Doping Dependence of Electromagnetic Response in Cuprate Superconductors

Abstract

The study of the electromagnetic response in cuprate superconductors plays a crucial role in the understanding of the essential physics of these materials. Here the doping dependence of the electromagnetic response in cuprate superconductors is studied within the kinetic-energy driven superconducting mechanism. The kernel of the response function is evaluated based on the linear response approximation for a purely transverse vector potential, and can be broken up into its diamagnetic and paramagnetic parts. In particular, this paramagnetic part exactly cancels the corresponding diamagnetic part in the normal-state, and then the Meissner effect is obtained within the entire superconducting phase. Following this kernel of the response function, the electromagnetic response calculation in terms of the specular reflection model qualitatively reproduces many of the striking features observed in the experiments. In particular, the local magnetic-field profile follows an exponential law, while the superfluid density exhibits the nonlinear temperature behavior at the lowest temperatures, followed by the linear temperature dependence extending over the most of the superconducting temperature range. Moreover, the maximal value of the superfluid density occurs at around the critical doping δ critical ∼ 0.16, and then decreases in both lower doped and higher doped regimes. The theory also shows that the nonlinear temperature dependence of the superfluid density at the lowest temperatures can be attributed to the nonlocal effects induced by the d-wave gap nodes on the electron Fermi surface.

Electromagnetic response of cuprate superconductors with coexisting electronic nematicity

“…Soon after the discovery of superconductivity in cuprate superconductors, it has been proposed that the essential physics of the doped copper-oxide plane can be captured by the t-J model on a square-lattice 3 . However, for discussions of the electromagnetic response of cuprate superconductors with coexisting electronic nematicity, the coupling between an external magnetic-field and the electrons can be treated via the Peierls construction, in which the electron creation and annihilation operators develop a phase factor, and then the resulting t-J model is obtained as 55 ,…”

“…then the electron current density is obtained by the calculation of the time-derivative of this electron polarization operator (10) as 55 ,…”

“…ς , while the diamagnetic and paramagnetic parts J are obtained in the linear response theory as 55 ,…”

“…If the gauge invariant is kept in the theory, it is crucial to derive properly the above electron correlation function (15) in a way maintaining local charge conservation 25,[70][71][72] . In the following calculations, we work with a fixed gauge of the vector potential as in the previous discussions 55 . For a convenience in the calculation of the above electron current-current correlation function (15), the electron operators can be rewritten in the Nambu representation as…”

“…xx (ς, q → 0, 0)| T =0 = 0 and K (p) ŷ ŷ (ς, q → 0, 0)| T =0 = 0, reflecting a fact that as in the case of the absence of the electronic nematicity 55 , the zero temperature electromagnetic response of cuprate superconductors with coexisting electronic nematicity in the long wavelength limit is also determined by the diamagnetic part of the response kernel only, i.e., K xx (ς, q, 0) and K ŷ ŷ (ς, q, 0) in Eq. ( 21) are reduced as,…”