethora of experimental findings that constitute the high-c puzzle. Characteristics of various observed phases, such as the superconducting, pseudo gap and strange metal phases, are discussed on the basis off acts accumulated through various experimental probes, e.g. nuclear magnetic resonance(NMR), neutron scattering, specific heat, transport and optical conductivity measurements as well as photo emission, tunnelling and Raman spectroscopies. As elucidated, these experiments point toward the need for an unconventional mechanism of superconductivity in cuprates and, more so, for the description of the rather abnormal high-temperature normal state that is realized above the superconducting transition temperature c. Keeping in mind the fact that there is no consensus even about the minimal microscopic electronic model, I review two models, namely the three band model and the t - J model; various approximate treatments of these models have dominated the theoretical developments in this field. A large number of theoretical pictures have been proposed based on different microscopic, semi-microscopic and phenomenological approaches in the past two decades for explaining the genesis of the observed strange phenomena in high-c cuprates. I include brief discussions on only a few of them while citing relevant references.
As mentioned above, a variety of approximate microscopic theories, based on both strong and weak coupling approaches, as well as numerical techniques have been tried to understand the cuprate phase diagram and capture the aspects of strong correlations in-built in Hubbard and t -J models. On the other hand, in conventional superconductors and, in general, for the study of phase transitions, phenomenological Ginzburg-Landau(GL) functionals written down from very general symmetry grounds have provided useful description for a variety of systems. Specially, Ginzburg-Landau theory has been proven to be complementary to the BCS theory for attacking a plethora of situations in superconductors, e.g., in homogeneities, structures of an isolated vortex and the vortex lattice etc. The GL functional has found wide applicability for the study of vortex matter in high-c superconductors as well. Inspired by the success of this type of phenomenological route, we propose and develop in Chapter 3 an approach, analogous in spirit to that of Ginzburg and Landau, for the superconducting and pseudogap phases of cuprates. We encompass a large number of well known phenomenologies of cuprate superconductivity in the form of a low-energy effective lattice functional of complex spin-singlet pair amplitudes with magnitude Δm and phase m, i.e. m =Δm exp(i m), that resides on the Cu-Cubonds(indexed by m)of the CuO2 planes of cuprates. The functional respects general symmetry requirements, e.g. the -wave symmetry of the superconducting order parameter as found in experiments. The assumptions and the specific physical picture behind such an approach as well as the key empirical inputs that go into it are discussed in this chapter. We calculate the superconducting transition temperature c and the average magnitude of the local pair amplitude, Δ= (Δm), using single-site mean-field theory for the model. We show that this approximation leads to general features of the doping-temperature(x - T )phase diagram in agreement with experiment. In particular, we find a phase coherent superconducting state with d-wave symmetry below a parabolic Tc (x) dome and a phase incoherent state with a perceptible local gap that persists up to a temperature around which can be thought of as a measure of the pseudogap temperature scale T* . Further, effects of thermal fluctuations beyond the mean-field level are captured via Monte Carlo(MC) simulations of the model for a finite two-dimensional (2D) lattice. We exhibit results for Tc obtained from MC simulations as well as that estimated in a cluster mean field approximation. Based on our picture we remark on contrasting scenarios proposed for the doping dependence of the pseudogap temperature.
Chapter 4 describes fluctuation phenomena related to pairing degrees of freedom and manifestations of these effects in various quantities of interest, e.g. superfluid density, specific heat etc., at finite temperature. Fluctuation effects have been studied in detail in superconductors over the years and pursued mainly using either the conventional GL functional or the BCS-framework at a microscopic level. However, the picture, in which the pseudogap phase is viewed as one consisting of bond-pairs with a d-wave symmetry correlation length growing as T approaches Tc, implies fluctuation phenomena of quite a different kind, as we discuss here. The contribution of the bond-pair degrees of freedom to thermal properties is obtained here from the lattice free-energy functional using MC simulation, as mentioned in the preceding paragraph. The results for the superfluid density or superfluid stiffness ps, a quantity measured e.g. via the penetration depth, are discussed. As shown, its doping and temperature dependence compare well with experimental results. In this chapter, I also report the calculation of the fluctuation specific heat Cv(T) and find that there are two peaks in its temperature dependence, a sharp one connected with Tc (ordering of the phase of m)and a relatively broad one(hump)connected to T* (rapid growth of the magnitude of Δm). The former is specially sensitive to the presence of a magnetic field, as we find in agreement with experiment. Vortices are relevant excitations in a superconductor and, in particular, in 2D orquasi-2D systems vortices influence the finite temperature properties in a major way. The results for the temperature dependence of vortex density obtained in the MC simulation of the GL-like model are also mentioned in Chapter 4. I report an estimate of the correlation length as well. These results might have relevance for the large Nernst signal observed over a broad temperature range above c in cuprates, as pointed out there.
Properties of an isolated vortex and collective effects arising due to interaction between vortices are of much significance for understanding mixed state of type-II superconductors and thus of cuprates. The superconducting order is destroyed in the core region around the centre of a vortex and the vortex core carries signatures of the normal state in a temperature regime where it is generally unattainable due to occurrence of superconductivity. As mentioned in Chapter 5, vortex properties(e.g. electronic excitation spectrum at the vortex core) in BCS superconductors have been explored theoretically, at a microscopic level through the Bogoliubov-deGennes(BdG) theory as well as using the Ginzburg-Landau functional. However, properties of vortices in cuprate superconductors have been found to be much more unusual than could possibly be captured by straightforward extensions of BCS theory to a -wave symmetry case. Chapter 5 briefly reviews the experimental findings on vortices in the superconducting state of cuprates, mainly as probed by Scanning Tunnelling Microscopy(STM) as well as from other probes such as NMR, neutron scattering, SR etc. I discuss some of the consequences of our GL-like functional regarding vortex properties, namely that of the vortex core and the region around it. We use our model to find Δm and m at different sites m for a 2π vortex whose core is at the midpoint of a square plaquette of Cu lattice sites. The vortex is found to change character from being primarily a phase or Josephson vortex for small x to a more BCS-like or Abrikosov vortex with a large diminution in the magnitude Δm as one approaches the vortex core, for large . Here I do not make any direct comparison with experimental data but discuss implications of our results in the background of existing experimental facts.
Unravelling the mysteries of high-Tc cuprates should necessarily involve the understanding of electronic excitations over a broad regime of doping and temperature encompassing the pseudo gap, superconducting and strange metal states. A phenomenological theory which aims to describe the pseudo gap phase as one consisting of preformed bond-pairs, is required to include both unpaired electrons and Cooper pairs of the same electrons coexisting and necessarily coupled with each other. In our Ginzburg Landau approach only the latter are explicit, while the former are integrated out. However, effects connected with the pair degrees of freedom are often investigated via their coupling to electrons, one very prominent examples being Angle Resolved Photoemmision Spectroscopy(ARPES),in which the momentum and energy spectrum of electrons ejected from the metal impinged by photons is investigated. In Chapter 6, we develop a unified theory of electronic excitations in the superconducting and pseudo gap phases using a model of electrons quantum mechanically coupled to spatially and temporally fluctuating Cooper pairs(the nearest neighbour singlet bond pairs). We discuss the theory and a number of its predictions which seem to be in good agreement with high resolution ARPES measurements, which have uncovered a number of unusual spectral properties of electrons near the Fermi energy with definite in-plane momenta. We show here that the spectral function of electrons with momentum ranging over the putative Fermi surface(recovered at high temperatures above the pseudogap temperature scale) is strongly affected by their coupling to Cooper pairs. On approaching Tc i.e. the temperature at which the Cooper pair phase stiffness becomes nonzero, the inevitable coupling of electrons with long-wavelength(d-wave symmetry) phase fluctuations leads to the observed characteristic low-energy behavior as reported in Chapter 6. Collective d-wave symmetry superconducting correlations develop among the pairs with a characteristic correlation length ξ which diverges on approaching the continuous transition temperature Tc from above. These correlations have a generic form for distances much larger than the lattice spacing. As we show here, the effect of these correlations on the electrons leads, for example, to a pseudogap in electronic density of states for T > T c persisting till T* , temperature-dependent Fermi arcs i.e. regions on the Fermi surface where the quasiparticle spectral density is non zero for a zero energy excitation and to the filling of the antinodal pseudogap in the manner observed. Further, the observed long-range order(LRO) below c leads to a sharp antinodal spectral feature related to the non zero superfluid density, and thermal pair fluctuations cause a deviation(‘bending’) of the inferred ‘gap’ as a function of k from the expected d-wave form (cos kxa - cos kya). The bending, being of thermal origin, decreases with decreasing temperature, in agreement with recent ARPES measurements.
I conclude in Chapter 7 by mentioning some natural directions in which the functional and the approach used here could be taken forward. The phenomenological theory proposed and developed in this thesis reconciles and ties together a range of cuprate superconductivity phenomena qualitatively and confronts them quantitatively with experiment. The results, and their agreement with a large body of experimental findings, strongly support the mechanism based on nearest neighbor Cooper pairs, and emergence of long-range -wave symmetry order as a collective effect arising from short range interaction between these pairs. This probably points to the way in which high-c superconductivity will be understood
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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