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arXiv:1009.5587 · Physical Review B

Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states

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

Published Jan 13, 2011• 15 citations
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Abstract

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 $2{k}_{\mathrm{F}}$, 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 ${\mathrm{Sr}}_{14}$${\mathrm{Cu}}_{24}$${\mathrm{O}}_{41}$. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.

DOI
10.1103/physrevb.83.035111

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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 {\mathrm{Sr}}_{14}$${\mathrm{Cu}}_{24}$${\mathrm{O}}_{41}. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.
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 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 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.
Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder, these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\ensuremath{\epsilon}$, the single-particle Green function decays in real space like $G(x,\ensuremath{\epsilon})\ensuremath{\propto}{(1/x)}^{3/2}$. It follows that at these energies the correlations in the disordered system are strong --- even stronger than in the pure system without the gap. At distances $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}\ensuremath{\propto}{\mathrm{ln}}^{2}(1/\ensuremath{\epsilon})$, the Green function crosses over to a standard exponential decay. The scale ${L}_{\ensuremath{\epsilon}}$ is different from the Thouless localization length ${\ensuremath{\lambda}}_{\ensuremath{\epsilon}}\ensuremath{\propto}\mathrm{ln}(1/\ensuremath{\epsilon})$. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as 1/x1/\sqrt{x}1/x​ saturating at $x\ensuremath{\sim}{L}_{\ensuremath{\epsilon}}.$ We also discuss some implications of these results for the spin systems and their relation to the investigations based on the real-space renormalization group approach.