Session A66: Exotic Collective Excitations and Topology-Driven Dynamics in Quantum Materials

Long-Lived Excitations, Directional Memory and Hydrodynamic Transport in Two-Dimensional Electron Fluids

It was found recently that 2D electron fluids can support collective excitations that are not subject to Landau's T² dissipation [1,2,3]. This surprising collective behavior originates from the head-on carrier collisions, a process that dominates angular relaxation at not-too-high temperatures T<<T_F due to the interplay of Pauli blocking and kinematic constraints. As a result, a large family of exceptionally long-lived excitations emerges, associated with the odd-parity harmonics of momentum distribution. This leads to "tomographic" dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The abnormally slow angular relaxation originates from correlated angular dynamics involving "lock-step'' angular displacements along the Fermi surface occurring in collinear two-particle collisions. The slow loss of directional memory is described as non-Brownian angular random walk, "superdiffusion" on the Fermi surface. The collective behavior with directional memory dominates at moderately long times, pushing the onset of conventional hydrodynamics to abnormally large timescales. The tomographic regime features an unusual hierarchy of time scales and scale-dependent transport coefficients manifest in fractional-power current flow profiles and unusual conductance scaling vs. temperature and sample size. This exotic behavior can be directly probed by transport measurement techniques, as well as by momentum-resolved tunneling measurements.
1. P J Ledwith, H Guo, L Levitov, The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases,
Annals of Physics 411, 167913 (2019)
2. P J Ledwith, H Guo, A V Shytov, L Levitov,
Tomographic Dynamics and Scale-Dependent Viscosity in Two-Dimensional Electron Systems,
Phys Rev Lett 123, 116601 (2019)
3. P J Ledwith, H Guo, L Levitov, Angular Dynamics and Directional Memory in Two-Dimensional Electron Fluids,
2019   

Levy flights and non-local transport in Dirac and Weyl systems

We show that hydrodynamic collision processes of Dirac and Weyl systems can be described in terms of a Fokker-Planck equation with fractional derivative, corresponding to a Lévy flight in momentum space. Thus, electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to superdiffusive dynamics of collective excitations. We argue that such superdiffusive dynamics is of more general importance to the out-of-equilibrium dynamics of quantum-critical systems.   

Mirage and hidden collective modes in two dimensional Fermi liquids

I will show that two-particle correlation functions in 2D Fermi liquids have a nontrivial topological structure. The structure manifests itself in two exotic types of zero-sound collective modes: sharp propagating “hidden” modes that cannot be detected by spectroscopy and “mirage” modes that appear as sharp peaks in spectroscopy but don’t determine the Fermi liquid’s response. I will discuss how these features are associated with the existence of a two-sheet Riemann surface defined by the dynamical susceptibility χ(q,ω). The hidden modes reside below the branch cut gluing the sheets, and the illusory modes reside on an unphysical sheet of the Riemann surface. Although neither the existence of a hidden mode, nor the illusory nature of a mirage mode, appear in spectroscopic probes, both can be readily identified in time-dependent measurements in pump-probe configurations.   

Collective modes in pumped unconventional superconductors with competing ground states: Bardasis-Schrieffer mode and time-reversal symmetry broken states

Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band and multiband superconductors, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse can be used to control the symmetry of the non-equilibrium state as well as frequencies and relative intensities of the contributions of different collective modes. We find particularly strong signatures of the Bardasis-Schrieffer mode in the dynamics of the quasiparticle distribution function. In the multiband superconductors we partculary address the collective modes and the short time dynamics of the superconducting state with s + is-wave order parameter using an effective four-band model with two hole and two electron pockets. The amplitude and phase modes are coupled giving rise to a variety of collective modes and we further uncover a new coupled collective soft mode. Our works shows the potential of modern ultrafast experiments to address the collective excitations in unconventional superconductors and highlights the importance of sub-dominant interactions for the non-equilibrium dynamics in these systems.
  

Spectroscopies of superconducting collective modes: new advances and open questions

In the last few years, a number of experiments carried out with very intense THz fields, either in transmission or in pump-probe configuration, have shown the possibility to excite superconducting collective modes via light pulses. The signatures of the superconducting excitations manifest either in third-harmonic generation, in the case of narrowband pulses, or in well-defined oscillations of the transmitted field as a function of the pump-probe delay, in the case of broadband pulses. In the latter case, the phenomenon is completely analogous to the well-known excitations of Raman-active phonons in insulating and metallic systems. Despite the clear interest in the fundamental and applicative aspects of these techniques, a clear theoretical paradigm for the description of these experiments is still lacking. In this talk I will present a general scheme we recently developed [1,2] to describe step-by-step the processes behind the pump-probe detection of collective excitations, that can be equally well applied to ordinary phonons as well as electronic collective modes. I will then discuss a direct application of our interpretative scheme to the light-induced excitation of the so-called superconducting phase Leggett mode in the multi band MgB2 superconductor[2], and its connection to the phenomenon of the third-harmonic generation in superconductors[3,4]. Finally, I will present some recent results [5] on the role of the superconducting phase mode for the non-linear optical response in unconventional curate superconductors.


[1] M. Udina, T. Cea and L. Benfatto, Phys. Rev. B 100, 165131 (2019)
[2] F. Giorgianni, T. Cea, C. Vicario, C. P. Hauri, W. K. Withanage, X. Xi, and L. Benfatto, Nat. Phys. 15, 341 (2019).
[3]T. Cea, C. Castellani, L. Benfatto, Phys. Rev. B 93, 180507(R) (2016)
[4] T. Cea, P. Barone, C. Castellani, L. Benfatto, Phys. Rev. B 97, 094516 (2018)
[5] F. Gabriele and L. Benfatto, preprint 2020.