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Register a new userRenormalization group analysis of magnetic and superconducting instabilities near van Hove band fillings
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Phase diagrams of the two-dimensional one-band t-t Hubbard model are obtained within the two-patch and the temperature-cutoff many-patch renormalization group approach. At small t and at van Hove band fillings antiferromagnetism dominates, while with increasing t or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.
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The phase diagram of the two-dimensional extended one-band U-V-J Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization group (RG) approaches near the van Hove band fillings. At small t and J>0 mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach, which predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. At the same time, there is a complex competition between SDW, CF phases, and d-wave superconductivity in two- and many-patch RG approaches. While the spin-flux (SF) phase is not stable at the mean-field level, it is identified as a possible ground state at J<0 in both RG approaches. With increasing t the results of all three approaches merge: d-wave superconductivity at J>0 and ferromagnetism at J<0 become the leading instabilities. For large enough V the charge-density-wave (CDW) state occurs.
Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is found that at the transition a repulsive interaction is marginally relevant and an attractive interaction is marginally irrelevant. We corroborate the results obtained from the RG calculation by studying a microscopic model whose ground state and Greens functions can be obtained exactly. We find that away from the transition, the system displays an instability towards forming and excitonic condensate.
Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.
We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous propagators and anomalous effective interactions. In addition to the anomalous interactions arising already in the reduced BCS model, effective interactions with three incoming legs and one outgoing leg (and vice versa) occur. We accomplish their integration into the usual diagrammatic formalism by introducing a Nambu matrix for the effective interactions. From a random-phase approximation generalized through use of this matrix we conclude that the impact of the 3+1 effective interactions is limited, especially considering the effective interactions important for the determination of the order parameter. The exact hierarchy of flow equations for one-particle irreducible vertex functions is truncated on the two-particle level, with higher-order self-energy corrections included in a scheme proposed by Katanin. Using a parametrization of effective interactions by patches in momentum space, the flow equations can be integrated numerically to the lowest scales without encountering divergences. Momentum-shell as well as interaction-flow cutoff functions are used, including a small external field or a large external field and a counterterm, respectively. Both approaches produce momentum-resolved order parameter values directly from the microscopic model. The size of the superconducting gap is in reasonable agreement with expectations from other studies.
We review our recent work on magnetic properties of graphite and related carbon materials. The results demonstrate that a structural disorder, topological defects, as well as adsorbed foreign atoms can be responsible for the occurrence of both ferromagnetic and superconducting patches in graphitic structures.
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