No Arabic abstract
A highlight of Fermi-liquid phenomenology, as explored in neutral $^3$He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this $$transverse zero sound$$ requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable differences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic. We present an experimental setup that should be exquisitely sensitive in this regard: the transmission of terahertz radiation through a thin slab of heavy-fermion material will be strongly enhanced at low temperature and accompanied by giant oscillations, which reflect the interference between light itself and the $$material photon$$ being the actual manifestation of transverse zero sound in the charged Fermi liquid.
The concept of Fermi liquid lays a solid cornerstone to the understanding of electronic correlations in quantum matter. This ordered many-body state rigorously organizes electrons at zero temperature in progressively higher momentum states, up to the Fermi surface. As such, it displays rigidity against perturbations. Such rigidity generates Fermi-surface resonances which manifest as longitudinal and transverse collective modes. Although these Fermi-liquid collective modes have been analyzed and observed in electrically neutral liquid helium, they remain unexplored in charged solid-state systems up to date. In this paper I analyze the transverse shear response of charged three-dimensional Fermi liquids as a function of temperature, excitation frequency and momentum, for interactions expressed in terms of the first symmetric Landau parameter. I consider the effect of momentum-conserving quasiparticle collisions and momentum-relaxing scattering in relaxation-time approximation on the coupling between photons and Fermi-surface collective modes, thus deriving the Fermi-liquid optical conductivity and dielectric function. In the high-frequency, long-wavelength excitation regime the electrodynamic response entails two coherent and frequency-degenerate polaritons, and its spatial nonlocality is encoded by a frequency- and interaction-dependent generalized shear modulus; in the opposite high-momentum low-frequency regime anomalous skin effect takes place. I identify observable signatures of propagating shear collective modes in optical spectroscopy experiments, with applications to the surface impedance and the optical transmission of thin films.
We demonstrate that the plasmon in one-dimensional Coulomb interacting electron fluids can develop a finite-momentum maxon-roton-like nonmonotonic energy-momentum dispersion. Such an unusual nonmonotonicity arises from the strongly interacting $1/r$ Coulomb potential going beyond the conventional band linearization approximation used in the standard bosonization theories of Luttinger liquids. We provide details for the nonmonotonic plasmon dispersion using both bosonization and RPA theories. We also calculate the specific heat including the nonmonotonicity and discuss possibilities for observing the nonmonotonic plasmon dispersion in various physical systems including semiconductor quantum wires, carbon nanotubes, and the twisted bilayer graphene at sub-degree twist angles, which naturally realize one-dimensional domain-wall states.
We predict the enhanced transmissivity of modulated slabs of layered superconductors for terahertz radiation due to the diffraction of the incident wave and the resonance excitation of the eigenmodes. The electromagnetic field is transferred from the irradiated side of a slab of layered superconductor to the other one by excited waveguide modes (WGMs) which do not decay deep into the slab, contrary to metals, where the enhanced light transmission is caused by the excitation of the evanescent surface waves. We show that a series of resonance peaks (with $T sim 1$) can be observed in the dependence of the transmittance $T$ on the varying incidence angle $theta$, when the dispersion curve of the diffracted wave crosses successive dispersion curves for the WGMs.
We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e. unitarity, regime. The Bogoliubov-deGennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and FFLO type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.
Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landaus Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit `strange metal behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal---the d-wave metal. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian---the usual t-J model with electron kinetic energy $t$ and two-spin exchange $J$ supplemented with a frustrated electron `ring-exchange term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.