We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. 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.
Conventional wisdom had 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 functio
n. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. Therefore, contrary to the 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 consistent with the dipole picture of composite particles and Kohns theorem. Based on the dynamics, we determine the dispersions of magneto-phonon excitations numerically. We find an emergent magneto-roton 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.
Electrons/atoms can flow without dissipation at low temperature in superconductors/superfluids. The phenomenon known as superconductivity/superfluidity is one of the most important discoveries of modern physics, and is not only fundamentally importan
t, but also essential for many real applications. An interesting question is: can we have a superconductor for heat current, in which energy can flow without dissipation? Here we show that heat superconductivity is indeed possible. We will show how the possibility of the heat superconductivity emerges in theory, and how the heat superconductor can be constructed using recently proposed time crystals. The underlying simple physics is also illustrated. If the possibility could be realized, it would not be difficult to speculate various potential applications, from energy tele-transportation to cooling of information devices.
We obtain a set of general formulae for determining magnetizations, including the usual electromagnetic magnetization as well as the gravitomagnetic energy magnetization. The magnetization corrections to the thermal transport coefficients are explici
tly demonstrated. Our theory provides a systematic approach for properly evaluating the thermal transport coefficients of magnetic systems, eliminating the unphysical divergence from the direct application of the Kubo formula. For an anomalous Hall system, the corrected thermal Hall conductivity obeys the Wiedemann-Franz law.
We propose a surface-edge state theory for half quantized Hall conductance of surface states in topological insulators. The gap opening of a single Dirac cone for the surface states in a weak magnetic field is demonstrated. We find a new surface stat
e resides on the surface edges and carries chiral edge current, resulting in a half-quantized Hall conductance in a four-terminal setup. We also give a physical interpretation of the half quantized conductance by showing that this state is the product of splitting of a boundary bound state of massive Dirac fermions which carries a conductance quantum.
Super-high resolution laser-based angle-resolved photoemission spectroscopy measurements have been carried out on a heavily overdoped (Bi,Pb)2Sr2CuO6 (Tc> 5 K) superconductor. Taking advantage of the high-precision data on the subtle change of the qu
asi-particle dispersion at different temperatures, we develop a general procedure to determine the bare band dispersion and extract the bosonic spectral function quantitatively. Our results show unambiguously that the 70 meV nodal kink is due to the electron coupling with the multiple phonon modes, with a large mass enhancement factor Lamda= 0.42 even in the heavily over-doped regime.
Using the random matrix theory, we investigate the ensemble statistics of edge transport of a quantum spin Hall insulator with multiple edge states in the presence of quenched disorder. Dorokhov-Mello-Pereyra-Kumar equation applicable for such a syst
em is established. It is found that a two-dimensional quantum spin Hall insulator is effectively a new type of one-dimensional (1D) quantum conductor with the different ensemble statistics from that of the ordinary 1D quantum conductor or the insulator with an even number of Kramers edge pairs. The ensemble statistics provides a physical manifestation of the Z2-classification for the time-reversal invariant insulators.
We establish the general form of effective interacting Hamiltonian for LaOFeAs system based on the symmetry consideration. The peculiar symmetry property of the electron states yields unusual form of electron-electron interaction. Based on the genera
l effective Hamiltonian, we determine all the ten possible pairing states. More physical considerations would further reduce the list of the candidates for the pairing state.
We develop a general theory of electric polarization induced by inhomogeneity in crystals. We show that contributions to polarization can be classified in powers of the gradient of the order parameter. The zeroth order contribution reduces to the wel
l-known result obtained by King-Smith and Vanderbilt for uniform systems. The first order contribution, when expressed in a two-point formula, takes the Chern-Simons 3-form of the vector potentials derived from the Bloch wave functions. Using the relation between polarization and charge density, we demonstrate our formula by studying charge fractionalization in a two-dimensional dimer model recently proposed.
Based on standard perturbation theory, we present a full quantum derivation of the formula for the orbital magnetization in periodic systems. The derivation is generally valid for insulators with or without a Chern number, for metals at zero or finit
e temperatures, and at weak as well as strong magnetic fields. The formula is shown to be valid in the presence of electron-electron interaction, provided the one-electron energies and wave functions are calculated self-consistently within the framework of the exact current and spin density functional theory.
