Odd integer quantum Hall effect in graphene

A possible realization of Hall conductivity, quantized at odd integer factors of $e^2/h$ for graphene's honeycomb lattice is proposed. I argue that, in the presence of \emph{uniform} real and pseudo-magnetic fields, the valley degeneracy from the higher Landau levels can be removed. A pseudo-magnetic field may arise from bulging or stretching of the graphene flake. This may lead to observation of plateaus in the Hall conductivity at quantized values $f e^2/h$, with $f=\pm 3, \pm 5$ etc, which have not been observed in measurement of Hall conductivity. However, in a collection of noninteracting Dirac fermions living in the honeycomb lattice subject to real and pseudo field, the zeroth Landau level still enjoys the valley and the spin degeneracy. Upon including the Zeeman coupling, the spin degeneracy is removed from all the Landau levels. The effects of short ranged electron-electron interactions are also considered, particularly, the onsite Hubbard repulsion (U) and the nearest-neighbor Coulomb repulsion (V). Within the framework of the extended Hubbard model with only those two components of finite ranged Coulomb repulsion, it is shown that infinitesimally weak interactions can place the system in a gapped insulating phase by developing a \emph{ferrimegnatic} order, if $U>>V$. Therefore, one may expect to see the plateaus in the Hall conductivity at all the integer values, $f=0,\pm 1,\pm 2, \pm3,...$. Scaling behavior of interaction induced gap at $f=1$ in presence of finite pseudo flux is also addressed. Qualitative discussion on finite size effects and behavior of the interaction induced gap when the restriction on uniformity of the fields are relaxed, is presented as well. Possible experimental set up that can test relevance of our theory has been proposed.Comment: 9 pages, 1 figure, 1 table, Published Versio

Thermoelectric study of dissipative quantum dot heat engines

This paper examines the thermoelectric response of a dissipative quantum dot heat engine based on the Anderson-Holstein model in two relevant operating limits: (i) when the dot phonon modes are out of equilibrium, and (ii) when the dot phonon modes are strongly coupled to a heat bath. In the first case, a detailed analysis of the physics related to the interplay between the quantum dot level quantization, the on-site Coulomb interaction and the electron-phonon coupling on the thermoelectric performance reveals that an n-type heat engine performs better than a p-type heat engine. In the second case, with the aid of the dot temperature estimated by incorporating a {\it{thermometer bath}}, it is shown that the dot temperature deviates from the bath temperature as electron-phonon interaction becomes stronger. Consequently, it is demonstrated that the dot temperature controls the direction of phonon heat currents, thereby influencing the thermoelectric performance. Finally, the conditions on the maximum efficiency with varying phonon couplings between the dot and all the other macroscopic bodies are analyzed in order to reveal the nature of the optimum junction.Comment: 10 pages, 9 figures, To be published in Phys Rev.

Optical conductivity of an interacting Weyl liquid in the collisionless regime

Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed matter systems. We here show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal $\sigma(\Omega)=\sigma_0(\Omega)\left[ 1+\frac{1}{N+1} \right]$, where of $\sigma_0(\Omega)=Ne^2_0 \Omega/(12 h v)$ is the OC in the non-interacting system, with $v$ as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency $\Omega$, and $e_0$ is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes near the Fermi level ($N$), is a remarkable consequence of an intriguing conspiracy among the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl as well as Dirac materials. By contrast, a local density-density interaction produces a non-universal correction to the OC, stemming from the non-renormalizable nature of the corresponding interacting field theory.Comment: 21 Pages, 1 Figure: Published Version in PR

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene

Flat electronic bands can accommodate a plethora of interaction driven quantum phases, since kinetic energy is quenched therein and electronic interactions therefore prevail. Twisted bilayer graphene, near so-called the "magic angles", features \emph{slow} Dirac fermions close to the charge-neutrality point that persist up to high-energies. Starting from a continuum model of slow, but strongly interacting Dirac fermions, we show that with increasing chemical doping away from the charge-neutrality point, a time-reversal symmetry breaking, valley pseudo-spin-triplet, topological $p+ip$ superconductor gradually sets in, when the system resides at the brink of an anti-ferromagnetic ordering (due to Hubbard repulsion), in qualitative agreement with recent experimental findings. The $p+ip$ paired state exhibits quantized spin and thermal Hall conductivities, polar Kerr and Faraday rotations. Our conclusions should also be applicable for other correlated two-dimensional Dirac materials.Comment: 5 Pages, 2 Figures: Published Version in PRB (Supplementary Materials: 4 Pages, Ancillary file

Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter

A spatially non-uniform superconducting phase is proposed as the electronic variational ground state for the attractive interactions between nearest neighbors on graphene's honeycomb lattice, close to and right at the filling one half. The state spontaneously breaks the translational invariance of the lattice into the Kekule pattern of bond order parameters, and it is gapped, spin triplet, and odd under the sublattice exchange. With the increase of attractive interactions we first find the transition from the semimetallic phase into the p-Kekule superconductor, defined as being odd under the exchange of Dirac points, with the additional discontinuous superconductor-superconductor transition into the even s-Kekule state, deep within the superconducting phase. Topological excitations of the Kekule superconductor and its competition with other superconducting states on the honeycomb lattice are discussed.Comment: 8 RevTex pages, 3 figures; typos corrected, published versio