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Résumé |
Strange metals and bad metals constitute exotic but ubiquitous metallic phases, endowed with anomalous thermodynamic and spectroscopic properties, that do not comply with the conventional Landau Fermi-liquid (FL) paradigm [1,2].
Functional materials such as heavy fermions, pnictides, and high-temperature superconducting cuprates all host strange/bad metallic states of strongly interacting electrons; specifically, these states occur in the crossover region between distinct stable phases, as a function of a non-thermal tuning parameter like chemical doping or pressure. Such tunability suggests the presence of quantum critical points (QCPs) or extended quantum critical phases, i.e., zero-temperature phase transitions in the phase diagram, which engender non-Fermi liquid (NFL) physics at finite temperature through strong fluctuations of an associated soft bosonic mode (e.g., charge/spin density, nematic, or magnetic fluctuations)[1]. These soft modes are characterized by a proper frequency that decreases with decreasing distance from the QCP, and eventually vanishes at the quantum phase transition.
Within this context, the two-dimensional (2D) spatially disordered Yukawa-Sachdev-Ye-Kitaev (YSYK) theory provides an exactly solvable platform to analyze non-Fermi liquid states and their associated phenomenology, microscopically rooted in quantum criticality [3-8]. Specifically, this model entails 2D dispersive fermions and bosons, coupled through interactions that are random in all internal degrees of freedom (“flavours”), and are spatially disordered (contact-like). The theory becomes exactly solvable in the limit of large number of flavours, and after averaging over disordered interactions, yielding self-consistent saddle-point (mean-field) equations analogous to an Eliashberg problem for strong-coupling superconductivity.
As shown in an ongoing series of works, the 2D-YSYK model qualitatively reproduces several unconventional properties of strange metals: a linear-in-temperature (-linear) DC resistivity [9-12], which crosses over into the bad-metal regime when the resistivity becomes larger than the 2D quantum unit ; universal scalings of the optical conductivity as a function of frequency [13], due to a marginal Fermi liquid (MFL) ground state; superconductivity below a critical temperature , maximal when the system is tuned to quantum criticality; a finite superfluid phase stiffness and associated coherence peaks in the superconducting spectral functions, born out of incoherent, NFL normal-state spectra [14-16].
The most recent addition to this survey considers the evolution of normal-state transport in the presence of an applied magnetic field . By exactly solving the interacting Landau-level problem for our 2D-YSYK model with quadratic fermionic dispersion, we find an effective cyclotron resonance frequency in the conductivity that shifts linearly with applied magnetic field and is renormalized by disordered interactions [7], analogously to recent magnetoconductivity experiments on cuprates [17].
In addition, we present exact numerical results for the DC magnetoconductivity tensor
on a square lattice, at first order in applied perpendicular magnetic field [8]. We calculate the longitudinal and Hall conductivities, the Hall coefficient, the carrier mobility, and the cotangent of the Hall angle, at fixed fermion density. From the interplay between YSYK interactions and square-lattice embedding, and the non-Boltzmann frequency-dependent self-energies, we find a superlinear evolution of the Hall-angle cotangent and the inverse carrier mobility with temperature, concomitant with linear-in-temperature resistivity, in an extended crossover regime above the low-temperature MFL ground state. These findings qualitatively agree with the superlinear (-like) behaviour of the Hall angle cotangent [18-20] in cuprates.
References
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