Theoretical Studies For Mott Insulator

The discovery of high-Tccuprate superconductors has triggered enormous interests on the nature of Mott insulator as the high-Tccuprate superconductors are doped Mott insulator.Although there are controversies about the nature of the pairing mechanism of high temperature superconductivity and the non-Fermi liquid behavior in the corresponding normal state,there is a general consensus that the the physics of high-Tcsuperconductivity is the physics of doped Mott insulator.For this reason,it is important to find a comprehensive description of undoped Mott insulator in the first place.In the Mott insulator,the high-energy charge fluctuations and low-energy spin fluctuations are mixed,so we should treat them on an equal footing in order to gain insight into undoped Mott insulator and doped Mott insulator.In this dissertation,we propose a new theoretical framework to study the full nature of Mott insulator by accurately considering the interplay of the spin and charge degrees of freedom in the strong coupling limit.We have chosen to tackle this problem in the slave-fermion representation other than the widely used slave-boson representation.There are two reasons for this.The first is that it is physically much more intuitive to ascribe the fermionic statistics to the charge degrees of freedom in order to have holon–doublon binding,in analogy with the electron binding mechanism of Bardeen–Cooper–Schrieffer(BCS)superconductivity.The holon-doublon bindind state would give rise to the Mott gap at zero temperature and pseudogap at finite temperature.The second is that long-range antiferromagnetic fluctuation at zero temperature and short-range antiferromagnetic fluctuation at finite temperature can be much more easily described if we ascribe the bosonic statistics to the spin degrees of freedom.Using the self-consistent Born approximation to treat the coupling between the spin and charge degrees of freedom,we calculate the average double occupancy,the spectral function and the density of states.Although vertex corrections are neglected in this approximation,our results are in semi-quantitative agreement with many numerical studies performed by a range of methods.Thus,we conclude that our method captures all the essential physics of Mott insulator.In the slave-fermion representation,the electron Green function is the convolution of the charge Green functions and spin Green functions.So the Mott gap is the holon-doublon gap further subtracted by the amount coming from particle-hole spin fluctuations.We show that holon-doublon binding energy decreases with increasing temperature and Mott gap decreases faster than the holon-doublon gap since the effective spin excitation width increases with the increase of temperature.Our results suggest that the upper and lower Hubbard bands are temperature dependent and are not rigid band in contrast with the conventional rigid bands for the band insulator.More importantly,we give the finite temperature phase diagram of Mott insulator.The Mott insulator regime is a fully gapped regime where both Mott gap and holon-doublon binding gap are finite.The pseudogap regime is where Mott gap closes while holon-doublon binding gap is still finite.This finite holon-doublon gap implies the suppression of density of states at Fermi level compared with the metallic regime where both Mott gap and holon-doublon binding gap are closed.We believe that such pseudogap behavior at half-filling is the precursor of the pseudogap at doped cases where short-range spin fluctuations play a central role in the low-energy physics and weaken the holon-doublon binding gap.