High-Temperature Superconductivity in the Lanthanide Hydrides at Extreme Pressures

Hydrogen-rich superhydrides are promising high-Tc superconductors, with superconductivity experimentally observed near room temperature, as shown in recently discovered lanthanide superhydrides at very high pressures, e.g., LaH10 at 170 GPa and CeH9 at 150 GPa. Superconductivity is believed to be closely related to the high vibrational modes of the bound hydrogen ions. Here, we studied the limit of extreme pressures (above 200 GPa) where lanthanide hydrides with large hydrogen content have been reported. We focused on LaH16 and CeH16, two prototype candidates for achieving a large electronic contribution from hydrogen in the electron–phonon coupling. In this work, we propose a first-principles calculation platform with the inclusion of many-body corrections to evaluate the detailed physical properties of the Ce–H and La–H systems and to understand the structure, stability, and superconductivity of these systems at ultra-high pressure. We provide a practical approach to further investigate conventional superconductivity in hydrogen-rich superhydrides. We report that density functional theory provides accurate structure and phonon frequencies, but many-body corrections lead to an increase of the critical temperature, which is associated with the spectral weight transfer of the f-states.

Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

Diffusion and Superdiffusion from Hydrodynamic Projections

Hydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green–Kubo formula for the Onsager matrix has a natural expression within the diffusive space. This space is associated with quadratically extensive charges, and projections onto any such charge give generic lower bounds for diffusion. In particular, bilinear expressions in linearly extensive charges lead to explicit diffusion lower bounds calculable from the thermodynamics, and applicable for instance to generic momentum-conserving one-dimensional systems. Bilinear charges are interpreted as covariant derivatives on the manifold of maximal entropy states, and represent the contribution to diffusion from scattering of ballistic waves. An analysis of fractionally extensive charges, combined with clustering properties from the superdiffusion phenomenology, gives lower bounds for superdiffusion exponents. These bounds reproduce the predictions of nonlinear fluctuating hydrodynamics, including the Kardar–Parisi–Zhang exponent 2/3 for sound-like modes, the Levy-distribution exponent 3/5 for heat-like modes, and the full Fibonacci sequence.

Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction

We unravel the out-of-equilibrium quantum dynamics of a few interacting bosonic clouds in a two-dimensional asymmetric double-well potential at the resonant tunneling scenario. At the single-particle level of resonant tunneling, particles tunnel under the barrier from, typically, the ground-state in the left well to an excited state in the right well, i.e., states of different shapes and properties are coupled when their one-particle energies coincide. In two spatial dimensions, two types of resonant tunneling processes are possible, to which we refer to as longitudinal and transversal resonant tunneling. Longitudinal resonant tunneling implies that the state in the right well is longitudinally-excited with respect to the state in the left well, whereas transversal resonant tunneling implies that the former is transversely-excited with respect to the latter. We show that interaction between bosons makes resonant tunneling phenomena in two spatial dimensions profoundly rich, and analyze these phenomena in terms of the loss of coherence of the junction and development of fragmentation, and coupling between transverse and longitudinal degrees-of-freedom and excitations. To this end, a detailed analysis of the tunneling dynamics is performed by exploring the time evolution of a few physical quantities, namely, the survival probability, occupation numbers of the reduced one-particle density matrix, and the many-particle position, momentum, and angular-momentum variances. To accurately calculate these physical quantities from the time-dependent many-boson wavefunction, we apply a well-established many-body method, the multiconfigurational time-dependent Hartree for bosons (MCTDHB), which incorporates quantum correlations exhaustively. By comparing the survival probabilities and variances at the mean-field and many-body levels of theory and investigating the development of fragmentation, we identify the detailed mechanisms of many-body longitudinal and transversal resonant tunneling in two dimensional asymmetric double-wells. In particular, we find that the position and momentum variances along the transversal direction are almost negligible at the longitudinal resonant tunneling, whereas they are substantial at the transversal resonant tunneling which is caused by the combination of the density and breathing mode oscillations. We show that the width of the interparticle interaction potential does not affect the qualitative physics of resonant tunneling dynamics, both at the mean-field and many-body levels. In general, we characterize the impact of the transversal and longitudinal degrees-of-freedom in the many-boson tunneling dynamics at the resonant tunneling scenarios.

Hole probability for non-interacting fermions in a d-dimensional trap

The hole probability, i.e., the probability that a region is void of particles, is a benchmark of correlations in many body systems. We compute analytically this probability P (R) for a sphere of radius R in the case of N noninteracting fermions in their ground state in a d-dimensional trapping potential. Using a connection to the Laguerre-Wishart ensembles of random matrices, we show that, for large N and in the bulk of the Fermi gas, P (R) is described by a universal scaling function of kF R, for which we obtain an exact formula (kF being the local Fermi wave-vector). It exhibits a super exponential tail P (R) / e-κd(kF R)d+1 where κdis a universal amplitude, in good agreement with existing numerical simulations. When R is of the order of the radius of the Fermi gas, the hole probability is described by a large deviation form which is not universal and which we compute exactly for the harmonic potential. Similar results also hold in momentum space.

Ultrafast Multidimensional Spectroscopy with Field Resolution and Noncollinear Geometry at Mid-Infrared Frequencies

Energetic correlations and their dynamics govern the fundamental properties of condensed matter materials. Ultrafast multidimensional spectroscopy in the mid infrared is an advanced technique to study such coherent low-energy dynamics. The intrinsic many-body phenomena in functional solid-state materials, in particular few-layer samples, remain widely unexplored to this date, because complex and weak sample responses demand versatile and sensitive detection. Here, we present a novel setup for ultrafast multidimensional spectroscopy with noncollinear geometry and complete field resolution in the 15-40 THz range. Electric fields up to few-100 kV cm-1 drive coherent dynamics in a perturbative regime, and an advanced modulation scheme allows to detect nonlinear signals down to a few tens of V cm-1 entirely background-free with high sensitivity and full control over the geometric phase-matching conditions. Our system aims at the investigation of correlations and many-body interactions in condensed matter systems at low energy. Benchmark measurements on bulk indium antimonide (InSb) reveal a strong six-wave mixing signal and map ultrafast changes of the band structure with access to amplitude and phase information. Our results pave the way towards the investigation of functional thin film materials and few-layer samples.