Nandini Trivedi

Inhomogeneous pairing in highly disordered s -wave superconductors

We study a simple model of a two-dimensional s-wave superconductor in the presence of a random potential as a function of disorder strength. We first use the Bogoliubov--de Gennes (BdG) approach to show that, with increasing disorder, the pairing amplitude becomes spatially inhomogeneous, and the system cannot be described within conventional approaches for studying disordered superconductors that assume a uniform order parameter. In the high-disorder regime, we find that the system breaks up into superconducting islands, with large pairing amplitude, separated by an insulating sea. We show that this inhomogeneity has important implications for the physical properties of this system, such as superfluid density and the density of states. We find that a finite spectral gap persists in the density of states, even in the weak-coupling regime, for all values of disorder, and we provide a detailed understanding of this remarkable result. We next generalize Andersons idea of the pairing of exact eigenstates to include an inhomogeneous pairing amplitude, and show that it is able to qualitatively capture many of the nontrivial features of the full BdG analysis. Finally, we study the transition to a gapped insulating state driven by quantum phase fluctuations about the inhomogeneous superconducting state.

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity. The Hubbard model—a simplified representation of fermions moving on a periodic lattice—is thought to describe the essential details of copper oxide superconductivity. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realization of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realization of the three-dimensional Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques, particularly at metallic densities. We reach these low temperatures using a compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinant quantum Monte Carlo simulations and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for producing and characterizing other novel quantum states of matter, such as the pseudogap regime and correlated metallic states of the two-dimensional Hubbard model.

Single- and two-particle energy gaps across the disorder-driven superconductor–insulator transition

After decades of research, the microscopic details of the superconductor–insulator transition in two-dimensions, which is driven by the presence of disorder, are revealed by simulations. These include a phase transition from a gapped superconductor to a gapped insulator, for example.

Conductor--insulator quantum phase transitions

PART I: METAL-INSULATOR TRANSITIONS 1. Introduction to Metal-Insulator Transitions 2. Anderson Localisation 3. Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1??xMnxAs 4. Local approaches to strongly correlated disordered systems 5. Penultimate fate of a dirty-Fermi-liquid 6. Glassy dynamics of electrons near the metal-insulator transition 7. Phase Competition and Inhomogeneous States as a New Paradigm for Complex Materials 8. Numerical Studies of Metal-Insulator Transitions in Disordered Hubbard Models PART II: SUPERCONDUCTOR-INSULATOR TRANSITIONS 9. Superconductor-Insulator Transitions: Present Status and Open Questions 10. Scaling Analysis of Direct Superconductor-Insulator Transitions in Disordered Ultrathin Films of Metals 11. Spin Effects Near the Superconductor-Insulator Transition 12. Magnetic field-induced novel insulating phase in 2D superconductors 13. SITs in ultrathin a-Pb films: comparisons of disorder, magnetic field and magnetic impurity tuned 14. Evidence of Cooper Pairs on the Insulating Side of the SIT 15. Spectroscopic Imaging STM Studies of Electronic Structure in both the Superconducting and Pseudogap Phases of Underdoped Cuprates 16. Suppression of Tunneling of Superconducting Vortices Caused by a Remote Gate: Andersons orthogonality catastrophe and localization 17. Theoretical Studies of Superconductor-Insulator TransitionsIn this article we study superconductor-insulator transitions within the general framework of an attractive Hubbard model. This is a well-defined model of s-wave superconductivity which permits different tuning parameters (disorder and field). Furthermore, it allows a comparison of various analytical and computational approaches in order to gain a complete understanding of the various effects of amplitude and phase fluctuations. We present a systematic pedagogical approach, aiming to equip the lay reader with enough apparatus to be able to understand the numerical calculations, reproduce some of the simpler results, and be able to tackle future problems related to inhomogeneous phases. We go into considerable detail on mean-field theory (MFT) and the Bogoliubov-de Gennes (BdG) approach, as these are a first line of attack which can capture much of the physics, but we also outline cases where this fails to capture phase fluctuations and more sophisticated Quantum Monte Carlo (QMC) calculations are necessary. We discuss the behavior of many observables, including densities of states, superfluid stiffness, and dynamical conductivity, for the disorder-tuned superconductor-insulator transition. We also discuss SITs tuned by parallel magnetic field, which are quite different due to pairbreaking.

High Tc Superconductors: A Variational Theory of the Superconducting State

We use a variational approach to gain insight into the strongly correlated

Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model

d

DEVIATIONS FROM FERMI-LIQUID BEHAVIOR ABOVE TC IN 2D SHORT COHERENCE LENGTH SUPERCONDUCTORS

-wave superconducting state of the high

Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity.

{T}_{c}

Temperature-Induced Lifshitz Transition in WTe2.

cuprates at

The Higgs mode in disordered superconductors close to a quantum phase transition

T=0