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arXiv:cond-mat/0308364 · Journal of the Physical Society of Japan

On the Mott Glass in the One-Dimensional Half-Filled Charge Density Waves

Yoshikazu Suzumura, Masato Isobe

Published Nov 15, 2003• 1 citation
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Abstract

We study the effect of impurity pinning on a one-dimensional half-filled electron system, which is expressed in terms of a phase Hamiltonian with the charge degree of freedom. Within the classical treatment, the pinned state is examined numerically. The Mott glass, which has been pointed out by Orignac et al. [Phys. Rev. Lett 83 (1999) 2378], appears in the intermediate region where the impurity potential competes with the commensurate potential. Such a state is verified by calculating the soliton formation energy, the local restoring force around the pinned state and the optical conductivity.

DOI
10.1143/jpsj.72.2908

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We study the effect of impurity pinning on a one-dimensional half-filled electron system, which is expressed in terms of a phase Hamiltonian with the charge degree of freedom. Within the classical treatment, the pinned state is examined numerically. The Mott glass, which has been pointed out by Orignac et al. [Phys. Rev. Lett 83 (1999) 2378], appears in the intermediate region where the impurity potential competes with the commensurate potential. Such a state is verified by calculating the soliton formation energy, the local restoring force around the pinned state and the optical conductivity.
We study one-dimensional density wave, which is pinned by impurity potential and commensurate potential at half-filling. The former pinning leads to Anderson glass (AG) state while the latter pinning results in Mott insulator (MI) state. The Mott glass (MG) state, which has been found in the classical case, is located between AG state and MI state, and exhibits a gap for a single particle excitation but no gap for the collective excitation. We examine the effect of quantum fluctuation on such a MG state by calculating a soliton-formation energy and an optical conductivity at low frequencies. The self-consistent harmonic approximation is applied to calculate the spring constant for the potential, which determines the magnitude of pinning frequency. It is found that the MG state still exists for small quantum fluctuation and that further increase of the fluctuation leads to the disappearance of the MG state due to the large reduction of the soliton-formation energy. The results are discussed in terms of the local distribution of pinning frequency.
We study the low-energy limit of a quarter-filled one-dimensional Mott insulator. We analytically determine the local density of states in the presence of a strong impurity potential, which is modeled by a boundary. To this end we calculate the Green function using field theoretical methods. The Fourier transform of the local density of states shows signatures of a pinning of the spin-density wave at the impurity as well as several dispersing features at frequencies above the charge gap. These features can be interpreted as propagating spin and charge degrees of freedom. Their relative strength can be attributed to the ``quasi-fermionic'' behavior of charge excitations with equal momenta. Furthermore, we discuss the effect of bound states localized at the impurity. Finally, we give an overview of the local density of states in various one-dimensional systems and discuss implications for scanning tunneling microscopy experiments.
We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.
We consider the ground state reorganization driven by an increasing nearest neighbor repulsion U for spinless fermions in a strongly disordered ring. When U -> 0, the electrons form a glass with Anderson localized states. At half filling, a regular array of charges (Mott insulator) is pinned by the random substrate when U -> \infty. Between those two insulating limits, we show that there is an intermediate regime where the electron glass becomes more liquid before crystallizing. The liquid-like behavior of the density-density correlation function is accompanied by an enhancement of the persistent current.
The effect of an alternating potential on a one-dimensional half-filled Hubbard model with repulsive interaction has been examined by applying the renormalization group method to the bosonized Hamiltonian. The electronic state, which is determined by the competition between alternating potential and umklapp scattering, is calculated where the relevance and the irrelevance of the alternating potential leads to the band insulator and the Mott insulator respectively. The excitation gaps for charge and spin fluctuations are calculated for both states.
The effect of impurities on a spin-density wave (SDW) state in one-dimensional interacting electron systems is investigated by applying a phase representation and the theory of the weak impurity pinning. With the help of numerical simulation, it is shown that the pinned SDW is characterized by both a rapidly varying phase variable of the spin-density fluctuation and a slowly varying phase variable of the charge-density fluctuation. Based on this, the critical condition on the magnitude of interactions for localization-delocalization transition is determined by use of the self-consistent harmonic approximation.