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arXiv:1803.04977 · Physical review. B./Physical review. B

Itinerant fermions on a triangular lattice: Unconventional magnetism and other ordered states

Mengxing Ye, Andrey V. Chubukov

Published Jun 7, 2018• 3 citations
arXivHTMLPDF

Abstract

We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either ${120}^{\ensuremath{\circ}}$ ``triangular'' order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and nonmagnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.

DOI
10.1103/physrevb.97.245112

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We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either 120\ensuremath∘{120}^{\ensuremath{\circ}}120\ensuremath∘ ``triangular'' order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and nonmagnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.
Group theoretically possible spin density waves (SDWs) of the Hubbard model on a triangular lattice are found and classified for ordering vectors q of K and M in the Brillouin zone by finding the maximal subgroups of the symmetry group of the Hamiltonian. It is found that classifications of SDWs with these ordering vectors are reduced to classifications of SDWs on molecules with D 3 and T d symmetries, respectively. From this reduction the authors found two axial-type ASDWs (ASDW) and one plane-type SDW (PSDW) for point K and three ASDWs, two PSDWs and one cubic- (three-dimensional-) type SDW (CSDW) for point M. The standard mean-field Hamiltonians and their invariance groups are listed for each class.
We investigate the magnetic order of a one-dimensional spin-1/2 fermion dynamical lattice, where itinerant fermions are coupled to bond-centered localized spins via an Ising-like spin dependent hopping. The model provides an anisotropic dynamical extension of conventional spin-1/2 fermion systems, in which the motion of itinerant fermions is directly modulated by the configuration of localized spins. Using density matrix renormalization group simulations, we map out the ground state phase diagram in various parameter spaces. Depending on the interplay among the hopping dependent on localized spins, the longitudinal field, and the external Zeeman field, two distinct phases are obtained: a paramagnetic phase and a spin-density-wave phase. Most notably, in the partially spin-polarized fermion phase, the spin-density wave ordering wave vector exhibits two distinct phenomena, corresponding respectively to the nesting vectors 2kF↑2k_{F\uparrow}2kF↑​ and 2kF↓2k_{F\downarrow}2kF↓​ of the spin-resolved Fermi surfaces. We further demonstrate that the two spin-density wave phases are robust against the repulsive Hubbard interaction between itinerant fermions. Our results reveal a novel route for tuning magnetic modulations in one-dimensional correlated systems and enrich the microscopic understanding of dynamical lattice magnetism.
We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\ensuremath{\delta}$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\ensuremath{\delta}\ensuremath{\lesssim}10%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, $\ensuremath{\delta}\ensuremath{\approx}10%\ensuremath{\sim}20%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\ensuremath{\delta}\ensuremath{\gtrsim}20%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.
Interaction-induced charge orders with electronic origin occur as states of spontaneously broken symmetry in several materials platforms. An electronic mechanism for charge order requires an attractive component in the effective charge vertex. We put forward such a mechanism for the formation of unconventional charge density waves in a metal. These states result from the condensation of particle-hole pairs with finite wave vector and nonzero angular momentum and correspond to bond or loop current order on a lattice. The mechanism we describe can be viewed as Kohn Luttinger analysis in the particle-hole channel with finite transferred momentum. It incorporates one-loop spin and pairing corrections, which are then used as an input for a summation in the charge channel triggering an instability. We extend our analysis to a spin-fluctuation approach, where the effective charge interaction is dressed by the particle-hole ladder with exchanged momentum. We argue that this mechanism works for weakly interacting metals with a nested Fermi surface and a large number of fermion flavors. We apply the Kohn-Luttinger-like approach to square–PLXINSERT-, and triangular-lattice Hubbard models with SU ( N f ) flavour symmetry and show that it leads to different types of p -wave charge density waves. We also study effects beyond weak coupling at and away from Van Hove filling in terms of a phenomenological model with additional exchange interaction. In the vicinity of Van Hove filling, we obtain d -wave charge density waves with wave vectors determined by nesting as leading instabilities. In addition, we find another charge density wave with wave vector K / 4 on the triangular lattice on both sides of the Van Hove filling. We demonstrate that this K / 4 instability can win the competition against pairing for N f = 4 via an unbiased functional renormalization group calculation.
Using a path-integral formalism and decomposing the Hubbard interaction into charge and spin order parameters, we develop a 1/S loop expansion of the two-dimensional Hubbard model. At the saddle-point level, we present a detailed study of the energetics of twisted antiferromagnetic order. Doping the antiferromagnetic state leads to a rich mean-field phase diagram at zero temperature, which includes spiral phases, a column phase, and ferromagnetism. The on-site magnetization, the density of states, the plasma frequency, and the quasiparticle weights are evaluated for the twisted spin-density-wave (SDW) states as a function of doping and U/t. Doping-induced frustration remarkably leads to a closure of the Mott-Hubbard band gap for any U/t. At one-loop order, we delineate the collective spin and charge fluctuations of the mean-field SDW state. The action for the two transverse spin modes at half-filling maps to a nonlinear \ensuremath{\sigma} model, which tends to disorder upon doping. Twisted magnetic ground states exhibit a third Goldstone mode due to the complete breaking of rotational invariance. For the commensurate SDW, the charge fluctuations couple only to longitudinal spin fluctuations, whereas, for the incommensurate metallic SDW states, the charge modes are coupled nontrivially to the massless spin waves. This suggests a metallic state quite unlike traditional Fermi liquids.
We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We find, within mean field theory, that in a suitable range of parameters there is a tendency toward a novel form of ordering characterized by discrete symmetry breaking and a gap at the magnetic zone boundary, which supports hole-like semiconductor behavior near half filling despite an apparently normal Fermi surface. The effective quasiparticle couplings to phonons includes a significant d-wave piece, which plausibly leads to an especially robust tendency toward superconductivity.