arXiv subjects

Bitan Roy

Publications and source records attributed to Bitan Roy.

123 records · Page 7Linked to original sources

arXiv2014

Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system

The effective theory for bilayer graphene (BLG), subject to parallel/in-plane magnetic fields, is derived. With a sizable magnetic field the trigonal warping becomes irrelevant, and one ends up with two Dirac points in the vicinity of each valley in the low-energy limit, similar to the twisted BLG. Combining twisting and parallel field thus gives rise to a Dirac system with tunable Fermi velocity and cutoff. If the interactions are sufficiently strong, several fully gapped states can be realized in these systems, in addition to the ones in a pristine setup. Transformations of the order parameters under various symmetry operations are analyzed. The quantum critical behavior of various phase transitions driven by the twisting and the magnetic field is reported. The effects of an additional perpendicular fields, and possible ways to realize the new massive phases is highlighted.

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arXiv2013

Classification of massive and gapless phases in bilayer graphene

We here classify of all the fully gapped \emph{massive} and \emph{gapless} phases in bilayer graphene. The effective low energy theory in bilayer graphene is constructed, and various discrete and continuous symmetries of the non-interacting system is analyzed. Spinless fermions, placed in a quantizing magnetic field is considered. The quantum anomalous Hall insulator is properly defined. Constructing a particle-hole doubled 16 component Nambu-Dirac spinor, we recognize all the possible fully gapped, and the gapless states, which, on the other hand, split the parabolic dispersion into two anisotropic Dirac like conical ones. A thorough symmetry analysis of all the ordered states is performed. Altogether there are 8 insulating and 4 superconducting phases in bilayer graphene, that can lead to fully gapped spectrum. Among the gapped superconductors, \emph{three} are spin-singlet, which include uniform s-wave and two spatially inhomogeneous, translational symmetry breaking Kekule superconductors. The triplet pairing exhibits an f-wave symmetry. Besides the gapped phases, there are 8 semimetallic and 8 gapless superconducting states in total, available for fermions to condense into. We also find novel gapless superconducting states, which break the translational symmetry, dubbed as \emph{gapless-Fulde-Farrell-Larkin-Ovchinikov} superconductors. We also discuss the role of Coulomb interaction, and propose various experimental tools to determine the underlying ordered states.

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arXiv2013

Topological insulators in strained graphene at weak interaction

The nature of the electronic ground states in strained undoped graphene at weak interaction between electrons is discussed. After providing a lattice realization of the strain-induced axial magnetic field we numerically find the self-consistent solution for the time reversal symmetry breaking quantum anomalous Hall order-parameter, at weak second-nearest-neighbor repulsion between spinless fermions. The anomalous Hall state is obtained in both uniform and nonuniform axial magnetic fields, with the spatial profile of the order-parameter resembling that of the axial field itself. When the electron spin is included, the time reversal symmetric anomalous spin Hall state becomes slightly preferred energetically at half filling, but the additional anomalous Hall component should develop at a finite doping.

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arXiv2013

Theory of unconventional quantum Hall effect in strained graphene

We show through both theoretical arguments and numerical calculations that graphene discerns an unconventional sequence of quantized Hall conductivity, when subject to both magnetic fields (B) and strain. The latter produces time-reversal symmetric pseudo/axial magnetic fields (b). The single-electron spectrum is composed of two interpenetrating sets of Landau levels (LLs), located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, these two sets of LLs have opposite \emph{chiralities}, resulting in {\em oscillating} Hall conductivity between 0 and $\mp 2 e^2/h$ in electron and hole doped system, respectively, as the chemical potential is tuned in the vicinity of the neutrality point. The electron-electron interactions stabilize various correlated ground states, e.g., spin-polarized, quantum spin-Hall insulators at and near the neutrality point, and possibly the anomalous Hall insulating phase at incommensurate filling $\sim B$. Such broken-symmetry ground states have similarities as well as significant differences from their counterparts in the absence of strain. For realistic strength of magnetic fields and interactions, we present scaling of the interaction-induced gap for various Hall states within the zeroth Landau level.

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arXiv2013

Quantum superconducting criticality in graphene and topological insulators

The field theory of the semimetal-superconductor quantum phase transition for graphene and surface states of topological insulators is presented. The Lagrangian possesses the global U(1) symmetry, with the self-interacting complex bosonic order-parameter and the massless Dirac fermions coupled through a Yukawa term. The same theory also governs the quantum critical behavior of graphene near the transition towards the bond-density-wave (Kekule) insulator. The local U(1) gauged version of the theory which describes the quantum semimetal-superconductor transition in the ultimate critical regime is also considered. Due to the Yukawa coupling the transitions are found to be always continuous, both with and without the fluctuating gauge field. The critical behavior is addressed within the dimensional regularization near four space-time dimensions, and the calculation of various universal quantities, including critical exponents and the universal mass-ratio, is reported.

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arXiv2012

Effective field theory, chiral anomaly and vortex zero modes for odd parity topological superconducting state of three dimensional Dirac materials

The low energy quasiparticle dispersion of various narrow gap and gapless semiconductors are respectively described by three dimensional massive and massless Dirac fermions. The three dimensional Dirac spinor structure admits a time-reversal invariant, odd parity and Lorentz pseudoscalar topological superconducting state. Here we derive the effective field theory of this topological paired state for massless Dirac fermions in the presence of a fluctuating Zeeman term, which appears as a chiral gauge field. The effective theory consists of a mixed electromagnetic and chiral anomaly term in the bulk, and a combination of pure and mixed anomalies for the surface. In this paper we demonstrate the existence of fermion zero modes in the dilute vortex phase under generic conditions. Guided by the existence of the zero modes and its intimate connection with the anomaly, we propose an effective topological field theory in the presence of Dirac mass. We briefly discuss the experimental consequences of the effective field theory and the zero modes for the low temperature unconventional superconducting states of $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$.

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arXiv2012

Conserved charges of order-parameter textures in Dirac systems

A simple expression for the induced fermion current in the presence of a texture in mass-order-parameters in two-dimensional condensed-matter Dirac systems is derived using the representation theory of Clifford algebras. In particular, it is shown that every texture in three mutually anticommuting order parameters, in graphene for example, implies an induced density of a properly defined conserved charge. The sufficient condition for the general charge to be the familiar electrical charge is that the remaining two anticommuting order parameters allowed by the particle-hole symmetry are the two phase components of some superconducting order. This allows eight different types of electrically charged textures in graphene or in the $π$-flux Hamiltonian on the square lattice. Generalized charge of mass-textures on the surfaces of thin films of topological insulators, or in spinless Dirac fermions hopping on the honeycomb lattice is also discussed.

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arXiv2012

Asymmetric spatial structure of zero modes for birefringent Dirac fermions

We study the zero energy modes that arise in an unusual vortex configuration involving both the kinetic energy and an appropriate mass term in a model which exhibits birefringent Dirac fermions as its low energy excitations. We find the surprising feature that the ratio of the length scales associated with states centered on vortex and anti-vortex topological defects can be arbitrarily varied but that fractionalization of quantum numbers such as charge is unaffected. We discuss this situation from a symmetry point of view and present numerical results for a specific lattice model realization of this scenario.

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arXiv2012

Magnetic field induced inequivalent vortex zero modes in strained graphene

Zero energy states in the Dirac spectrum with U(1) symmetric massive vortices of various underlying insulating orders in strained graphene are constructed in the presence of the magnetic field. An easy plane vortex of antiferromagnet and quantum spin Hall orders host two zero energy states, however, with two different length scales. Such inequivalent zero modes can lead to oscillatory charge and magnetization, and their usual quantizations get restored only far from the vortex core. Otherwise, these zero modes can be delocalized from each other by tuning the mutual strength of two fields. One can, therefore, effectively bind a single zero mode in the vortex core. A possible experimental set up to capture signature of this theory in real graphene as well as in optical honeycomb lattices is mentioned. Generalization of this scenario with underlying topological defects of Kekule superconductors can localize a single Majorana mode in the vicinity of the defect-core.

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arXiv2011

Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene

Multi-critical behavior of interacting fermions in graphene's honeycomb lattice is presented. In particular, we considered the spin triplet insulating orders, where the spin rotational symmetry of the order parameter is explicitly broken. By casting the problem in terms of Gross-Neveu-Yukawa theory we show that such symmetry-breaking terms are irrelevant near the metal-insulator critical point. A finite Yukawa coupling among bosons and fermions improves the stability of such critical point against the symmetry-breaking perturbations. Physical sources of such symmetry-breaking terms are pointed out. Critical exponents are calculated near the transitions as well.

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arXiv2011

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.

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arXiv2011

Inhomogeneous magnetic catalysis on graphene's honeycomb lattice

We investigate the ordering instability of interacting (and for simplicity, spinless) fermions on graphene's honeycomb lattice by numerically computing the Hartree self-consistent solution for the charge-density-wave order parameter in presence of both uniform and non-uniform magnetic fields. For a uniform field the overall behavior of the order parameter is found to be in accord with the continuum theory. In the inhomogeneous case, the spatial profile of the order parameter resembles qualitatively the form of the magnetic field itself, at least when the interaction is not overly strong. We find that right at the zero-field critical point of the infinite system the local order parameter scales as the square-root of the local strength of the magnetic field, apparently independently of the assumed field's profile. The finite size effects on various parameters of interest, such as the critical interaction and the universal amplitude ratio of the interaction-induced gap to the Landau level energy at criticality are also addressed.

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arXiv2010

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.

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arXiv2009

Theory of interacting electrons on the honeycomb lattice

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.

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arXiv2008

Quantum critical scaling in magnetic field near the Dirac point in graphene

Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene we discuss the scaling of the interaction-induced gaps in vicinity of the Dirac point with the magnetic field. The gap at f=1 is shown to be bounded from above by E(1)/C, where E(n) are the Landau level energies and C = 5.985 + O(1/N) is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions N. We find a sublinear dependence of the gap at the laboratory magnetic fields for realistic values of short-range repulsion between electrons, and in quantitative agreement with observation.

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