Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.
Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.
Black Holes as Tools When confronted with a difficult problem, physicists often resort to mapping it to a more tractable one. A good example of this strategy is provided by new developments linking string theory and condensed-matter physics to make theoretical connections between gravity and complex systems of interacting electrons. This theoretical convergence provides a description of Fermi liquids, which can be thought of as interacting systems of electrons whose excitations can be expressed in terms of non-interacting quasiparticles. Several interesting systems elude quasiparticle description, but Faulkner et al. (p. 1043 , published online 5 August) have now developed a mathematical framework that describes the non-Fermi liquid represented by the strange metal phase of cuprate high-temperature superconductors. They calculate the electronic response and, for a particular value of a tunable parameter, recover the linear resistivity. Further development of this framework may allow elucidation of other exotic properties of the cuprates and similar complex systems.
A class of strongly interacting many-body fermionic systems in 2+1-dimensional nonrelativistic conformal field theory is examined via the gauge-gravity duality correspondence. The five-dimensional charged black hole with asymptotic Schr\"odinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\ensuremath{\beta}$ at zero temperature. On the larger $\ensuremath{\beta}$ side, we find the signal of a sharp quasiparticle pole on the spectral function $A(k,\ensuremath{\omega})$, indicating a well-defined Fermi surface. On the smaller $\ensuremath{\beta}$ side, we find only a hump with no sharp peak for $A(k,\ensuremath{\omega})$, indicating the disappearance of the Fermi surface. The dynamical exponent z of quasiparticle dispersion goes from being Fermi-liquid-like $z\ensuremath{\simeq}1$ scaling at larger $\ensuremath{\beta}$ to a non-Fermi-liquid scaling $z\ensuremath{\simeq}3/2$ at smaller $\ensuremath{\beta}$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.
The authors introduce exactly solvable models of the quantum phase transition, marking the breakdown of the heavy Fermi liquid in heavy-fermion materials. The solutions capture the puzzling non-Fermi liquid transport with linear-in-temperature resistivity, as seen in experiments. Furthermore, they reveal a broad regime in which a ``Planckian'' strange metal is established, namely the quasiparticle lifetime in this regime is set only by fundamental constants and the temperature. The new large-N approach introduced in the paper may be useful for describing a broader class of quantum critical points in systems with strong electronic correlations.
We studied the mysterious behavior of a class of materials known as cuprates, of particular practical interests due to their high transition temperature to a superconducting phase, where electricity is carried without resistance. Due to the strong interactions among the electrons, these systems cannot be described in terms of any conventional theory of metals and new approaches are needed. One such approach is the holographic duality, that allows us to model strongly interacting quantum system through an higher-dimensional, but easier to treat, theory of gravity. In this thesis we used the duality to study certain features of the non-superconducting phase of cuprates, known as the strange metal. We presented how to introduce the long-range Coulomb interaction, that allowed us to model plasmon excitations experimentally observed in multilayer cuprates, and to study a phenomenon of a two-layer system known as Coulomb drag. Furthermore, we showed that a prediction from the duality of a peculiar momentum-dependet scaling of the Fermionic self-energy is able to very accurately model a recently-observed feature of the spectral function measured in high-quality photoemission-spectroscopy measurements on a cuprate.
Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.
Abstract. The normal state metallic behavior above the superconducting transition temperature (Tsc) remains one of the least understood properties since its discovery in cuprates by Bednorz and Müller [1]. Apart from the pseudogap (T ∗) phenomenon above Tsc, there is this T-linear resistivity that was first recognized by Anderson [2] as strange simply because it does not obey the low-temperature T 2 electron-electron scattering rate predicted from the Fermi liquid theory. Here, we prove that the finite temperature continu-ous quantum phase transition (CTQPT) is responsible for the transition from a strange metal to a Fermi liquid for a given chemical composition. Our proof follows the Green function formalism and the energy-level spacing renormal-ization group method. Interestingly, the CTQPT stated above can be related to the proof derived by Parameswaran, Shankar and Sondhi [3], in which, the one-to-one correspondence between the Fermi gas and Fermi liquid is indeed a special case. The theory is further exploited to give unambiguous explanations as to why and how doping gives rise to spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements for the La-Sr-Cu-O system. PACS: 74.72.-h, 71.10.Hf, 74.25.F-, 74.25.Jb 1.