Spontaneous mass generation due to phonons in a two-dimensional Dirac fermion system

Abstract

Fermions with one and two Dirac nodes are coupled to in-plane phonons to study a spontaneous transition into the Hall insulating phase. At sufficiently strong electron-phonon interaction a gap appears in the spectrum of fermions, signaling a transition into a phase with spontaneously broken parity and time-reversal symmetry. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern-Simons excitations. Evaluating the Kubo formula for both models we find quantized Hall plateaux in each case, with conductance of binodal model exactly twice as large as of the mononodal model.

Position-dependent mass effects on a bilayer graphene catenoid bridge

“…Indeed, the curvature breaks the homogeneity of the lattice which compose the layer, thus modifying the electron effective mass. The PDM can be produced by p − n junctions driven by curvature [28], as well as phonon interactions [29]. Although the position-dependent mass Hamiltonians in flat surfaces are widely studied [30][31][32][33], only recently an extension of the da Costa method including position-dependent mass effects on curved surfaces was proposed [34].…”

Hall viscosity for optical phonons

“…The presence of chiral vector fields through the action Eq. (2) not only results in a change in the expression of the chiral anomaly, ∂ µ J µ 5 = e 2 6π 2 (3B · E + B 5 · E 5 ), but it also modifies the effective acoustic phonon dynamics [13][14][15][16]. In the absence of time-reversal symmetry, a nonozero phonon Hall viscosity (a non-dissipative, parityodd four-rank tensor η H ijlr appearing in the effective continuum elasticity theory) [17,18].…”

Quantum Hall effect induced by electron-phonon interaction

“…In the lattice model the phonon field is attached to each bond while in low-energy approximation the phonon becomes local, is attached to each sublattice and accounts for the scattering between both Dirac nodes. The choice of the phonon part is not arbitrary though, but is dictated by the properties of the C 6v group [29,32] and models the E 1 -in-plane optical modes. The spectrum of these modes reveals a pronounced weak alteration over the entire Brillouin zone [30,33,34], which makes it possible to model them in the form of dispersionless monochromatic lattice vibrations.…”

“…Representation change and variational procedure: Following the procedure developed in Ref. [32] we integrate the phonons A µ , µ = 1, 2, which creates a four-fermion interaction term. The latter can be decoupled anew by 4×4 matrix fields…”

“…with the 32-dimensional real vector field Q assembled from the elements of the matrices Q 1,2 [32]. The stability of each phase follows from the positivity of the Proca matrices D −1 rr ′ ∼ Mδ rr ′ .…”