Role of fluctuations for density-wave instabilities: Failure of the mean-field description

Abstract

Density-wave instabilities have been observed and studied in a multitude of materials. Most recently, in the context of unconventional superconductors like the iron-based superconductors, they have excited considerable interest. We analyze the fluctuation corrections to the equation of state of the density-wave order parameter for commensurate charge-density waves and spin-density waves due to perfect nesting. For XY magnets, we find that contributions due to longitudinal and transverse fluctuations cancel each other, making the mean-field analysis of the problem controlled. This is consistent with the analysis of fluctuation corrections to the BCS theory of superconductivity [Š. Kos, A. J. Millis, and A. I. Larkin, Phys. Rev. B 70, 214531 (2004)]. However, this cancellation does not occur in density-wave systems when the order parameter is a real N -component object with N = 2. Then, the number of transverse fluctuating modes differs from the number of longitudinal fluctuating modes. Indeed, in the case of charge-density waves as well as spin-density waves with Heisenberg symmetry, we find that fluctuation corrections are not negligible, and hence mean-field theories are not justified. These singular fluctuations originate from the intermediate length-scale regime, with wavelengths between the lattice constant and the T = 0 correlation length. The resulting logarithmic fluctuation contributions to the gap equation originate from the derivative of the anomalous polarization function, and the crucial process is an interaction of quasiparticles through the exchange of fluctuations.

Short-distance breakdown of the Higgs mechanism and the robustness of the BCS theory for charged superconductors

“…Another interesting implication of our analysis is with regard to many-body theories that have structural similarities to the BCS theory, such as density-wave instabilities with perfect nesting. In this case, it can be shown that the cancellation of transverse and longitudinal modes is not always guaranteed, leading to important limitations of the mean-field theory of density-wave systems [30]. The diagrammatic representation of the fluctuation corrections to the gap equation (22) along with the discussion of the importance of the different contributions is presented in Ref.…”

“…The diagrammatic representation of the fluctuation corrections to the gap equation (22) along with the discussion of the importance of the different contributions is presented in Ref. 30 for a closely related problem.…”

Heat capacity of URu$_{2-x}$Os$_x$Si$_2$ at low temperatures

“…29,30 In particular, in the weak coupling limit, the retardation effects are implemented as an ultraviolet cutoff Λ = ω D in the self-consistent calculation of the order parameter. There are known limitations to this line of arguments, 31 but we think that these limitations are not relevant for the 'hidden-order' transition. To summarize, to the best of our knowledge there is no experimental evidence for the retardation effects being observed through the 'hidden order' transition and the emergence of an energy scale (analogous to ω D in the BCS theory) that would be much smaller than the Fermi energy.…”

Fluctuation-dominated quantum oscillations in excitonic insulators

“…The action S fluct describes the effects of quantum fluctuations beyond mean field theory. The consequences of these fluctuations for the thermodynamics of related BCS superconductors have been worked out in detail previously [46][47][48]. Much can be gleaned from these studies for our B = 0 model of the excitonic insulator Eq.…”

“…This leads to a total free energy Ω(B) that is the sum of mean-field Ω MF (B) and fluctuation Ω fluct (B) contributions. Despite the nonzero magnetic field, the fluctuation free energy can be written in the same form as for B = 0 [46][47][48],…”