Collective modes in an ‘‘ultraquantum crystal.’’ I. Field-induced spin-density-wave phases

Abstract

A strongly anisotropic metallic electron gas with quasi-two-dimensional open Fermi surface is unstable with respect to formation of a spin- or charge-density wave when a uniform magnetic field is applied perpendicular to the most conducting plane. In this paper, we study the collective modes of the field-induced density-wave phase. The latter is characterized by two lengths, the spin-density-wave wavelength, and the magnetic length which is much larger, and results from electronic orbital motion under field. As a result, spin-spin correlation functions exhibit structure for wave vectors of the order of the inverse magnetic length. We find that both spin waves and phase fluctuations modes exhibit, besides the trivial Goldstone bosons, a series of rotonlike modes. Those are local minima of the energy dispersion surface along values of the (parallel) momentum which are quantized in terms of the inverse magnetic length. Those modes lie below the single-particle excitation gap at all temperatures; their relative position within the single-particle gap shifts to lower energies as the temperature decreases. Each rotonlike mode may be viewed as a precursor of neighboring phases which are stabilized when the magnetic field varies sufficiently. Within the approximation which neglects coupling between the order-parameter fluctuations and spin fluctuations along the external field axis, spin-wave modes and phase-fluctuation modes are degenerate. The structure of the collective modes proves that field-induced charge- or spin-density waves are quantum crystals with properties distinct from ordinary charge- or spin-density waves, which justifies the generic name of ``ultraquantum crystals.'' The theory applies to Bechgaard salts.