We develop a non-perturbative approach for calculating the superconducting transition temperatures (\$T\_\c\\$) of liquids. The electron-electron scattering amplitude induced by electron-phonon coupling (EPC), from which the effective pairing interaction can be inferred, is related to the fluctuation of the \$T\$-matrix of electron scattering induced by ions. By applying the relation, EPC parameters can be extracted from a path-integral molecular dynamics simulation. For determining \$T\_\c\\$, the linearized Eliashberg equations are re-established in the non-perturbative context. We apply the approach to estimate \$T\_\c\\$ of metallic hydrogen liquids. It indicates that metallic hydrogen liquids in the pressure regime from \$0.5\$ to \$1.5$\backslash$mathrm\$\backslash$,TPa\\$ have \$T\_\c\\$ well above their melting temperatures, therefore are superconducting liquids.

We derive the definition of the Berry phase for adiabatic transport of a composite Fermion (CF) in a half-filled composite Fermi-liquid (CFL). It is found to be different from that adopted in previous investigations by Geraedts et al. With the definition, the numerical evaluation of the Berry phase becomes robust and free of extraneous phase factors. We show that the two forms of microscopic wave-functions of the CFL, i.e., the Jain-Kamilla type wave function and the standard CF wave function, yield different distributions of the Berry curvature in the momentum space. For the former, the Berry curvature has a continuous distribution inside the Fermi sea and vanishes outside, whereas for the latter, the Berry curvature is uniform in the whole momentum space. To facilitate an analytic derivation for the latter, we reveal a simple structure of standard CF wave functions by establishing their connections to the Segal-Bargmann transform. We conclude that the CF with respect to both the microscopic wave-functions is not a massless Dirac particle.

We study the effects of infrared radiation on a two-dimensional Bardeen–Cooper–Schrieffer superconductor coupled with a normal metal substrate through a tunneling barrier. The phase transition is analyzed by inspecting the stability of the system against perturbations of pairing potentials. We find an oscillating gap phase with a frequency not directly related to the radiation frequency, but instead resulting from the asymmetry of electron density of states of the system as well as the tunneling amplitude. When such a superconductor is in contact with another superconductor, gives rise to an unusual alternating Josephson current .

Conventional wisdom has long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave function. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. While the dissipationless viscosity is the Chern-Simons field counterpart for the Wigner crystal, the Berry curvature is a feature not presented in the conventional composite fermion theory. Hence, contrary to general belief, composite particles follow the more general Sundaram-Niu dynamics instead of the ordinary Newtonian one. We show that the presence of the Berry curvature is an inevitable feature for a dynamics conforming to the dipole picture of composite particles and Kohn's theorem. Based on the dynamics, we determine the dispersions of magnetophonon excitations numerically. We find an emergent magnetoroton mode which signifies the composite-particle nature of the Wigner crystal. It occurs at frequencies much lower than the magnetic cyclotron frequency and has a vanishing oscillator strength in the long-wavelength limit.

The many-body ground state wave function of a fractional Chern insulator (FCI) can be constructed by mapping a fractional quantum Hall state to a FCI state through a substitution of the Bloch state of the flat Chern band for the magnetic Bloch state of the Landau level. There is a gauge freedom in choosing the single particle Bloch basis of the flat Chern band. Instead of considering only one form of interaction in FCI when choosing the gauge as done in previous works, we determine the optimal gauges for FCIs with different forms of interaction, including a short-range interaction, the Coulomb interaction, and an interpolation between them, by applying the variational principle proposed by Zhang et al. [Phys. Rev. B 93, 165129 (2016)]. We find that the optimal gauge strongly depends on the form of interaction. It contradicts with the common belief that the wave function of FCI is not sensitive to the interaction. In comparing the optimal gauge with the previous gauges proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al. [Phys. Rev. B 86, 085129 (2012)], we find Wu et al.'s gauge is close to the optimal one when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases.

We propose a Chern-Simons field theoretical description of the fractional quantum Hall effect in 1+4 dimensions. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from microscopic wave functions, we further show that the momentum manifold has a uniformly distributed Berry curvature. As a result, composite fermions do not follow the ordinary Newtonian dynamics as commonly believed, but the more general symplectic one. For a Landau level with the particle-hole symmetry, the theory correctly predicts its Hall conductance at half-filling as well as the symmetry between an electron filling fraction and its hole counterpart.

We investigate the spin–orbit coupling effect in a two-dimensional (2D) Wigner crystal. It is shown that sufficiently strong spin–orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system. We demonstrate the existence of chiral phonon edge modes in finite size samples, as well as the robustness of the modes in the topological phase. We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure. It is found that the spin–orbit coupling is too weak for driving a topological phase transition in these systems. It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin–orbit coupling.

We derive the phonon dynamics of magnetic metals in the presence of strong spin-orbit coupling. We show that both a dissipationless viscosity and a dissipative viscosity arise in the dynamics. While the dissipationless viscosity splits the dispersion of left-handed and right-handed circularly polarized phonons, the dissipative viscosity damps them differently, inducing circular phonon dichroism. The effect offers a new degree of manipulation of phonons, i.e., the control of the phonon polarization. We investigate the effect in Weyl semimetals. We find that there exists strong circular phonon dichroism in Weyl semimetals breaking both the time-reversal and the inversion symmetry, making them potential materials for realizing the acoustic circular polarizer.

We establish a variational principle for properly mapping a fractional quantum Hall state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground-state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized two-dimensional projected Wannier functions of a Landau level.

Proton transfer through hydrogen bonds plays a fundamental role in many physical, chemical and biological processes. Proton dynamics is susceptible to quantum tunnelling, which typically involves many hydrogen bonds simultaneously, leading to correlated many-body tunnelling. In contrast to the well-studied incoherent single-particle tunnelling, our understanding of many-body tunnelling is still in its infancy. Here we report the real-space observation of concerted proton tunnelling in a cyclic water tetramer using a cryogenic scanning tunnelling microscope. This is achieved by monitoring the reversible interconversion of the hydrogen-bonding chirality of the water tetramer with a chlorine-terminated scanning tunnelling microscope tip. We found that the presence of the Cl anion at the tip apex may either enhance or suppress the concerted tunnelling process, depending on the details of the coupling symmetry between the Cl ion and the protons. Our work opens up the possibility of controlling the quantum states of protons with atomic-scale precision.

We construct a density functional theory for two-dimensional electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the systems form composite fermion liquids. Our theory provides a systematic and rigorous approach to determine the properties of ground states in a fractional quantum Hall regime that is modified by artificial structures. We also propose a practical way to construct an approximated functional.