Stability of a spin-triplet nematic state near to a quantum critical point

Abstract

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards d-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spinrotation and spatial rotation symmetries. This order is characterized by spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a helical spin-triplet d-density wave. Such a state is closely related to d-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, p-wave superconducting state.

Quantum Order-by-Disorder in Strongly Correlated Metals

“…[83]. It was later shown [84], using fermionic quantum order-by-disorder, that in fact fluctuations promote the formation of a new phase near to the quantum critical point that intertwines magnetic modulation and d-wave orbital order in a continuum version of bond density wave order(see Fig.6). These unusual phases have some intriguing observable consequences.…”

Introducing fluctuation-driven order into density functional theory using the quantum order-by-disorder framework

“…This is achieved in QOBD by self-consistently evaluating the free energy of fluctuations about an ordered state. Since an arbitrary number of electronic orders maybe considered simultaneously and on equal footing, this method excels when studying the phase diagram reconstruction in the vicinity of quantum critical points due to critical fluctuations [18,[20][21][22][23]. It has had success in describing the helimagnetic phase of MnSi [24], the inhomogeneous magnetic phases of Sr 3 Ru 2 O 7 under applied field [25] and modulated magnetic phase of PrPtAl both in the presence and absence of applied field [26,27].…”

“…Collective order may alternatively be introduced into a system via a Hubbard-Stratonovich transformation, which decouples the quartic electronic interaction in a desired channel to leave an effective theory for a collective field [18,23]. Fluctuations in the collective field are then be evaluated in the presence of a finite, static (iω n = 0) component, which is the order parameter.…”

“…where d k ≡ Φ l=2,m,k is the form factor of a component in the d-wave channel. In the uniform electron gas, spin nematicity amounts to spin-antisymmetric d-wave distortions of the spherical spin Fermi surfaces [20,23]. In this case the volumes of the spin Fermi surfaces are conserved and the order is non-magnetic.…”

“…In spite of this, the full stationary equations for n(r) and η remain highly coupled. Of course, spin nematic order along the z axis that is considered here is a particularly simple case; spin nematic order in other directions/channels will lead to more complicated modifications to the full spin density matrix, n σσ (r) [23].…”