A new superfluid in organic molecular metals at high magnetic fields

We show that the coexistence of a quasi-two-dimensional Fermi-surface exhibiting Landau quantisation and a charge-density wave leads to a screening of electromagnetic fields at the sample surface. Hall potential experiments demonstrate that this screening is responsible for some of the unusual phenomena observed in the high-field CDWx state of α-(BEDT-TTF)2KHg(SCN)4. The high-magnetic-field properties of α-(BEDT-TTF)2KHg(SCN)4 have generated considerable interest (see Ref. [1] and refs. therein). Below a temperature of 8 K, the material is in the CDW0 chargedensity-wave (CDW) phase [2], caused by the nesting of the quasi-one-dimensional (1D) Fermi-surface sections; at a field of around 23 T, the “kink” transition into the CDWx phase occurs [1, 3]. The CDWx phase exhibits several phenomena normally associated with superconductors [1, 3], including criticalstate-type hysteresis of the magnetisation. In this paper we show that the coexistence of a gapped CDW state and sharp Landau quantisation lead to effects that screen the sample from spatially-varying electromagnetic fields. Experiments show that this leads to an unusual distribution of the Hall potential in α-(BEDT-TTF)2KHg(SCN)4. We treat a simplified version of the α-(BEDT-TTF)2KHg(SCN)4 bandstructure [4], comprising a 1D electron band and a two-dimensional (2D) hole band with dispersions ε1D = vF|kx − kF| and ε2D = εF− 2(|kx−kX |2+ |ky−kY |2)/2m respectively; here m is the effective mass, vF is the Fermi velocity of the 1D band, and kX and kY define the centre of the 2D hole pocket. Each band intersects the Fermi energy (εF). The simplest scenario is that where only the 1D Fermi-surface section is subject to CDW formation, giving a gap 2∆0 in its density of electronic states, while the 2D hole section remains ungapped. Under equilibrium conditions, the average volume charge densities ̄1D and ̄2D associated with the 1D and 2D Fermi-surface sections respectively would be subject to the conservation equation ̄1D + ̄2D + bg = 0, where bg is the density of charge due to the ionic cores. However, below we consider slight local deviations ∆ 1D and ∆ 2D in the charge density from the equilibrium values (i.e. the total local charge densities become 1D = ∆ 1D + ̄1D and 2D = ∆ 2D + ̄2D); as the CDW is present, the conservation equation need no longer hold locally. However, the charge densities must obey Poisson’s equation − ∇2V(r) = ∆ 2D + ∆ 1D, (1) where V is the electrostatic potential and is the permittivity. We are at liberty to set the origin of potential; we choose V = 0 in the absence of spatial charge variations. Equation 1 implies that the presence of a local charge-density variations will lead to an in-plane, spatially-varying electric field E = −∇V . We now introduce the magnetic field B0 applied along z (i.e ⊥ to the 2D (x, y) planes). This has two effects; first, the crossed E and B fields force the 2D hole wavefunction centres to drift at a velocity 258 JOURNAL DE PHYSIQUE IV E × B0/B0, leading to a spatially-varying in-plane current density j = 2DE × B0/B0. Integration of Maxwell’s fourth equation (∇ × H = j) shows that this current produces an additional contribution ∆B = −μ0 2D(V/B0) (2) to the magnetic field parallel to z, which then becomes B = B0 + ∆B. A second effect of B is to produce Landau quantisation of the 2D holes; this is treated using the Landau gauge A = (0, Bx, 0). After manipulation [5], the Schrödinger equation for the in-plane wavefunctions ψ and eigenenergies E may be written as ( − 2 2m ∂ 2 ∂x2 + 1 2 mω 2 c(x − x0) ) ψ = Eψ. Here, the effect of the crystalline potential is taken into account by the effective mass m; the cyclotron frequency is ωc = qB/m, with q the charge; x0 represents the wavefunction guiding-centre coordinate. The in-plane electric field also modifies the Landau-level energies [6]. To quantify this, we consider the case V(r) = V(x), i.e. the potential varies only in the x direction (variation in an arbitrary direction in the x, y plane is reintroduced below). If V(x) varies slowly over lengthscales ∼ x0, it can be expanded about x0 in a Taylor’s series V(x) = V(x0) + (x − x0)V ′(x0) + 2 (x − x0)V ′′(x0) + ....., where the primes indicate differentiation with respect to x. After a little algebra, the Schrödinger equation becomes