Theses and Dissertations from UMD
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Item Phonon Transport and Nonequilibrium Kinetics with Stimulation Modeling in Molecular Crystals(2024) Liu, Zhiyu; Chung, Peter W.; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An important family of materials known as molecular crystals has been used extensively in fields such as organic semiconductors, energy, optoelectronics, and batteries. Due to their periodic crystal structure, phonons are the predominant heat and energy carriers. Phonons and their transport behaviors are crucial to the performance of semiconductors, the figure of merit of thermoelectrics, shock-induced properties of molecular crystals, and light-matter interactions of materials. Recent decades have seen significant advancements in the understanding of the phonon transport behaviors in inorganic crystals. However, a comprehensive understanding of phonon properties in molecular crystals is still lacking. While various theoretical models and computational simulations have been developed to study vibrational energy transfer in molecular crystals and to correlate vibrational structure with the stability of materials, these approaches often suffer from limitations. Many of these studies either neglect anharmonic scattering entirely or rely on simplified representations of phonon scattering. In this dissertation, we focus on investigating the phonon transport and nonequilibrium kinetics in molecular crystals. In the first work, we study the harmonic phonon properties of cellulose Iβ using tapered reactive force fields (ReaxFF). While geometry optimization with the original ReaxFF potential often results in structures with negative eigenvalues, indicating structural instability, the modified potential with a tapering function yields structures with no associated negative eigenvalues. Three ReaxFF parameterizations are evaluated by comparing lattice properties, elastic constants, phonon dispersion, temperature-dependent entropy, and heat capacity with experimental results from the literature. In the second study, we study the phonon transport behavior of Si, Cs2PbI2Cl2, cellulose Iβ, and α-RDX by calculating the thermal conductivity using different thermal transport models including the Phonon gas model, Cahill-Watson-Pohl, and the Allen-Feldman model and the Wigner formulation. By comparing the calculated thermal conductivity with experimental values, we highlight the significant contributions of wave-like heat carriers in cellulose Iβ and α-RDX. We show how different phonon properties influence particle-like and wave-like behavior in various materials and reveal unusual mechanisms present in molecular crystals. Lastly, we investigate nonequilibrium phonon kinetics resulting from direct vibrational excitations by employing the phonon Boltzmann transport equations. The results of our mid-IR pump-probe spectroscopy simulations align closely with experimental data from the literature. Additionally, by exciting different phonon modes at varying frequencies, we uncover distinct stages and pathways of vibrational energy transfer. To gain insights into the decomposition mechanism of RDX under excitation, we further calculate the bond activities of the N-N and N-O bonds, identifying possible stimuli that could trigger bond cleavage.Item Chiral light-matter interaction in fermionic quantum Hall systems(2024) Session, Deric Weston; Hafezi, Mohammad; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Achieving control over light-matter interactions is crucial for developing quantum technologies. This dissertation discusses two novel demonstrations where chiral light was used to control light-matter interaction in fermionic quantum Hall systems. In the first work, we demonstrated the transfer of orbital angular momentum from vortex light to itinerant electrons in quantum Hall graphene. In the latter, we demonstrated circular-polarization-dependent strong coupling in a 2D gas in the quantum Hall regime coupled to a microcavity. Our findings demonstrate the potential of chiral light to control light-matter interactions in quantum Hall systems. In the first part of this dissertation, we review our experimental demonstration of light-matter interaction beyond the dipole-approximation between electronic quantum Hall states and vortex light where the orbital angular momentum of light was transferred to electrons. Specifically, we identified a robust contribution to the radial photocurrent, in an annular graphene sample within the quantum Hall regime, that depends on the vorticity of light. This phenomenon can be interpreted as an optical pumping scheme, where the angular momentum of photons is transferred to electrons, generating a radial current, where the current direction is determined by the vorticity of the light. Our findings offer fundamental insights into the optical probing and manipulation of quantum coherence, with wide-ranging implications for advancing quantum coherent optoelectronics. In the second part of this dissertation, we review our experimental demonstration of a selective strong light-matter interaction by harnessing a 2D gas in the quantum Hall regime coupled to a microcavity. Specifically, we demonstrated circular-polarization dependence of the vacuum Rabi splitting, as a function of magnetic field and hole density. We provide a quantitative understanding of the phenomenon by modeling the coupling of optical transitions between Landau levels to the microcavity. This method introduces a control tool over the spin degree of freedom in polaritonic semiconductor systems, paving the way for new experimental possibilities in light-matter hybrids.Item EXPLORING QUANTUM MANY-BODY SYSTEMS IN PROGRAMMABLE TRAPPED ION QUANTUM SIMULATORS(2024) De, Arinjoy; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum simulation is perhaps the most natural application of a quantum computer, where a precisely controllable quantum system is designed to emulate a more complex or less accessible quantum system. Significant research efforts over the last decade have advanced quantum technology to the point where it is foreseeable to achieve `quantum advantage' over classical computers, to enable the exploration of complex phenomena in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. While the realization of a universal fault-tolerant quantum computer remains a future goal, analog quantum simulators -- featuring continuous unitary evolution of many-body Hamiltonians -- have been developed across several experimental platforms. A key challenge in this field is balancing the control of these systems with the need to scale them up to address more complex problems. Trapped-ion platforms, with exceptionally high levels of control enabled by laser-cooled and electromagnetically confined ions, and all-to-all entangling capabilities through precise control over their collective motional modes, have emerged as a strong candidate for quantum simulation and provide a promising avenue for scaling up the systems. In this dissertation, I present my research work, emphasizing both the scalability and controllability aspects of \ion based trapped-ion platforms, with an underlying theme of analog quantum simulation. The initial part of my research involves utilizing a trapped ion apparatus operating within a cryogenic vacuum environment, suitable for scaling up to hundreds of ions. We address various challenges associated with this approach, particularly the impact of mechanical vibrations originating from the cryostat, which can induce phase errors during coherent operations. Subsequently, we detail the implementation of a scheme to generate phase-stable spin-spin interactions that are robust to vibration noise. In the second part, we use a trapped-ion quantum simulator operating at room temperature, to investigate the non-equilibrium dynamics of critical fluctuations following a quantum quench to the critical point. Employing systems with up to 50 spins, we show that the amplitude and timescale of post-quench fluctuations scale with system size, exhibiting distinct universal critical exponents. While a generic quench can lead to thermal critical behavior, a second quench from one critical state to another (i.e., double quench) results in unique critical behavior not seen in equilibrium. Our results highlight the potential of quantum simulators to explore universal scaling beyond the equilibrium paradigm. In the final part of the thesis, we investigate an analog of the paradigmatic string-breaking phenomena using a quantum spin simulator. We employ an integrated trapped-ion apparatus with $13$ spins that utilizes the individual controllability of laser beams to program a uniform spin-spin interaction profile across the chain, alongside 3-dimensional control of the local magnetic fields. We introduce two static probe charges, realized through local longitudinal magnetic fields, that create string tension. By implementing quantum quenches across the string-breaking point, we monitor non-equilibrium charge evolution with spatio-temporal resolution that elucidates the dynamical string breaking. Furthermore, by initializing the charges away from the string boundary, we generate isolated charges and observe localization effects that arise from the interplay between confinement and lattice effects.Item TOWARDS FULLY AUTOMATED ENHANCED SAMPLING OF NUCLEATION WITH MACHINE-LEARNING METHODS(2024) Zou, Ziyue; Tiwary, Pratyush; Chemistry; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Molecular dynamics (MD) simulation has become a powerful tool to model complex molecular dynamics in physics, materials science, biology, and many other fields of study as it is advantageous in providing temporal and spatial resolutions. However, phenomena of common research interest are often considered rare events, such as nucleation, protein conformational changes, and ligand binding, which occur on timescales far beyond what brute-force all-atom MD simulations can achieve within practical computer time. This makes MD simulation difficult for studying the thermodynamics and kinetics of rare events. Therefore, it is a common practice to employ enhanced sampling techniques to accelerate the sampling of rare events. Many of these methods require performing dimensionality reduction from atomic coordinates to a low-dimensional representation that captures the key information needed to describe such transitions. To better understand the current challenges in studying crystal nucleation with computer simulations, the goal is to first apply developed dimensionality reduction methods to such systems. Here, I will present two studies on applying different machine learning (ML) methods to the study of crystal nucleation under different conditions, i.e., in vacuum and in solution. I investigated how such meaningful low-dimensional representations, termed reaction coordinates (RCs), were constructed as linear or non-linear combinations of features. Using these representations along with enhanced sampling methods, I achieved robust state-to-state back-and-forth transitions. In particular, I focused on the case of urea molecules, a small molecule composed of 8 atoms, which can be easily sampled and is commonly used in daily practice as fertilizer in agriculture and as a nitrogen source in organic synthesis. I then analyzed my samples and benchmarked them against other experimental and computational studies. Given the challenges in studying crystal nucleation using molecular dynamics simulations, I aim to introduce new methods to facilitate research in this field. In the second half of the dissertation, I focused on presenting novel methods to learn low-dimensional representations directly from atomic coordinates without the aid of a priori known features, utilizing advanced machine learning techniques. To test my methods, I applied them to several representative model systems, including Lennard Jones 7 clusters, alanine dipeptide, and alanine tetrapeptide. The first system is known for its well-documented dynamics in colloidal rearrangements relevant to materials science studies, while the latter two systems represent problems related to conformational changes in biophysical studies. Beyond model systems, I also applied my methods to more complex physical systems in the field of materials science, specifically iron atoms and glycine molecules. Notably, the enhanced sampling method integrated with my approaches successfully sampled robust state-to-state transitions between allotropes of iron and polymorphs of glycine.Item NOVEL QUASI-FREESTANDING EPITAXIAL GRAPHENE ELECTRON SOURCE HETEROSTRUCTURES FOR X-RAY GENERATION(2024) Lewis, Daniel; Daniels, Kevin M; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Graphene, the 2D allotrope of carbon, boasts numerous exceptional qualities like strength, flexibility, and conductivity unmatched for its scale, and amongst its lesser-known capabilities is electron emission at temperatures and electric fields too low to allow for conventional thermionic or field emission sources to function. Driven by the mechanism of Phonon-Assisted Electron Emission (PAEE), planar microstructures fabricated from quasi-freestanding epitaxial graphene (QEG) on silicon carbide have exhibited emission currents of up to 8.5 μA at temperatures and applied fields as low as 200 C and 1 kV/cm, orders of magnitude below conventional electron source requirements.These emission properties can be influenced through variations in microstructure design morphology, and performance is controllable via device temperature and applied field in the same manner as thermionic or field emission sources. As 2D planar devices, graphene microstructure electron emitters can also be encapsulated with a thermally evaporated oxide, granting electrical isolation and environmental resistance, and can even exhibit emission current enhancement under these conditions. Graphene electron emitters expressed as heterostructure material stacks could see implementation as electron emission sources in environments or devices where conventional thermionic or field emission sources can’t be supported due to thermal, power system, or physical size limitations, the presence of contaminants, or even poor vacuum containment. An explorable application could see an oxide-encapsulated graphene electron source paired with a layered interaction-emission anode to create a micron-scale vertical alignment x-ray source with no need of vacuum containment. We investigate these properties with using hydrogen-intercalated quasi-freestanding bilayer epitaxial graphene, a rare and difficult to manufacture formulation that allows the graphene to behave as if it were a freestanding structure, while still benefiting from the macro-scale mechanical strength and fabrication process compatibility afforded by its silicon carbide substrate. The quasi-freestanding nature of the graphene limits substrate phonon interactions, allowing the graphene phonon-electron interactions to dominate, in turn empowering the PAEE mechanic. Our devices benefit from an ease of interaction that is untenable for processes not employing QEG, with the speed and simplicity of fabrication being a hallmark of our investigations. We begin our exploration of how the PAEE mechanism itself can be influenced in our designs, and how process and fabrication optimizations can be leveraged for device applications. Graphene’s role in the fields of microelectronics, condensed matter physics, and materials science is still novel, and rapidly expanding, and our investigations explore a unique facet of this wonder material’s capabilities.Item CHARGE ORDER AND STRUCTURAL TRANSITION IN TOPOLOGICAL SEMIMETAL FAMILY AAL4(2023) Saraf, Prathum; Paglione, Johnpierre; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The BaAl$_4$-type structure hosts a variety of interesting and exotic properties, with descendant crystal structure resulting numerous interesting ground states of matter including magnetic, super-conducting and strongly correlated electron phenomena. BaAl$_4$ itself has recently been shown to host a non-trivial topological band structure, but is otherwise a paramagnetic metal. However, the other members of the 1-4 family, such as SrAl$_4$ and EuAl$_4$, exhibit symmetry-breaking ground states including charge density wave (CDW) and magnetic order, respectively. SrAl$_4$ hosts a second transition at 94K that is hysteretic in temperature and is a structural transition to a monoclinic structure. Here I report on the charge density wave in SrAl$_4$ and the effect of the structural transition on the physical and electronic properties of the material. The structural transition is extremely subtle with deviation of around 0.5 degrees from the tetragonal structure but shows significant changes in resistivity, Hall and magnetic susceptibility measurements. This transition is extremely sensitive to disorder and can be suppressed completely by substituting 1$\%$ Ba nominally or using less pure Sr during crystal growth. Furthermore, magnetoresistance in this material is extremely large, and can be up to 140 times at 2K. A combination of magnetoresistance and Hall measurements are used to fit the data to a two band model to extract carrier density and mobility of the charge carriers at 2K. Finally, work was done on the evolution of the charge-ordered state in high quality single crystals of the solid solution series Ba$_{1-x}$Sr$_x$Al$_4$, using transport, thermodynamic and scattering experiments to track the 243 K CDW order in SrAl$_4$ as it is suppressed with Ba substitution until its demise at x =0.5. Neutron and x-ray diffraction measurements reveal a nearly commensurate CDW state in SrAl$_4$ with ordering vector (0,0,0.097) that evolves with Ba substitution to (0,0,0.18) and (0,0,0.21) for x=0.8 and x=0.55, respectively. DFT calculations show a softening of phonons in SrAl$_4$ hinting at electron phonon coupling strength being the source of the charge order in this material. Similar calculations are done on the Ba substitutions to investigate the nature of the charge density waves. With very little change in the lattice parameters in this series, this evolution raises important questions about the nature of the electronic structure that directs a dramatic change in charge ordering.Item Tight-binding simulations of random alloy and strong spin-orbit effects in InAs/GaBiAs quantum dot molecules(2023) Lin, Arthur; Bryant, Garnett W; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Self-assembled \ce{InAs} quantum dots (QDs), which have long hole-spin coherence times and are amenable to optical control schemes, have long been explored as building blocks for qubit architectures. One such design consists of vertically stacking two QDs to create a quantum dot molecule (QDM). The two dots can be resonantly tuned to form "molecule-like" coupled hole states with the hybridization of hole states otherwise localized in each respective dot. Furthermore, spin-mixing of the hybridized states in dots offset along their stacking direction enables qubit rotation to be driven optically, allowing for an all-optical qubit control scheme. Increasing the magnitude of this spin-mixing is important for optical quantum control protocols. We introduce the incorporation of dilute \ce{GaBi_xAs_{1-x}} alloys in the barrier region between the two dots, as \ce{GaBiAs} is expected to provide an increase in spin-mixing of the molecular states over \ce{GaAs}. Using an atomistic tight-binding model, we compute the properties of \ce{GaBi_xAs_{1-x}} and the modification of hole states that arise when the alloy is used in the barrier of an \ce{InAs} QDM. We show that an atomistic treatment is necessary to correctly capture non-traditional alloy effects of \ce{GaBiAs}. Additionally, an atomistic model allows for the study of configurational variances and clustering effects of the alloy. We find that in \ce{InAs} QDMs with a \ce{GaBiAs} inter-dot barrier, hole states are well confined to the dots up to an alloy concentration of 7\%. By independently studying the alloy-induced strain and electronic scattering off \ce{Bi} and As orbitals, we conclude that an initial increase in QDM hole state energy at low Bi concentration is caused by the alloy-induced strain. Additionally, a comparison between the fully alloyed barrier and a partially alloyed barrier shows that fully alloying the barrier applies an asymmetric strain between the top and bottom dot. By lowering the energetic barrier between the two dots, \ce{GaBiAs} is able to promote the tunnel coupling of hole states in QDMs. We obtain a three fold increase of hole tunnel coupling strength in the presence of a 7\% alloy. Additionally, we show how an asymmetric strain between the two dots caused by the alloy results in a shift in the field strength needed to bring the dots to resonance. We explore different geometries of QDMs to optimize the tunnel coupling enhancement the alloy can provide, as well as present evidence that the change in tunnel coupling may affect the heavy-hole and light-hole components of the ground state in a QDM. The strong spin-orbit coupling strength of \ce{GaBiAs} allows for the enhancement of spin-mixing in QDMs. A strong magnetic field can be applied directly in the TB Hamiltonian. In order to fit the TB results to a simple phenomenological Hamiltonian, we found it necessary to include second order magnetic field terms in the phenomenological Hamiltonian as a diamagnetic correction to the hole state energies. Fitting to the corrected phenomenological model, we obtain a three-fold enhancement for the spin-mixing strength of offset dots at 7\% \ce{Bi}. Additionally, at higher alloy concentrations, a combination of enhanced spin-mixing and increase resonance change in g-factor results in intra-dot spin-mixing between Zeeman split states of the lower energy dot. A perturbative analysis of the magnetic field shows that both the spin-mixing and resonance g-factor change are effects of the Peierls contribution, or the component of the magnetic field applied to the effective spatial angular momentum of the wavefunction. When spin-orbit coupling is removed from the system, there is no longer a preferred alignment between the spin of the system and the Peierls effective angular momentum, thus removing any magnetic field effects of the Peierls contribution. The analysis of spin-orbit effects can be extended to single dots with in-plane magnetic and electric fields. This thesis concludes with some preliminary results utilizing electric fields, in conjunction with spin-locking effects provided by spin-orbit coupling, to manipulate the spin polarization in single dots. TB calculations with a magnetic field are performed to show the preferred alignment of the effective angular momentum, given by the geometry of the dot, also spatially locks the spin-polarization of hole states. An electric field can then be applied to bias the charge density to either side of the dot, using the spatial texture of the spin to obtain a spin polarized in $z$ while both the magnetic and electric field is in the $xy$-plane. The same perturbative analysis with the QDMs can be applied to show sufficient spin-orbit coupling is needed to generate such an effect. We propose the utilization of spin texture and electric fields as a novel method for rotating the spin in QDs.Item THE EFFICIENT CONTROL OF TWO-DIMENSIONAL MAGNETISM BY MULTIPLE EXTERNAL STIMULI(2023) Xie, Ti; Gong, Cheng; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Magnetism has played a crucial role in both fundamental research and technological advancement, from ancient compasses to modern spintronics. With the advent of artificial intelligence and the increasing demand for high-volume data storage, there have been significant efforts to reduce the dimensionality of memory materials. Recently, the discovery of two-dimensional magnetic van der Waals materials has enabled the observation of long-range magnetic order in monolayer crystals, which exhibit high sensitivity to external stimuli such as optical incidence, mechanical strain, and chemical functionalization. Our systematic work focuses on the efficient control of two-dimensional magnetism through multiple external stimuli, including chemical, optical, electrical, and mechanical means. These works achieved the effective control of a wide range of magnetic properties of two-dimensional magnets, such as Curie temperatures, magnetic coercivities, domain profiles, and magnetic phases. These research achievements will provide valuable insights into the fundamentals of two-dimensional magnetism and its interplay with external stimuli, paving the way for advancing the nanoscale spintronic and photonic devices in ultrathin platforms.Item TUNNELING PROPERTIES AND ELECTROMAGNETIC RESPONSE IN IRON BASED SUPERCONDUCTORS AND OTHER SYSTEMS(2023) Barik, Tamoghna; Sau, Jay JS; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An iron-based chalcogenide compound, $\text{FeTe}_{1-x}\text{Se}_{x}$ (FTS), has recently attracted attention as a potential candidate for a readily available platform for hosting the exotic topological superconducting (TSC) phase on its surface. In its 3D sample the co-existence of the strong topological insulating (TI) phase and cylindrical Fermi sheets provide the two necessary ingredients for the TSC phase on its surface - i) the topologically protected helical surface states and ii) the intrinsically induced s-wave pairing from the bulk superconductivity. The strong TI phase in the FTS alloy is crucially dependent on the relative composition ratio between Te and Se atoms. The topological FTS sample, $\text{FeTe}_{.55}\text{Se}_{.45}$, that is widely studied for having the highest critical temperature ($T_c$) in this class, interestingly, lies close to the topological-trivial phase boundary (estimated to be close to $x=.5$ as observed by a recent experiment \cite{Brookhaven}). Furthermore, due to its alloy nature a typical sample of FTS suffers from spatial inhomogeneity in Te/Se composition at multiple length scales ranging from few nm to 100 $\mu \text{m}$. Thus, in a topological FTS sample there might be patches where the phase is driven out of its topological natures due to the local deficit of Te composition induced by Te/Se fluctuations. Such trivial domains would be scattered throughout the sample - hence, we call such a phase a topological domain disordered phase. The trivial domains in such a disordered sample would inflict inhomogeneity in the topological surface state (TSS) density distribution which we study in Chapter \ref{chap:chapter_2} of this thesis. After carefully exploring the effects of topological domain disordered phase in an effective model of FTS, we conclude that the non-topological domains on the surface are characterized by suppressed local density of states (LDOS) surrounded by ridges of enhanced LDOS throughout the energy range of the Dirac dispersion of the TSS. Moreover, the appropriately scaled LDOS at various energies within the Dirac window collapse on each other for a given disordered sample which, as we show, is in stark contrast to the case of conventional chemical potential disorder. Hence, these features are expected to appear in measurements of tunneling conductance such as in scanning tunneling spectroscopy (STS) of the FTS surface when the sample is not in the superconducting phase. Another kind of exotic modes, namely the helical Majorana modes, appear in the 2D TSC phase at a linear defect when the TSC gap on either side differs by a phase difference of $\pi$ from the other side - thus, forming a $\pi$ shifted Josephson junction (JJ) on the TSC surface. Signatures of such helical Majorana modes have been observed by a recent tunneling experiment on the surface of FTS. In FTS such signatures are characterized by the non-zero flat density of states (DOS) in an STS measurement at a crystalline domain wall (DW) which is associated with the in-plane half-unit-cell-shift (HUCS) of the lattice. Such non-zero flat DOS within the SC gap which is consistent with the existence of linearly dispersing 1D modes is absent in the non-topological $\text{FeSe}$ sample - hinting towards the topological origin of the same in FTS. Even though the TSC phase on the surface is expected in FTS, the origin of a $\pi$ shifted order parameter that is crucial to accommodate the helical Majorana modes at the DW, is yet to be fully understood. In chapter \ref{chap:chapter_3} of this thesis we propose a mechanism that stabilizes a $\pi$-junction at the HUCS domain wall when the intrinsic superconducting pairing is of $s_{\pm}$ character as is the case for bulk FTS superconductivity that consists of hole-like pockets around $\Gamma$ and electron-like pockets around $M$ point of the Brillouin zone (BZ). We argue that if the DW induces inter-pocket transmission between the $\Gamma$ and $M$ pockets strongly enough, the coupling between the order parameters (OPs) of the two pockets ($\Gamma$ and $M$) is also enhanced. Since the $s_{\pm}$ nature of the pairing implies an intrinsic $\pi$-phase difference between the OPs associated with the $\Gamma$ and $M$ pockets, strong DW-induced coupling between them can stabilize a Josephson junction with $\pi$-phase shift. We explore the possibility of such $\pi$-junction in FTS by constructing an effective model of the Fermi surface of FTS and computing the Bogoliubov-de-Gennes (BdG) spectrum with $s_{\pm}$ pairing at the HUCS DW. Varying our model parameters within the regime of the observed FTS Fermi surface we find that for a wide range of parameters the $\pi$-junction accommodates Andreev bound states (ABSs) that have lower occupied energies than those for trivial 0-phase shifted junction. Simultaneous numerical computation of the DW-induced scattering problem reveals that the strong inter-pocket transmission strength is positively correlated with the stability of the $\pi$-junction, supporting our proposed mechanism for the $\pi$-junction stability as described earlier. Such $\pi$-Josephson junctions can in principle be detected using superconducting quantum interference device (SQUID) using either a mesoscopic device or corner junction. In the next chapter \ref{chap:chapter_4} of the thesis we consider another setup of Josephson junction (JJ) consisting of an interacting one-dimensional quantum wire sandwiched between two semi-infinite SC leads of conventional s-wave pairing. The low energy Physics of such interacting 1D system which is known as Luttinger liquid (LL) is controlled by the two decoupled sets of eigen modes - namely, the charge and spin density waves. The SC leads in such a JJ thus allow easy access to the charge degrees of freedom in the LL - also known as plasmons which can also be probed optically using near field optical microscopy \cite{Wang2015,Wang2020}. An interesting aspect of an S-LL-S setup is that the NS interface blocks the flow of spin current due to the perfect Andreev reflection at low energies. Hence, the spin modes of the LL would typically be obscure to a transport measurement due to the aforementioned spin-charge decoupling. Hence, a conductivity measurement would not be able to detect the spin degrees of freedom if they are separated from the charge modes. However, we note that the impurity induced back-scattering processes which involve low energy but large momentum transfer can couple the spin and charge densities in the LL and we study the signatures of such spin-charge coupling in the electromagnetic (EM) response measurements. In our numerical evaluation which incorporates the impurity potential perturbatively and we calculate the resultant EM absorption spectrum using linear response theory which is measurable in a similar S-LL-S setup. We find that the signatures of back-scattering induced spin-charge coupling appear in the absorption spectrum as excitation peaks at the energies that are associated with the spin excitations of the LL. Tuning the total density of the 1D system and hence the Fermi momentum we find a regime where the spin peaks are roughly of equal amplitude as that of the charge peaks. Since in a 1D wire the density can be tuned by means of gating \cite{Wang2020}, such regime is accessible to a transport measurement. In that regime tuning the Coulomb interaction strength one can distinguish the charge peaks as they shift on the energy axis whereas the spin peaks are insensitive to such interaction strength variation. We conclude that such impurity induced signatures of spin modes can thus be probed in an S-LL-S setup by investigating the EM response of the sample in a conductivity measurement. In the last chapter \ref{chap:chapter_5} of the thesis we go beyond the regime of linear response formalism that is discussed in relation to the EM response of the S-LL-S setup in the previous paragraph and consider the optical response up to second order in the applied EM field. A fundamental feature of non-linear response is its non-equilibrium nature which is absent in linear responses. Such non-equilibrium character is manifested as the out-of-time-ordered correlators (OTOC) in response theory associated with the second power of the applied EM field magnitude. Such correlators for a generic interacting system cannot be described using the standard Feynman diagrams, rather one requires its non-equilibrium extension which is known as the Keldysh formalism. We focus on this non-equilibrium nature of the response by considering the bulk photovoltaic effect (BPVE) in a non-centrosymmetric system where we include electron-phonon (e-ph) coupling as the mode of relaxation. Considering the semi classical limit where the e-ph scattering is stronger than the applied field strength we show how the contribution of the OTOC appears in the BPVE induced DC current measurement when the system is illuminated by an inhomogeneous profile of optical intensity similar to the case of a irradiation on a finite portion of the sample. We also introduce the Floquet master equation approach to treat the e-ph coupling quantum mechanically and demonstrate a shift in the scaling of the DC response from quadratic to linear in the limit of the e-ph coupling strength being much smaller than the applied EM field.Item CLASSIFICATION AND CHARACTERIZATION OF CRYSTALLINE TOPOLOGICAL INVARIANTS IN QUANTUM MANY-BODY STATES(2023) Manjunath, Naren; Barkeshli, Maissam; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The theory of topological phases of matter, now a major direction in condensed matter physics, is framed around two complementary problems. The first is to mathematically classify topological states of matter given various symmetries, in terms of suitable topological invariants. The second is to characterize a given state by numerically or experimentally extracting the topological invariants associated with it. Although remarkable progress has been made for topological states with internal symmetries, major open questions remain in the case of many-body systems with crystalline symmetries, especially those with a nonzero Chern number and a magnetic field. The first part of this thesis develops a theory of crystalline topological response in (2+1) dimensions based on the idea of crystalline gauge fields and their effective actions, which we derive using topological quantum field theory. We use this to obtain a complete classification of topological states with $\U(1)$ charge conservation, discrete magnetic translation, and point group rotation symmetries, finding several new invariants. We separately consider symmetry-enriched topological states of bosons, which admit anyonic excitations with fractional statistics, and invertible fermionic states, which do not. The second part of this thesis focusses on numerically extracting these invariants from many-body invertible states. First we study two quantized invariants, the discrete shift, and a charge polarization which is quantized by rotational symmetries. We show how to extract these invariants in multiple different ways, which include the fractional charge bound to lattice defects, as well as the angular and linear momentum of magnetic flux. Thereafter, we obtain a \textit{complete} characterization of the theoretically predicted invariants, by studying the expectation value of the ground state under partial rotation operators. An immediate application of these ideas is to fully characterize the celebrated Hofstadter model of spinless free fermions on a square lattice. Although the Chern number and filling were first computed in this model in 1982, our theory predicts seven nontrivial invariants, including four new invariants which depend on the crystalline symmetry. We compute these numerically and obtain several additional colorings of Hofstadter's butterfly.