Orbital Antiferromagnetism Research Articles

Phase diagram of the half-filled extended Hubbard model in two dimensions

We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight binding Hamiltonian with nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements. In addition to the onsite Hubbard interaction (U) we also consider a nearest neighbour repulsion (V). We obtain the zero temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge and spin density wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with $d_{x^2-y^2}$ symmetry in the charge and spin channels respectively. For $t' = 0$, only the charge density wave and spin density wave states are energetically stable. For non-zero t', we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t'.

Disorder effects in two-dimensional Fermi systems with conical spectrum: exact results for the density of states

The influence of weak non-magnetic disorder on the single-particle density of states ϱ( ω) of two-dimensional electron systems with a conical spectrum is studied. We use a non-perturbative approach, based on the replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by abelian and non-abelian bosonization methods. Specifically, we consider a weakly disordered p- or d-wave superconductor, in which case the problem reduces to a model of (2+l)-dimensional massless Dirac fermions coupled to random, static, generally non-abelian gauge fields. It is shown that the density of states of a two-dimensional p- or d-wave superconductor, averaged over randomness, follows a non-trivial power-law behavior near the Fermi energy: ϱ( ω) ∼ 1 | ω| α . The exponent α > 0 is exactly calculated for several types of disorder. We demonstrate that the property ϱ(0) = 0 is a direct consequence of a continuous symmetry of the effective fermoic model, whose breakdown is forbidden in two dimensions. As a counter example, we also discuss another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite ϱ(0) due to the breakdown of a discrete (particle-hole) symmetry.

Low-temperature thermodynamics of the two-dimensional orbital antiferromagnet

We consider the low-temperature properties of a two-dimensional orbital anti-ferromagnet (OAF), which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice. Such a state can result from anisotropic electron-hole pairing due to the nesting property of the Fermi surface, and is characterized by nonzero local currents violating translational symmetry of the underlying lattice. Within a simple mean-field model, we show that, in the low-energy limit, the 2D OAF is described by (2+1)-dimensional quantum field theory of gapless fermion excitations associated with zeros of the gap function. The “relativistic” Landau quantization of the spectrum in external magnetic field shows up in unusual behavior of the magnetic susceptibility. Strong diamagnetism of the OAF is found in the perpendicular field, changing to paramagnetism upon the decreasing of the angle between the field and the plane. When the angle approaches zero, the susceptibility shows an oscillatory angle dependence.

Fermi-surface instabilities of a generalized two-dimensional Hubbard model.

Possible Fermi-surface-related instabilities in a Hubbard model, generalized so as to include finite-range and exchange interactions, are studied in the weak-coupling limit. In addition to the usual instabilities of superconducting, charge- or spin-density-wave type, two new types of instability are found. The first state is an orbital antiferromagnet, with currents circulating around each elementary plaquette. In the second phase, a spin current flows around the plaquettes. In both cases, there are low-temperature power laws in thermodynamic and transport properties. Two-dimensional fluctuation effects are shown to lead, for weak interactions, to a sharp crossover from a Fermi-liquid state to a regime governed by orientational fluctuations of the order parameter at fixed amplitude.

Alloy Analogy Approximation of the Degenerate Hubbard Model

AbstractAn expression of the degenerate Hubbard model energy in the alloy analogy approximation is given. A two sublattice system is considered in order to allow for spin or orbital antiferromagnetism ordering solutions. The Hartree‐Fock and Hubbard I approximations are shown to be specific limits of the CPA alloy analogy solutions.