Quantum theory of a nematic Fermi fluid

Abstract

We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the directorwave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of z = 3, implying stability of the gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi liquid theory in the nematic phase and to strongly angle dependent electronic self energies around the Fermi surface. Other metallic liquid crystal phases, e. g. a quantum hexatic, behave analogously.There is a growing body of both experimental and theoretical evidence for the relevance of inhomogeneous and/or anisotropic metallic phases in a wide array of highly correlated electronic systems. Quasi-one dimensional (stripe or "electronic smectic") phases have been observed in a large variety of transition metal oxides. 1More recently, 2,3 the dramatic discovery of a metallic phase with a strongly anisotropic resistivity tensor for a range of magnetic fields in ultra clean heterojunctions has provided clear evidence of the existence of a "quantum Hall nematic" phase. In parallel, theoretical work 4,5 has been carried out on electronic liquid crystal phases. These ground-state phases are classified, based on broken symmetries, by analogy with classical liquid crystals. So far, these studies have focused primarily on the smectic, which is a unidirectional density wave with broken translational symmetry in only one direction, but which supports liquid-like electron flow 6,7 , and to a lesser extent on the nematic, which is uniform but anisotropic (breaks rotational symmetry) 8,9 . A nematic state in the proximity to the smectic state can be visualized most naturally as a melted smectic, i. e. a smectic with dislocations. However, a theory of the nematic phase based on this picture has yet to be satisfactorily formalized.In this paper we approach the nematic metal via a complimentary route, from the isotropic and weakly correlated side. In this limit, the zero temperature isotropic to nematic transition is a Fermi surface instability. The director order parameter which characterizes the broken symmetry of the nematic state is a rank two symmetric traceless tensor which is even under time reversal. In two dimensions, but not in three, the order parameter is odd under 90• spatial rotation. For simplicity we first consider spinless fermions in two dimensions with full rotational symmetry, deferring until later any discussion of spin and the symmetry breaking effects of the crystal fields which are inevitable in actual solids. While many microscopic definitions of this order parameter are possible, we shall see that the natural one in the present context is the quadrupole densitŷ

Singular or non-Fermi liquids

“…That these problems may be discussed in such terms was only realized later, lending to the solutions additional elegance besides insight. 16 See, however, two recent papers [116,200]. In [273] the pseudogap in the underdoped cuprates arises as a consequence of a Landau-Pomeranchuk instability.…”

“…The predictions of (200) have been tested in detail in ARPES measurements only recently. ARPES measures the spectral function In ARPES experiments, the energy distribution curve at ÿxed momentum (EDC) and the momentum distribution curve at ÿxed energy (MDC) can both be measured.…”

Effective field theory of an anomalous Hall metal from interband quantum fluctuations

“…Diagonalization of this susceptibility kernel then leads to the usual transverse and longitudinal polarization modes. 9 Also note that 2D Lindhard function 75 is contained in this function as as a factor since…”

“…Electronic liquid crystal phases, the quantum analogs of classical liquid crystals, have been confirmed in several electronic condensed matter systems such as in quantum Hall fluids, 4,5 stripe and nematic phases in the cuprate superconductors, 2,6 and the ironbased superconductors, 7 and in S 3 Ru 2 O 7 . 8 Among the many possible soft electronic phases, there are those electron fluids that retain their translational symmetry but break orientational isotropy either spatially [9][10][11] and/or internally i.e. the spin degree of freedom [12][13][14] or a band ('pseudo-spin') degree of freedom.…”

Quantum critical metals ind=3+1dimensions

“…We find a wide range of energy scales where the electrons obtain an imaginary self-energy that varies linearly with frequency, signifying 'marginal Fermi liquid' behavior 1 . In d = 3 + 1, one also obtains marginal Fermi liquid behavior from RPA theories starting with Landau damped bosons in the bare action [14][15][16] . By contrast, here, we stress that the marginal Fermi liquid arises in systematic perturbative or large N theories involving undamped bosons, with quite different dynamic and thermodynamic properties.…”