Fermi surface of superconducting cuprates
Encyclopedia
The electronic structure of superconducting cuprates, also called high temperature superconductors (HTSC), is highly anisotropic. First, the cuprates are almost two-dimensional (2D): the conducting electrons are mainly localized in the CuO2 layers, the common building blocks of all HTSC compounds (e.g., see the crystal structure of YBCO or BSCCO). Therefore, the Fermi surface
of HTSC is very close to the Fermi surface of the doped CuO2 plane (or multi-planes, in case of multi-layer cuprates) and can be presented on the 2D reciprocal space
(or momentum space) of the CuO2 lattice. The typical Fermi surface within the first CuO2 Brillouin zone
is sketched in Fig. 1 (left). It can be derived from the band structure
calculations or measured by angle resolved photoemission spectroscopy
(ARPES
). Fig. 1 (right) shows the Fermi surface of BSCCO measured by ARPES
. In a wide range of charge carrier concentration (doping level), in which the hole-doped HTSC are superconducting, the Fermi surface is hole-like (i.e. open, as shown in Fig. 1). This results in an inherent in-plane anisotropy of the electronic properties of HTSC.
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
of HTSC is very close to the Fermi surface of the doped CuO2 plane (or multi-planes, in case of multi-layer cuprates) and can be presented on the 2D reciprocal space
Reciprocal lattice
In physics, the reciprocal lattice of a lattice is the lattice in which the Fourier transform of the spatial function of the original lattice is represented. This space is also known as momentum space or less commonly k-space, due to the relationship between the Pontryagin duals momentum and...
(or momentum space) of the CuO2 lattice. The typical Fermi surface within the first CuO2 Brillouin zone
Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. The boundaries of this cell are given by planes related to points on the reciprocal lattice. It is found by the same method as for the Wigner–Seitz cell in the Bravais lattice...
is sketched in Fig. 1 (left). It can be derived from the band structure
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
calculations or measured by angle resolved photoemission spectroscopy
Photoemission spectroscopy
Photoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
(ARPES
ARPES
Angle-resolved photoemission spectroscopy , also known as ARUPS , is a direct experimental technique to observe the distribution of the electrons in the reciprocal space of solids...
). Fig. 1 (right) shows the Fermi surface of BSCCO measured by ARPES
ARPES
Angle-resolved photoemission spectroscopy , also known as ARUPS , is a direct experimental technique to observe the distribution of the electrons in the reciprocal space of solids...
. In a wide range of charge carrier concentration (doping level), in which the hole-doped HTSC are superconducting, the Fermi surface is hole-like (i.e. open, as shown in Fig. 1). This results in an inherent in-plane anisotropy of the electronic properties of HTSC.