{
  "annotation_id": "19a91e95-9934-484d-958b-3a94d565eb12",
  "date_created": "2026-02-17T05:53:23.732000Z",
  "date_modified": "2026-02-17T05:53:23.732000Z",
  "file_hash": "959f132a6cb53860f5883eb234be49de778fb92c1fb27b54d93fda3b372d3e43",
  "private": false,
  "record": {
    "abstract": "Fascination with the concept of superconducting (SC) {\\it superfluid density} $\\rho_s$ has persisted since the beginning of superconductivity theory, with numerical values of an actual density rarely provided. Over time $\\rho_s$, addressed mostly in cuprate and following high temperature superconductors, has become synonymous with the normalized (unitless) inverse square of the magnetic penetration depth $\\lambda_L$ (the London expression, with superfluid density denoted $n_s$), with interest primarily on its temperature $T$ dependence that is expected to reflect the T-dependence of the SC gap amplitude and gap symmetry. In conventional superconductors, generalized expressions from the London penetration depth via Ginzburg-Landau theory, then to BCS theory provide updated pictures of the supercurrent density-vector potential relationship. The BCS value $\\lambda_{band}$ is distinct from any particle density, instead involving particle availability at the Fermi surface and Fermi velocity as the determining factors, thus providing a basis for a more fundamental theory and understanding of what is being probed in penetration depth studies. The number density of superconducting electrons ${\\cal N}_s(T$=0) -- the scalar SC {\\it condensate density} -- is provided, first from a phenomenological estimate but then supported by BCS theory. A straightforward relation connecting ${\\cal N}_s(0)$ to the density of dynamically transporting carriers in the normal state at $T_c$ is obtained. Numerical values of relevant material parameters including $\\lambda_{band}$ and ${\\cal N}_s$ are provided for a few conventional SCs.",
    "arxiv_id": "2601.10578",
    "authors": [
      "Warren E. Pickett"
    ],
    "categories": [
      "cond-mat.supr-con"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Superfluid Density, Penetration Depth, Condensate Density",
    "url": "https://arxiv.org/abs/2601.10578",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4a2036a9-d5c6-4ea1-a236-98d0e08e38c3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}