טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentYair Omer
SubjectCalculation of the Hall Conductivity of the 2D t-j
Model using Exact Diagonalization
DepartmentDepartment of Physics
Supervisor Professor Assa Auerbach
Full Thesis textFull thesis text - English Version


Abstract

In our work we have studied the two-dimensional t-J model which is believed to

describe the physics behind the superconductivity phenomena in the Cuprates

family. We have addressed the phenomenon known as the Hall anomaly, where

the Hall conductance changes it's sign a phenomena which has been measure in

a large variety of High Tc superconductors over the last two decades but has yet

to be satisfactorily explained. The t-J model is not analytically solvable, but

numerical solutions can be found for very small systems. We have used methods

of exact digonalization to calculate the energy spectrum and the Hall conductance

of a t-J model of 16 sites, for different electron fillings. These exact solutions fully

incorporate the strong correlation between the electrons in the system, which are

only approximated in other common methods used for modelling the behaviour

of the Hall conductance. We have compared our results to the non-interacting

band structure model at the same fillings. We found large deviations in the Hall

conductance as we approach half filling, especially for systems with an even number

of holes. Specifically, we observed a sign reversals of the Hall conductance which

does not exist in the non-interacting model below half filing. We argue that the

sign reversal of the Hall conductance might be attributed to the pair binding

phenomena which we point out to happen in the t-J model.