Yasufumi Araki

Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories

Abstract Due to effective enhancement of the Coulomb coupling strength in the vacuum-suspended graphene, the system may turn from a semimetal into an insulator by the formation of a gap in the fermionic spectrum. This phenomenon is analogous to the spontaneous breaking of chiral symmetry in the strong-coupling relativistic field theories. We study this “chiral symmetry breaking” and associated collective excitations on graphene in the strong coupling regime by taking U(1) lattice gauge theory as an effective model for graphene. Both compact and non-compact formulations of the U(1) gauge action show chiral symmetry breaking with equal magnitude of the chiral condensate (exciton condensate) in the strong coupling limit, while they start to deviate from the next-to-leading order in the strong coupling expansion. Phase and amplitude fluctuations of the order parameter are also investigated: in particular, a mass formula for the pseudo-Nambu–Goldstone mode ( π -exciton), which is analogous to Gell–Mann–Oakes–Renner relation for the pion in quantum chromodynamics (QCD), is derived from the axial Ward–Takahashi identity. To check the applicability of the effective field theory description, typical energy scales of fermionic and bosonic excitations are estimated by identifying the lattice spacing of the U(1) gauge theory with that of the original honeycomb lattice of graphene.

Chiral gap and collective excitations in monolayer graphene from strong coupling expansion of lattice gauge theory

Using the strong coupling expansion of the compact and noncompact U(1) lattice gauge theories for monolayer graphene, we show analytically that fermion band gap and pseudo-Nambu-Goldstone exciton ({pi} exciton) are dynamically generated due to chiral symmetry breaking. The mechanism is similar to the generation of quark mass and pion excitation in quantum chromodynamics (QCD). We derive a formula for the {pi}-exciton analogous to the Gell-Mann-Oakes-Renner (GOR) relation in QCD. Experimental confirmation of the GOR relation on a suspended monolayer graphene would be a clear evidence of chiral symmetry breaking.

Spin textures and spin-wave excitations in doped Dirac-Weyl semimetals

We study correlations and magnetic textures of localized spins, doped in three-dimensional Dirac semimetals. An effective field theory for magnetic moments is constructed by integrating out the fermionic degrees of freedom. The spin correlation shows a strong anisotropy, originating from spin-momentum locking of Dirac electrons, in addition to the conventional Heisenberg-like ferromagnetic correlation. The anisotropic spin correlation allows topologically nontrivial magnetic excitation textures such as a transient hedgehog state, as well as the ferromagnetic ground state. The spin-wave dispersion in ferromagnetic Weyl semimetal also becomes anisotropic, being less dispersed perpendicular to the magnetization.

Weak localization, spin relaxation, and spin diffusion: Crossover between weak and strong Rashba coupling limits

Disorder scattering and spin-orbit coupling are together responsible for the diffusion and relaxation of spin-density in time-reversal invariant systems. We study spin-relaxation and diffusion in a two-dimensional electron gas with Rashba spin-orbit coupling and spin-independent disorder, focusing on the role of Rashba spin-orbit coupling in transport. Spin-orbit coupling contributes to spin relaxation, transforming the quantum interference contribution to conductivity from a negative weak localization (WL) correction to a positive weak anti-localization (WAL) correction. The importance of spin channel mixing in transport is largest in the regime where the Bloch state energy uncertainty

Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice

\hbar/\tau

Strong coupling expansion in a correlated three-dimensional topological insulator

and the Rashba spin-orbit splitting

Skyrmion-induced anomalous Hall conductivity on topological insulator surfaces

\Delta_\mathrm{SO}

Effect of Strong Coulomb Interaction in a Three-Dimensional Topological Insulator

are comparable. We find that as a consequence of this spin channel mixing, the WL-WAL crossover is non-monotonic in this intermediate regime, and use our results to address recent experimental studies of transport at two-dimensional oxide interfaces.

Chiral symmetry of graphene and strong coupling lattice gauge theory

Phase structure of monolayer graphene is studied on the basis of a U(1) gauge theory defined on the honeycomb lattice. Motivated by the strong coupling expansion of U(1) lattice gauge theory, we consider on-site and nearest-neighbor interactions between the fermions. When the on-site interaction is dominant, the sublattice symmetry breaking (SLSB) of the honeycomb lattice takes place. On the other hand, when the interaction between nearest neighboring sites is relatively strong, there appears two different types of spontaneous Kekule distortion (KD1 and KD2), without breaking the sublattice symmetry. The phase diagram and phase boundaries separating SLSB, KD1 and KD2 are obtained from the mean-field free energy of the effective fermion model. A finite gap in the spectrum of the electrons can be induced in any of the three phases.

SO(5) symmetry in the quantum Hall effect in graphene

Motivated by recent studies which show that topological phases may emerge in strongly correlated electron systems, we theoretically study the strong electron correlation effect in a three-dimensional topological insulator, which effective Hamiltonian can be described by the Wilson fermions. We adopt 1/r long-range Coulomb interaction as the interaction between the bulk electrons. Based on the U(1) lattice gauge theory, the strong coupling expansion is applied by assuming that the effective interaction is strong. It is shown that the effect of the Coulomb interaction is equivalent to the renormalization of the bare mass of the Wilson fermions, and that as a result, the topological insulator phase survives in the strong coupling limit.