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Journal of the Physical Society of Japan

Ground State Properties in a Model of Quasi-Two-Dimensional Semiconductor

Hirosi Okamoto

Published Jul 15, 1997• 0 citations
Publisher

Abstract

A renormalization group treatment is applied to a model of (quasi)-two-dimensional semiconductor with a small band gap. Phase diagrams are derived based on the numerical solutions of the scaling equations. In the purely two-dimensional case, we find the singlet superconducting phase is induced by the repulsive interband interaction in the presence of the attractive intraband interaction. We also find the ferromagnetism and/or the ferroelectricity are stabilized in the presence of the repulsive interband and intraband interactions. The effects of the other kinds of interband and interplanar interactions are also discussed.

DOI
10.1143/jpsj.66.2068

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A renormalization group treatment is applied to a model of (quasi)-two-dimensional semiconductor with a small band gap. Phase diagrams are derived based on the numerical solutions of the scaling equations. In the purely two-dimensional case, we find the singlet superconducting phase is induced by the repulsive interband interaction in the presence of the attractive intraband interaction. We also find the ferromagnetism and/or the ferroelectricity are stabilized in the presence of the repulsive interband and intraband interactions. The effects of the other kinds of interband and interplanar interactions are also discussed.
Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.
The phase diagram for spin 1/2 fermions with attractive interband interactions (- V ) is obtained for the two-band Hubbard model in the space of - V , intraband repulsion ( U ), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude ( ∼ V ) and (ii) in non-half-filled bands.
We present a vector recursion based approach to study the effect of disorder on superconductivity in a system modeled by the two-band attractive Hubbard model. We use the augmented space formalism for the disorder averaging. In the presence of only intraband pairing in a two-band disordered system with disorder in either or both bands, our calculations reveal that the gap survives in the quasiparticle spectrum; similar to single band systems. However, for interband pairing the gap in the quasiparticle spectrum ceases to exist beyond a critical value of the disorder strength. In the presence of both interband and intraband pairing interaction, depending on the relative magnitude of the pairing strength, only a particular kind of pairing is possible for a half filled two-band system.
At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.
A two-band model of spinless fermions in one dimension is constructed. Density-density couplings, umklapp scattering, and interband transitions are included. Renormalization-group equations are derived and discussed. In addition, it is shown that with one condition on the couplings and the velocities the model may be transformed to two uncoupled sine-Gordon Hamiltonians, which makes it possible to obtain solutions in regions where the renormalization-group equations are not valid. An important property of the model is that there can be superconductivity with repulsive interactions.
We use the density-matrix renormalization group method to investigate the superconductor-insulator transition (SIT) in disordered quasi-one-dimensional systems. Focusing on the case of an interacting spinful Hamiltonian at quarter filling, we contrast the differences arising in the SIT when the parent noninteracting model features flat or dispersive bands. Furthermore, we unveil the critical disorder amplitude that triggers insulating behavior by comparing disorder distributions that preserve or not SU(2) symmetry. While scaling analysis suggests the transition be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder is the critical disorder nonvanishing. In this sense, the flat-band structure does strengthen superconductivity in the presence of attractive interactions. For both flat- and dispersive-band models, (i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; (ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.