Excitons in one-dimensional narrow gap semiconductors of anti-crossing quantum Hall edge states are investigated using a bosonization method. The excitonic states are studied by mapping the problem into a non-integrable sine-Gordon type model. We also find that many-body interactions lead to a strong enhancement of the band gap. We have estimated when an exciton instability may occur.PACS numbers: 71.27.+a, 71.35.Cc One-dimensional (1D) narrow gap semiconductors can be realized in anti-crossing quantum Hall edge states 1 and nanotubes 2 . The gaps in these systems are single particle gaps and not many body gaps. Theoretically, they provide the unusual condition that the bare band gap t is much smaller than the characteristic Coulomb energy scale E c . Moreover, strong quantum fluctuations are present in these systems, reflecting the 1D character. The ground state of these systems may be unstable against the spontaneous formation of excitons if the exciton binding energy exceeds the band gap 3,4 . In three dimensional semiconductors excitons can be treated successfully by solving the Bethe-Salpeter equation 4 . However, in the strong coupling regime of 1D systems, the perturbative approaches are not expected to be reliable due to large quantum fluctuations. If the Coulomb scale is much larger than the gap one might naively expect that exciton instability would occur. However, this simple picture neglects screening which is expected to be large due to the smallness of the gap. It is unclear whether a bound state of an "electron" and a "hole" can exists in the presence of strong quantum fluctuations. Not much is known about the physics of excitons in 1D narrow gap semiconductors.This problem can be addressed within a bosonization approach, which is applicable as long as the the characteristic energy scale of the problem is smaller than the band width W . Thus bosonization provides a natural framework for studying 1D excitons. In this work we will consider anti-crossing of quantum Hall edge states in the barrier region of between two 2D electron gases. Assume that the applied magnetic field is sufficiently strong that the system is spin-polarized with the filling factor ν = 1 and that the Fermi level is in the gap of anti-crossing edge states. We find that the problem can be mapped into a sine-Gordon (sG) model with an extra term representing the long range Coulomb interaction. Due to this extra term the model becomes non-integrable and an exact solution is unavailable. However, the non-linear cosine term of this sG model can be expanded provided that δ ex ∼ v/v0 ln W/t < 1, where v is the Fermi velocity, v 0 = e 2 /ǫh, W =hv/a, and a is the smallest length scale in the problem 6 . In this regime a perturbative theory may be applied to calculate excitonic energies. Our work also indicates that a large enhancement of band gap occurs. Our perturbative approach suggests an approximate estimate for when an exciton instability may occur: δ ex > 1 . (We cannot exclude the possibility that the higher order corrections n...

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Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t′ on square lattices. By varying the value of t′, we find that the d-wave pairing is suppressed by the onset of t′, while the p + ip-wave pairing tends to emerge for low electron density and t′ around −0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.

The analyticity of the lowest Landau level wave functions and the relation between filling factor and the total angular momentum severely limits the possible forms of trial wave functions of a disk of electrons subject to a strong perpendicular magnetic field. For N , the number of electrons, up to 12 we have tested these disk trial wave functions for the half filled Landau level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies obtained from these two methods is excellent. We have also compared the profile of the occupation number near the edge with that obtained from a field-theoretical method. The results give qualitatively identical edge profiles. Experimental consequences are briefly discussed.