etd@IISc Collection:http://hdl.handle.net/2005/422016-06-22T04:16:54Z2016-06-22T04:16:54ZRaman Spectroscopy Of Graphene And Graphene Analogue MoS2 TransistorsChakraborty, Biswanathhttp://hdl.handle.net/2005/25392016-06-18T08:55:42Z2016-06-17T18:30:00ZTitle: Raman Spectroscopy Of Graphene And Graphene Analogue MoS2 Transistors
Authors: Chakraborty, Biswanath
Abstract: The thesis presents experimental studies of device characteristics and vibrational properties of atomic layer thin graphene and molybdenum disulphide (MoS2). We carried out Raman spectroscopic studies on field effect transistors (FET) fabricated from these materials to investigate the phonons renormalized by carrier doping thus giving quantitative information on electron-phonon coupling. Below, we furnish a synoptic presentation of our work on these systems.
Chapter1: Introduction
Chapter1, presents a detailed introduction of the systems studied in this the¬sis, namely single layer graphene (SLG), bilayer graphene (BLG) and single layer molybdenum disulphide (MoS2). We have mainly discussed their electronic and vibrational properties in the light of Raman spectroscopy. A review of the Raman studies on graphene layers is presented.
Chapter2: Methodology and Experimental Techniques
Chapter 2 starts with a description of Raman instrumentation. The steps for isolating graphene and MoS 2 flakes and the subsequent device fabrication procedures involving lithography are discussed in detail. A brief account of the top gated ﬁeld effect transistor (FET) using solid polymer electrolyte is presented.
Chapter3: Band gap opening in bilayer graphene and formation of p-n junction in top gated graphene transistors: Transport and Raman studies
In Chapter3 the bilayer graphene (BLG) ﬁeld effect transistor is fabricated in a dual gate configuration which enables us to control the energy band gap and the Fermi level independently. The gap in bilayer energy spectrum is observed through different values of the resistance maximum in the back gate sweep curves, each taken at a fixed top gate voltage. The gate capacitance of the polymer electrolyte is estimated from the experimental data to be 1.5μF/cm2 . The energy gap opened between the valence and conduction bands using this dual-gated geometry is es¬timated invoking a simple model which takes into account the screening of gate induced charges between the two layers. The presence of the controlled gap in the energy band structure along with the p-n junction creates a new possibility for the bilayer to be used as possible source of terahertz source. The formation of p-n junction along a bilayer graphene (BLG) channel is achieved in a electrolytically top gated BLG FET, where the drain-source voltage VDS across the channel is continuously varied at a fixed top gate voltage VT(VT>0). Three cases may arise as VDS is varied keeping VT fixed: (i) for VT-VDS0, the entire channel is doped with electron, (ii) for VT-VDS= 0, the drain end becomes depleted of carriers and kink in the IDS vs VDS curve appears, (iii) for VT-VDS « 0, carrier reversal takes place at the drain end, accumulation of holes starts taking place at the drain end while the source side is still doped with electrton.
The verification of the spatial variation of carrier concentration in a similar top gated single layer graphene (SLG) FET device is done using spatially resolved Ra¬man spectroscopy. The signature 2D Raman band in a single layer graphene shows opposite trend when doped: 2D peak position decreases for electron doping while it increases for hole doping. On the other hand, the G mode response being symmetric in doping can act as a read-out for the carrier concentration. We monitor the peak position of the G and the 2D bands at different locations along the SLG FET channel. For a fixed top gate voltage V T , both G and the 2D band frequencies vary along the channel. For a positive VTsuch that VT-VDS= 0, the peak frequencies ωGand ω2DωG/2D occur at the undoped frequency (ωG/2D)n=0 near the drain end while the source end corresponds to non-zero concentration. When VT-VDS<0, Raman spectra from hole doped regions (drain end) in the channels show an blue-shift in ω2Dwhile from the electron doped regions (near source) ω2Dis softened.
Chapter4: Mixing Of Mode Symmetries In Top Gated Bilayer And Multilayer Graphene Field Effect Devices
In Chapter4, the effect of gating on a bilayer graphene is captured by using Raman spectroscopy which shows a mixing of different optical modes belonging to differ¬ent symmetries. The zone-center G phonon mode splits into a low frequency (Glow) and a high frequency (Ghigh) mode and the two modes show different dependence on doping. The two G bands show different trends with doping, implying different electron-phonon coupling. The frequency separation between the two sub-bands in¬creases with increased doping. The mode with higher frequency, termed as Ghigh, shows stiffening as we increase the doping whereas the other mode, Glow, shows softening for low electron doping and then hardening at higher doping. The mode splitting is explained in terms of mixing of zone-center in-plane optical phonons rep¬resenting in-phase and out-of-phase inter-layer atomic motions. The experimental results are combined with the theoretical predictions made using density functional theory by Gava et al.[PRB 80, 155422 (2009)]. Similar G band splitting is observed in the Raman spectra from multilayer graphene showing inﬂuence of stacking on the symmetry properties.
Chapter5: Anomalous dispersion of D and 2D modes in graphene and doping dependence of 2D ′and 2D+G bands
Chapter 5 consists of two parts: Part A titled “Doping dependent anomalous dispersion of D and 2D modes in graphene” describes the tunability of electron-phonon coupling (EPC) associated with the highest optical phonon branch (K-A) around the zone corner K using a top gated single layer graphene ﬁeld effect transistor. Raman D and 2D modes originate from this branch and are dispersive with laser excitation energy. Since the EPC is proportional to the slope of the phonon branch, doping dependence of the D and 2D modes is carried out for different laser energies. The dispersion of the D mode decreases for both the electron and the hole doping, in agreement with the recent theory of Attaccalite et. al [Nano Letters, 10, 1172 (2010)]. In order to observe D-band in the SLG samples, low energy argon ion bombardment was carried out. The D peak positions for variable carrier concentration using top-gated FET geometry are determined for three laser energies, 1.96 eV, 2.41 eV and 2.54 eV. However, the dispersion of the 2D band as a function of doping shows an opposite trend. This most curious result is quantitatively explained us¬ing a ﬁfth order process rather than the usual fourth order double resonant process usually considered for both the D and 2D modes.
Part B titled “Raman spectral features of second order 2D’ and 2D+G modes in doped graphene transistor” deals with doping dependence of 2D’ and 2D+G bands in single layer graphene transistor. The phonon frequency blue shifts for the hole doping and whereas it red shifts for electron doping, similar to the behaviour of the 2D band. The linewidth of the 2D+G combination mode too follows the 2D trend increasing with doping while that of 2D’ mode remains invariant.
Chapter6: New Raman modes in graphene layers using 2eV light
Unique resonant Raman modes are identiﬁed at 1530 cm−1 and 1445 cm−1 in single, bi, tri and few layers graphene samples using 1.96 eV (633 nm) laser excitation energy (EL). These modes are absent in Raman spectra using 2.41 eV excitation energy. In addition, the defect-induced D band which is observed only from the edges of a pristine graphene sample, is observed from the entire sample region using E L = 1.96 eV. Raman images with peak frequencies centered at 1530 cm−1, 1445 cm−1 and D band are recorded to show their correlations. With 1.96 eV, we also observe a very clear splitting of the D mode with a separation of ∼32 cm−1, recently predicted in the context of armchair graphene nanoribbons due to trigonal warping effect for phonon dispersion. All these findings suggest a resonance condition at ∼2eVdue to homo-lumo gap of a defect in graphene energy band structure.
Chapter7: Single and few layer MoS2: Resonant Raman and Phonon Renormalization
Chapter 7 is divided into two parts. In Part A “Layer dependent Resonant Raman scattering of a few layer MoS2”, we discuss resonant Raman scattering from single, bi, four and seven layers MoS2. As bulk crystal of MoS2is thinned down to a few atomic layers, the indirect gap widens turning into a direct gap semiconductor with a band gap of 1.96 eV in its monolayer form. We perform Raman study from MoS 2 layers employing 1.96 eV laser excitation in order to achieve resonance condition. The prominent Raman modes for MoS 2 include first order E12g mode at ∼383 cm−1 and the A1gmode at ∼408 cm−1 which are observed under both non resonant and resonant conditions. A1gphonon involves the sulphur atomic vibration in opposite direction along the c axis (perpendicular to the basal plane) whereas for E12g mode, displacement of Mo and sulphur atoms are in the basal plane. With decreasing layer thickness, these two modes shifts in opposite direction, the E12g mode shows a blue shift of ∼2cm−1 while the A1gis red shifted by ∼4cm−1 . Under resonant condi¬tion, apart from E12g and A1gmodes, several new Raman spectral features, which are completely absent in bulk, are observed in single, bi and few layer spectra pointing out the importance of Raman characterization. New Raman mode attributed to the longitudinal acoustic mode belonging to the phonon branch at M along the Γ-M direction of the Brillouin zone is seen at ∼230 cm−1 for bi, four and seven layers. The most intense region of the spectrum around 460 cm−1 is characterized by layer dependent frequencies and spectral intensities with the band near 460 cm−1 becoming asymmetric as the sample thickness is increased. In the high frequency region between 510-630 cm−1, new bands are seen for bi, four and seven layers.
In Part B titled “Symmetry-dependent phonon renormalization in monolayer MoS2transistor”, we show that in monolayer MoS2the two Raman-active phonons, A1g and E21 g, behave very differently as a function of doping induced by the top gate voltage in FET geometry. The FET achieves an on-off ratio of ∼ 105 for electron doping. We show that while E12g phonon is essentially unaffected, the A1gphonon is strongly influenced by the level of doping. We quantitatively understand our experimental results through the use of first-principles calculations to determine frequencies and electron-phonon coupling for both the phonons as a function of carrier concentration. We present symmetry arguments to explain why only A1g mode is renormalized significantly by doping. Our results bring out a quantitative under¬standing of electron-phonon interaction in single layer MoS2.2016-06-17T18:30:00ZMesophases Of Active Matter : Translational Order, Critical Rheology And ElectrostaticsAdhyapak, Tapan Chandrahttp://hdl.handle.net/2005/25192016-04-26T06:51:52Z2016-04-25T18:30:00ZTitle: Mesophases Of Active Matter : Translational Order, Critical Rheology And Electrostatics
Authors: Adhyapak, Tapan Chandra
Abstract: This thesis consists of research work in the broad area of soft condensed matter theory with a focus on active matter. The study of long wavelength, low frequency collective behavior of active particles (bacterial suspensions, fish schools, motor-microtubule extracts, active gels) forms an interesting modification to liquid-crystal hydrodynamics, in which the constituent particles carry permanent stresses that stir the fluid. Activity introduces novel instabilities and many novel aspects emerge. Our works focus on the dynamics, order, fluctuations and instabilities in these systems. In particular, we investigated the dynamics, order and fluctuation properties emerging from effective hydrodynamic descriptions of translationally ordered active matter and also studied those in microwave-driven quantum Hall nematics. We also investigated the rheological properties of active suspensions subjected to an applied orienting field. A summary of the works carried out is as follows.
Translationally ordered active phases – active smectics and active cholesterics: Active or self-propelled particles consume and dissipate energy generating permanent stresses that stir the fluid around them. The collective behavior of systems of active particles, in systems with translational order, pose interesting questions and possibilities of new physics that differ strikingly from those in systems at thermal equilibrium with the same spatial symmetry. We developed the hydrodynamic equations of motion for (a) an active system with spontaneously broken translational symmetry in one direction, i.e., smectic and (b) the simplest uniaxially ordered phase of active chiral objects, namely, an active cholesteric. We analyze the fluctuation properties as well as the nature of characteristic instabilities that these systems can display and make a number of predictions. For example, in the case of an active smectic, we show that active stresses generate an effective active layer tension which, if positive, sup-presses the Landau-Peierls effect, leading to long-range smectic order in dimension d =3 and quasi-long-range in d =2, in sharp contrast with thermal equilibrium systems. Negative active layer tension in bulk systems, however, lead to a spontaneous Helfrich-Hurault undulation instability of the layers, accompanied by spontaneous flow. Also, active smectics, unlike orientationally ordered active systems, normally have finite concentration fluctuations. Similarly, for the case of cholesterics we show that cholesteric elasticity intervenes to suppress some of the instabilities present in active nematics.
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Numerical simulation of active smectics: We present results from a Brownian Dynamics simulation, with no hydrodynamic interaction, of a system of apolar active particles form-ing translational liquid-crystalline order in a suspension. The particles interact through a prolate-ellipsoidal Gay-Berne potential. We model activity minimally through different noise temperatures for movement along and normal to the orientation axis of each particle. We present preliminary results on the disruptive effect of activity on smectic order for the parameter values investigated. Future work will test the predictions of our theory [1] on active smectics.
Rheology of active suspensions near field-induced critical points : Shear induces orientation of active stresses in a suspension, through flow alignment. Depending on the sign, activity then either enhances or reduces the viscosity. The change in viscosity, in the zero frequency limit, is proportional to the product of the magnitude of active stress and the system relaxation time. A strong enough orienting field can make the system approach a critical point and the relaxation time diverges. We show that, this results in the divergence of viscosity at zero frequency making the system strongly viscoelastic. Depending on the sign, activity strengthens or reduces the effect of the field. We also investigate the rheological property of an active suspension with mixed polar and nematic oreder.
Active quantum Hall systems: We construct the hydrodynamic theory for a 2d charged active nematic with 3d electrostatics. We have investigated the interplay of the Coulomb interaction and activity in these systems. We show that activity competes to enhance the charge density fluctuations normally suppressed by long-ranged Coulomb interactions. The charge structure factor Sq of the corresponding passive charged nematic goes to zero as q, whereas in charged active nematics, activity leads to a nonvanishing charge structure factor at small wavenumber. We also show how the effect of an applied magnetic field can be incorporated into the dynamics of the system and leave scope for further studies on these effects.2016-04-25T18:30:00ZProlate Shaped Dark Matter Halo And The Galactic WarpRahul Nath, Rhttp://hdl.handle.net/2005/25222016-04-26T09:57:49Z2016-04-25T18:30:00ZTitle: Prolate Shaped Dark Matter Halo And The Galactic Warp
Authors: Rahul Nath, R
Abstract: The physical explanation for the existence of the galactic warp is one of the major research areas in Astronomy. People have proposed various theories but nobody has yet given a convincing explanation. Most of the spiral galaxies are observed to be warped which reveals that the galactic warp is a stable characteristic. In the theory of kinematic bending wave, warp is considered as a wave that is propagated through the galactic disk with a speed called pattern speed.
If the pattern initially had straight line of nodes, according to bending wave theory, the warp would tend to wind up rapidly in the gravitational field of galactic disk. But still we observe warped galaxies in the sky. In the literature, it has been claimed that the winding problem of galactic warp may be solved by incorporating the effect of gravitational field of the dark matter halo in which the galactic disk is embedded. Recently some works on the dynamics of galactic disk claim that the shape of the dark matter halo is pro late spheroid. In this thesis, the effect of the gravitational field of a prolate spheroidal dark matter halo with varying eccentricity to the galactic warp is calculated and discussed.
Chapter1 gives the general introduction of the topics discussed in the following chapters. The structure of the spiral galaxy, their classifications, and the disk dynamics are discussed in the first few sections. One of the revolutionary concepts that emerged in the previous century was the existence of the dark matter. Presently tracing the mass distribution and the constituent particles of dark matter is one of the major research areas in theoretical and experimental physics. In this thesis, the effect of a particular type of mass distribution in dark matter halo on the warp is discussed in detail.
In the next few sections, the following topics are discussed namely; how the concept of dark matter came into astrophysics, how to measure the total mass inside a given radius and what are the different distributions used for various purposes. A new theory called Modified Newtonian Mechanism was also proposed in the previous century as an alternative to the dark matter concept which is also discussed briefly. Kinematic bending wave theory and the winding problem of the galactic warp is also discussed in detail. In the last section a relation between the pattern speed of the warp and the shape of the dark matter halo is obtained.
The calculation of the potential of a prolate spheroidal mass distribution with varying eccentricity is not done in any literature as we know. The calculation of the potential and the patten speed of prolate spheroidal mass distributions and of the galactic disk are described in chapter 2. The calculations of oblate spheroidal mass distribution are also discussed in this chapter but that is out of main theme.
In chapter 3 we apply the equations obtained in the Chapter 2 to one simple toy model and to the Galaxy. The rotation curve and the pattern speed of a warp in the gravitational ﬁeld of prolate spheroidal mass distribution of varying eccentricity are described. Usually the Milky Way disk is treated as an in infinitesimally thin disk but for our calculations the three dimensional but thin disk is used. The usually people use some approximation to calculate the potential due to galactic infinitesimal thin disk. The difference of the work from earlier works done by different people(with the approximation mentioned in above line) is also discussed in this Chapter. Chapter 4 discusses the summary of the entire work.2016-04-25T18:30:00ZConfinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding SystemsNandi, Saroj Kumarhttp://hdl.handle.net/2005/25022016-02-17T11:38:05Z2016-02-16T18:30:00ZTitle: Confinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding Systems
Authors: Nandi, Saroj Kumar
Abstract: One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking.
Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion
of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis.
In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding.
In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters.
The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents.
In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases.
The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid.
When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials).
We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory.
In the final chapter, we summarize the problems studied in this thesis and point out some future directions.2016-02-16T18:30:00Z