Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect

Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal invariant gauge field, leading to the formation of pseudo-Landau levels (PLL). Here we study periodic pseudo-magnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, due to the strain superlattice and PLL electronic structure, a valley-ordered state spontaneously breaking time-reversal and realizing a quantum Hall phase is favored, while others are suppressed.Comment: 13 pages + 2 appendices, 9 figure

Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node

Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum space. The nematic superconductor generally has a full quasi-particle gap, whereas the chiral superconductor with a three-dimensional (3D) Fermi surface has point nodes with lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk and topological Majorana arcs on the surface.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published versio

Three-Dimensional Majorana Fermions in Chiral Superconductors

Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs$_4$Sb$_{12}$ and related materials as promising candidates for non-unitary chiral superconductors hosting three-dimensional Majorana fermions.Comment: 12 pages, 3 figures + appendices; published versio

Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory shades light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene

Vacuum induced Berry phases in single-mode Jaynes-Cummings models

Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquire the photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even the filed is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with cavity quantum electrodynamics (QED) system is designed to detect the vacuum-induced Berry phase.Comment: 10 pages, 4 figures

Tunable Quantum Fluctuation-Controlled Coherent Spin Dynamics

Temporal evolution of a macroscopic condensate of ultra cold atoms is usually driven by mean field potentials, either due to scattering between atoms or due to coupling to external fields; and coherent quantum dynamics have been observed in various cold-atom experiments. In this article, we report results of studies of a class of quantum spin dynamics which are purely driven by zero point quantum fluctuations of spin collective coordinates. Unlike the usual mean-field coherent dynamics, quantum fluctuation-controlled spin dynamics or QFCSD studied here are very sensitive to variation of quantum fluctuations and can be tuned by four to five order of magnitude using optical lattices. They have unique dependence on optical lattice potential depths and quadratic Zeeman fields. QFCSD can be potentially used to calibrate quantum fluctuations and investigate correlated fluctuations and various universal scaling properties near quantum critical points.Comment: 14 pages, 12 figures included; including detailed discussions on thermal effects, trapping potentials and spin exchange losses. (To appear in PRA

Quantum fluctuation-induced uniaxial and biaxial spin nematics

It is shown that zero point quantum fluctuations (ZPQFs) completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin 2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry ${Dih}_4$. There is a novel first order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of $^{87}Rb$ atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.Comment: 4 pages, 2 figures included; published versio

The Luminosity - E_p Relation within Gamma--Ray Bursts and Implications for Fireball Models

Using a sample of 2408 time-resolved spectra for 91 BATSE gamma-ray bursts (GRBs) presented by Preece et al., we show that the relation between the isotropic-equivalent luminosity (L_iso) and the spectral peak energy (E_p) in the cosmological rest frame, L_iso \propto E_p^2, not only holds within these bursts, but also holds among these GRBs, assuming that the burst rate as a function of redshift is proportional to the star formation rate. The possible implications of this relation for the emission models of GRBs are discussed. We suggest that both the kinetic-energy-dominated internal shock model and the magnetic-dissipation-dominated external shock model can well interpret this relation. We constrain the parameters for these two models, and find that they are in a good agreement with the parameters from the fittings to the afterglow data (abridged).Comment: 3 pages plus 5 figures, emulateapj style, accepted for publication in ApJ Letter