(PHD, 2021)

Abstract:

This thesis presents studies of different schemes to probe and manipulate quantum matter using light with an aim to discover novel routes to efficiently control the properties of quantum materials. A special focus is placed on developing new schemes utilizing light-matter interactions (1) to modify exchange interactions in magnetic insulators, and (2) to probe and modify band topology in quantum matter.

In part II, new schemes are presented to probe local band topology of Bloch bands. First, we study the effects of time-dependent band topology on adiabatic evolution of a Bloch wavepacket. We find that it results in an electric-field analog in semi-classical equation of motion, and can be demonstrated in a honeycomb lattice by varying the sublattice offset energy. We then extend these methods to include non-adiabatic processes, and found interesting connections between the anomalous drift during band excitation and a quantum geometric quantity known as shift-vector. We generalize the concept of shift-vector to include different kinds of band transition protocols beyond light-induced dipole transitions. The idea of electric-field analog and the shift-vector are then combined to develop a novel charge pumping scheme. Motivated by these interesting consequences of band topology in non-adiabatic processes, we study shift-current response in moiré materials, and find that the highly topological nature of flat bands along with their very large unit cells significantly enhances these shift-vector related effects. This response also displays a strong dependence on interaction-induced changes in the band structure and quantum geometric quantities. These results suggest that shift-current response can possibly serve as a very reliable probe for interactions in twisted bilayer graphene. In addition to studying consequences of band topology on single-particle transport, we also consider Berry curvature effects on exciton transport. We find that the non-trivial band topology of underlying electron and hole bands allows us to manipulate excitons with a uniform electric field. We examine the conditions necessary to observe such transport and propose that transition metal dichalcogenide heterobilayers with moiré structure can prove an ideal platform for these effects.

In part III, we propose novel drive protocols based on manipulating orbital and lattice degrees of freedom in quantum materials with light. We found that light induced changes in orbital hybridization and their electronic energies results in a significant change in exchange interactions in quantum magnets. We also accounted for the role of ligands in periodically driven quantum magnets, and found that the predictions made by the minimal model based on direct-hopping can be wrong in certain regimes of drive parameters. This understanding of light induced modifications in ligand-mediated exchange interactions was used to explain the phase shift observed in coherent phonon oscillations of CrSiTe₃ upon the onset of short-range spin correlations. We also demonstrate that light induced coherent lattice vibrations can provide a new route to realize space-time symmetry protected topological phases. Our results suggest that manipulating additional degrees of freedom (not included in commonly employed minimal models of periodically driven systems) with light can provide novel routes for ultrafast control of quantum materials.

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(PHD, 2019)

Abstract:

This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.

In Part I we first give a new algorithm for simulating the dynamics of one-dimensional systems that thermalize (that is, come to local thermal equilibrium). The core of this algorithm is a new truncation for matrix product operators, which reproduces local properties faithfully without reproducing non-local properties (e.g. the information required for OTOCs). To the extent that the dynamics depends only on local operators, timesteps interleaved with this truncation will reproduce that dynamics.

We then apply this to algorithm to Floquet systems: first to clean, non-integrable systems with a high-frequency drive, where we find that the system is well-described by a natural diffusive phenomenology; and then to disordered systems with low-frequency drive, which display diffusion — not subdiffusion — at appreciable disorder strengths.

In Part II, we study the utility of many-body localization as a medium for a thermodynamic engine. We first construct a small (“mesoscale”) engine that gives work at high efficiency in the adiabatic limit, and show that thanks to the slow spread of information in many body localized systems, these mesoscale engines can be chained together without specially engineered insulation. Our construction takes advantage of precisely the fact that MBL systems do *not* thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.

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(PHD, 2018)

Abstract:

Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of *engineering* new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature.

In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the “Floquet insulator.” We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term “near-integrability.” These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a “dual” interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.

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(PHD, 2016)

Abstract:

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in *all* the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner’s Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

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(PHD, 2014)

Abstract: We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi_{2}Se_{3} and Bi_{2}Te_{3} exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green’s function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.

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(PHD, 2013)

Abstract:

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

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(PHD, 2011)

Abstract: The study of various quantum phases and the phase transitions between them in low-dimensional disordered systems has been a central theme of recent developments of condensed matter physics. Examples include disordered thin film superconductors, whose critical temperature and density of states can be affected by a normal metallic layer deposited on top of them; amorphous thin films exhibiting superconductor-insulator transitions (SIT) tuned by disorder or magnetic field; and bilayer two-dimensional electron systems at total filling factor ν=1, which exhibit interlayer coherent quantum Hall state at small layer separation and have a phase transition tuned by layer separation, parallel magnetic field, density imbalance, or temperature. Although a lot of theoretical and experimental investigations have been done, many properties of these phases and natures of the phase transitions in these systems are still being debated. Here in this thesis, we report our progress towards a better understanding of these systems. For disordered thin film superconductors, we first propose that the experimentally observed lower-than-theory gap-T_{c} ratio in bilayer superconducting-normal-metal films is due to inhomogeneous couplings. Next, for films demonstrating superconductor-insulator transitions, we propose a new type of experiment, namely the drag resistance measurement, as a method capable of pointing to the correct theory among major candidates such as the quantum vortex picture and the percolation picture. For bilayer two-dimensional electron systems, we propose that a first-order phase transition scenario and the resulting Clausius-Clapeyron equations can describe various transitions observed in experiments quite well. Finally, in one-dimensional optical lattices, we show that one can engineer the long-sought-after random hopping model with only off-diagonal disorder by fast-modulating an Anderson insulator.

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