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arXiv:0802.1544 · Physical Review Letters

Local Density of States of One-Dimensional Mott Insulators and Charge-Density Wave States with a Boundary

Dirk Schuricht, Fabian H. L. Eßler, Akbar Jaefari, Eduardo Fradkin

Published Aug 20, 2008• 18 citations
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Abstract

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.

DOI
10.1103/physrevlett.101.086403

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We determine the local density of states (LDOS) for spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. We calculate the boundary contribution to the single-particle Green function in the low-energy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum 2kF2{k}_{\mathrm{F}}2kF​, which is indicative of the pinning of the CDW order at the impurity. We further observe several dispersing features at frequencies above the spin gap, which provide a characteristic signature of spin-charge separation. This demonstrates that the boundary LDOS can be used to infer properties of the underlying bulk system. In the presence of a boundary magnetic field, midgap states localized at the boundary emerge. We investigate the signature of such bound states in the LDOS. We discuss the implications of our results for scanning tunneling microscopy experiments on quasi-one-dimensional systems such as two-leg ladder materials like Sr14{\mathrm{Sr}}_{14}Sr14​Cu24{\mathrm{Cu}}_{24}Cu24​O41{\mathrm{O}}_{41}O41​. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.
We numerically calculate the local density of states (LDOS) of a one-dimensional Mott insulator with open boundaries, which is modelled microscopically by a (extended) Hubbard chain at half filling. In the Fourier transform of the LDOS we identify several dispersing features corresponding to propagating charge and spin degrees of freedom, thus providing a visualization of the spin-charge separation in the system. We also consider the effect of an additional boundary potential, which, if sufficiently strong, leads to the formation of a boundary bound state which is clearly visible in the LDOS as a nondispersing feature inside the Mott gap.
We study the tunneling density of states (TDOS) in one-dimensional (1D) Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.
We study the tunneling density of states (TDOS) in one-dimensional (1D) Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.