Local Density of States of a Three-Dimensional Conductor in the Extreme Quantum Limit

Physical properties of a single vortex in d-wave superconductors are studied theoretically. After a brief review on a single vortex in "conventional" s-wave superconductors and the d-wave superconductivity underlying the hole-doped high-T c cuprates, we go on to study the quasiparticle spectrum around a single vortex in the high-T c superconductors. One of the characteristics of the high-T c superconductors is that they are close to the "quantum limit" (pFξ ~ O(1)). A new picture emerges of the quasiparticle spectrum. Instead of thousands of bound states in a "conventional" s-wave superconductor, we find only a few peaks in the local density of states at the vortex center. Further there are low-lying excitations stretched in four diagonal directions and they have no counterpart in s-wave superconductors.

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Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09375-5 ◽

2021 ◽

Vol 24 (1) ◽

Author(s):

Luca Fresta

Keyword(s):

Density Of States ◽

Local Density ◽

Schrödinger Operators ◽

Random Schrödinger Operators ◽

Schrodinger Operators ◽

Local Density Of States ◽

Weak Disorder ◽

Cluster Expansions ◽

Strong Disorder ◽

Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

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Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model

Nanomaterials ◽

10.3390/nano11040998 ◽

2021 ◽

Vol 11 (4) ◽

pp. 998

Author(s):

Diego R. Abujetas ◽

José A. Sánchez-Gil

Keyword(s):

Magnetic Dipole ◽

Density Of States ◽

Bound States ◽

Local Density ◽

Near Field ◽

Field Pattern ◽

Local Density Of States ◽

Optical Modes ◽

Source Excitation ◽

The Continuum

Resonant optical modes arising in all-dielectric metasurfaces have attracted much attention in recent years, especially when so-called bound states in the continuum (BICs) with diverging lifetimes are supported. With the aim of studying theoretically the emergence of BICs, we extend a coupled electric and magnetic dipole analytical formulation to deal with the proper metasurface Green function for the infinite lattice. Thereby, we show how to excite metasurface BICs, being able to address their near-field pattern through point-source excitation and their local density of states. We apply this formulation to fully characterize symmetry-protected BICs arising in all-dielectric metasurfaces made of Si nanospheres, revealing their near-field pattern and local density of states, and, thus, the mechanisms precluding their radiation into the continuum. This formulation provides, in turn, an insightful and fast tool to characterize BICs (and any other leaky/guided mode) near fields in all-dielectric (and also plasmonic) metasurfaces, which might be especially useful for the design of planar nanophotonic devices based on such resonant modes.

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