Amit Ghosal

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.

Correlation-induced inhomogeneity in circular quantum dots

Properties of the ‘electron gas’—in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected—change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood1. For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner crystal phase. The physics at intermediate densities, however, remains a subject of fundamental research2,3,4,5,6,7,8. Here, we study the intermediate-density electron gas confined to a circular disc, where the degree of confinement can be tuned to control the density. Using accurate quantum Monte Carlo techniques9, we show that the electron–electron correlation induced by an increase of the interaction first smoothly causes rings, and then angular modulation, without any signature of a sharp transition in this density range. This suggests that inhomogeneities in a confined system, which exist even without interactions, are significantly enhanced by correlations.

Competing ferromagnetism in high-temperature copper oxide superconductors.

The extreme variability of observables across the phase diagram of the cuprate high-temperature superconductors has remained a profound mystery, with no convincing explanation for the superconducting dome. Although much attention has been paid to the underdoped regime of the hole-doped cuprates because of its proximity to a complex Mott insulating phase, little attention has been paid to the overdoped regime. Experiments are beginning to reveal that the phenomenology of the overdoped regime is just as puzzling. For example, the electrons appear to form a Landau Fermi liquid, but this interpretation is problematic; any trace of Mott phenomena, as signified by incommensurate antiferromagnetic fluctuations, is absent, and the uniform spin susceptibility shows a ferromagnetic upturn. Here, we show and justify that many of these puzzles can be resolved if we assume that competing ferromagnetic fluctuations are simultaneously present with superconductivity, and the termination of the superconducting dome in the overdoped regime marks a quantum critical point beyond which there should be a genuine ferromagnetic phase at zero temperature. We propose experiments and make predictions to test our theory and suggest that an effort must be mounted to elucidate the nature of the overdoped regime, if the problem of high-temperature superconductivity is to be solved. Our approach places competing order as the root of the complexity of the cuprate phase diagram.

Interaction-induced strong localization in quantum dots

We argue that Coulomb blockade phenomena are a useful probe of the crossover to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to

Diamagnetism of nodal fermions

{r}_{s}\ensuremath{\sim}55

Antiferromagnetism and charged vortices in high- T c superconductors

), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This crossover (which occurs near

Interaction Effects in the Mesoscopic Regime: A Quantum Monte Carlo Study of Irregular Quantum Dots

{r}_{s}\ensuremath{\sim}20

Magnetic field induced emergent inhomogeneity in a superconducting film with weak and homogeneous disorder

for spin-polarized electrons) is, then, a signature of interaction-driven localization. As the addition energy is directly measurable in Coulomb blockade conductance experiments, this provides a direct probe of localization in the low density electron gas.

Effects of strong disorder in strongly correlated superconductors

Free nodal fermionic excitations are simple but interesting examples of fermionic quantum criticality, in which the dynamic critical exponent

Modulation of the local density of states within the d -density wave theory of the underdoped cuprates

z=1