Mott metal-insulator transition and magnetism: Difference between revisions

From PhyWiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(4 intermediate revisions by 3 users not shown)
Line 1: Line 1:
The explanation of the nature of the Mott-Hubbard metal-insulator transition, i.e., the transition between a paramagnetic metal and a paramagnetic insulator driven by electronic interactions, is one of the classic and fundamental problems in condensed matter physics
When we want to determine which material is a conductor, semiconductor or an insulator we turn to the Band Theory of Solids. This is done by plotting the energies of electrons which forms bands. In a conductor you have available electrons in the conduction band. With the insulators their is a gap between the conduction and the valence band. With semiconductor their is a small gap, small enough that if the electrons were excited to a certain energy they could actually leap the gap. Some materials do not follow the predictions of the Band Theory. Metal oxides, according to the Band theory were suppose to be conductors but actually turned out to be insulators. This is known as a Mott insulator. This is due to the fact that when each individual site is half full the electron electron repulsion is much larger than the hopping element. This makes the electrons immobile, declaring it an insulator. The Hubbard Model can explain this phenomena by introducing a new term when calculating the Hamiltonian.


==Animal Magnetism==
<math> H = -t \sum_{<i,j>,\sigma}( c^{\dagger}_{i,\sigma} c^{}_{j,\sigma}+ h.c.) + U \sum_{i=1}^{N} n_{i\uparrow} n_{i\downarrow} </math>, where <math> <i,j> </math> represents nearest-neighbor interaction on the lattice.
Action at a distance
* Coulomb forces and charges
* Gravitational force
* Magnetic force


[[Image:doping cartoon.jpg|thumb|Fig. 2. The orange circles represent Cu atoms. In A, there is a one spin half state at every vertex. However, B shows after some spins are removed, allowing for the hopping of electrons]]
This will give a new term U which will open a gap between the previous two bands. If t/U is too large then the two separate bands will merge. This will make the Mott insulator turn into a conductor. This t/U fraction will determine what is and what isn't a Mott insulator when considering materials such as metal oxides.


For high <math>T_c</math> cuprate superconductors, the most studied are those with immediately adjacent Cu-O planes.  This is due to the agreed upon (by both theorists and experimentalists) notion that charge transport and superconductivity are both in the CuO2 planes. For these Cu02 planes, electron hopping from Cu to Cu is prevented due to strong Coulomb repulsion.
[[Image:Mott.gif|300px|center]]
 
This coupled with the fact that an anti-ferromagnetic order is energetically favorable leads to the dominating electronic state being an anti-ferromagnetic '''Mott Insulator''' (as shown in Fig 2A).  In order to allow for electrons to hop between Cu and Cu, some spins must be removed from these sites (as shown in Fig 2B).
 
Through this process, the insulating <math>CuO_2</math> layer becomes doped with holes or electrons, yielding new electronic ordered states; one of these states being high <math>T_c</math> superconductivity.
 
As previously mentioned, the properties and characteristics of these high <math>T_c</math> superconductors differ from conventional superconductors. The s-wave pairing symmetry exhibited by the conventional superconductors is absent in these high <math>T_c</math> cuprates, for which the pairing symmetry is <math>dx^2-y^2</math> symmetry. 
 
This is not the only notable difference between the two. The short coherence length, highly anisotropic critical current, and very high critical field are all different as well. One significant thing to note is that the length scales of these characteristics are all very similar in high <math>T_c</math> cuprates (~1 nm), while they often very by orders of magnitude in usual metals.  Specifically:
 
* the Fermi wavelength is ~1 nm
* the Cu-Cu distance is ~.38 nm
* the inter-dopant atomic distance ~1.5 nm
* the superconducting coherence length is ~1-2 nm. 
 
Theorists and experimentalists agree that these distances suggest that different electronic phenomena can interact strongly with each other.

Latest revision as of 14:20, 30 April 2011

When we want to determine which material is a conductor, semiconductor or an insulator we turn to the Band Theory of Solids. This is done by plotting the energies of electrons which forms bands. In a conductor you have available electrons in the conduction band. With the insulators their is a gap between the conduction and the valence band. With semiconductor their is a small gap, small enough that if the electrons were excited to a certain energy they could actually leap the gap. Some materials do not follow the predictions of the Band Theory. Metal oxides, according to the Band theory were suppose to be conductors but actually turned out to be insulators. This is known as a Mott insulator. This is due to the fact that when each individual site is half full the electron electron repulsion is much larger than the hopping element. This makes the electrons immobile, declaring it an insulator. The Hubbard Model can explain this phenomena by introducing a new term when calculating the Hamiltonian.

, where represents nearest-neighbor interaction on the lattice.

This will give a new term U which will open a gap between the previous two bands. If t/U is too large then the two separate bands will merge. This will make the Mott insulator turn into a conductor. This t/U fraction will determine what is and what isn't a Mott insulator when considering materials such as metal oxides.

Mott.gif
Retrieved from "http://wiki.physics.fsu.edu/index.php?title=Mott_metal-insulator_transition_and_magnetism&oldid=12329"