Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas

Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states and use it to analyze fluctuations, stability, and phase transitions in these enigmatic finite momentum-paired superfluids. Focusing on the unidirectional LO pair-density wave state, that spontaneously breaks the continuous rotational and translational symmetries, we show that it is characterized by two Goldstone modes, corresponding to a superfluid phase and a smectic phonon. Because of the liquid-crystalline "softness" of the latter, at finite temperature the 3d state is characterized by a vanishing LO order parameter, quasi-Bragg peaks in the structure and momentum distribution functions, and a "charge"-4, paired Cooper-pairs, off-diagonal-long-range order, with a superfluid-stiffness anisotropy that diverges near a transition into a nonsuperfluid state. In addition to conventional integer vortices and dislocations the LO superfluid smectic exhibits composite half-integer vortex-dislocation defects. A proliferation of defects leads to a rich variety of descendant states, such as the "charge"-4 superfluid and Fermi-liquid nematics and topologically ordered nonsuperfluid states, that generically intervene between the LO state and the conventional superfluid and the polarized Fermi-liquid at low and high imbalance, respectively. The fermionic sector of the LO gapless superconductor is also quite unique, exhibiting a Fermi surface of Bogoliubov quasiparticles associated with the Andreev band of states, localized on the array of the LO domain-walls.Comment: 56 pages, 21 figure

Randomized algorithms for low-rank matrix approximation: Design, analysis, and applications

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the procedures via theoretical analyses and numerical studies to highlight how the best choice of algorithm depends on spectral properties of the matrix and the computational resources available. Despite superior performance for many problems, randomized block Krylov iteration has not been widely adopted in computational science. The paper strengthens the case for this method in three ways. First, it presents new pseudocode that can significantly reduce computational costs. Second, it provides a new analysis that yields simple, precise, and informative error bounds. Last, it showcases applications to challenging scientific problems, including principal component analysis for genetic data and spectral clustering for molecular dynamics data.Comment: 60 pages, 14 figure

2011 Nanoelectronic Devices for Defense & Security (NANO-DDS) Conference: A Request for Funding to Support Attendee Participation. To be held Aug. 29 to Sept 1, 2011 at NYU-POLY

Intellectual Merit: The Nanoelectronic Devices for Defense & Security (NANO-DDS) Conference is a bi-annual science and technology event which has been organized for the purpose of reviewing the evolving research and development (R&D) activities in the arena of nanoelectronic devices that have direct relevance to critical capability needs for national defense & security in the future. The charter of this special conference is to unify and focus the very broad array of nanoelectronic and supporting nanotechnology activities that are currently engaged in reaching the long expected applications payoffs in core defense and security related areas such as sensing, data processing, computation and communications. Broader Impacts: The inherent multidisciplinary nature of the nanoscale science & technology (Nano-S&T) field and the potential for impacting high priority objectives motivate the unique organization of this 2011 conference. The conference will support participation of many new faculty and graduate students

STRONGLY CORRELATED PHASES IN QUANTUM HALL SYSTEMS

Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena. In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of interaction strengths, the ν= 4 bulk is unpolarized whereas the ν= 3 bulk is fully polarized. In the parameter space spanned by the interaction strength and width of the interface, we find two phases at the interface. Phase A has spin as a good quantum number, and the long-wavelength spin edge excitations are gapped. In phase B, spin rotation symmetry is spontaneously broken at the mean-field level. Using symmetry arguments we find the effective theory near the interface of phase B. This effective theory is known to have gapless long-wavelength spin excitations. In the second project, we study the ground state of a tunnel-decoupled double-layer graphene system when both layers are undoped. We find a simple Hamiltonian in the continuum limit from symmetries of the system. Using the Hartree-Fock approximation we find a state with inter-layer coherence with broken layer U(1) symmetry. This phase becomes magnetized in presence of a non-zero Zeeman field. A first-order phase transition can be driven from the ferromagnetic phase to the magnetized inter-layer coherent phase by increasing the Zeeman field. We predict the number of gapless modes in the bulk

Quasiparticle Energy and Excitons in Two-Dimensional Structures

Two-dimensional materials, such as graphene-related structures, transition metal dichalcogenides, are attracting enormous interest in nowadays condensed matter physics. They not only serve as ideal testbeds for rich physics in reduced-dimensional electron systems but are also of particular importance in nanoelectronic technology. Their electronic, transport, and optical properties are largely determined by the nature of excited states, such as quasiparticles and excitons. Understanding how these excited states emerge from a many-electron system is an intriguing intellectual process, which gives insight into experimental observation and sheds light on manipulating the materials\u27 properties. From this aspect, it is highly desirable to introduce many-body perturbation theories, which do not rely on data from experiments, to study these excited-state properties and their relations to experimental measurements.In thisthesis, I will present a comprehensive study on a variety of two-dimensional materials using first-principles calculation with many-body effects taken into account. Particular attention is given to the impact of electrical gating, stacking order, and doping on the quasiparticle and excitonic properties

From graphene and topological insulators to Weyl semimetals

Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, sil- icene, germanene and others.We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the exis- tence of strictly two-dimensional, at crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and di erences between Dirac materials and optics are also discussed