# Tapash Chakraborty - University of Manitoba

## Contact Details

NameTapash Chakraborty |
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AffiliationUniversity of Manitoba |
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CityWinnipeg |
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CountryCanada |
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## Pubs By Year |
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## Pub CategoriesPhysics - Mesoscopic Systems and Quantum Hall Effect (45) Physics - Materials Science (7) Physics - Computational Physics (1) Physics - Chemical Physics (1) Physics - Strongly Correlated Electrons (1) Physics - Soft Condensed Matter (1) |

## Publications Authored By Tapash Chakraborty

Landau level mixing plays an important role in the Pfaffian (or anti-Pfaffian) states. In ZnO the Landau level gap is essentially an order of magnitude smaller than that in a GaAs quantum well. We introduce the screened Coulomb interaction in a single Landau level to tackle that situation. Read More

The electronic states and optical transitions of a ZnO quantum ring containing few interacting electrons in an applied magnetic field are found to be very different from those in a conventional semiconductor system, such as a GaAs ring. The strong Zeeman and Coulomb interaction of the ZnO system, exert a profound influence on the electron states and on the optical properties of the ring. In particular, our results indicate that the Aharonov-Bohm (AB) effect in a ZnO quantum ring strongly depends on the electron number. Read More

Even denominator fractional quantum Hall states in a ZnO quantum well reveal interesting phase transitions in a tilted magnetic field. We have analyzed the planar electron gas in ZnO, confined in a parabolic potential in the third dimension, perpendicular to the plane of the electron gas. Since the Landau level gap is very small in this system we have included the screened Coulomb potential in order to include the effects of all the Landau levels. Read More

We have investigated the electronic states of planar quantum dots at the ZnO interface containing a few interacting electrons in an externally applied magnetic field. In these systems, the electron-electron interaction effects are expected to be much stronger than in traditional semiconductor quantum systems, such as in GaAs or InAs quantum dots. In order to highlight that stronger Coulomb effects in the ZnO quantum dots, we have compared the energy spectra and the magnetization in this system to those of the InAs quantum dots. Read More

We have studied the dynamical polarization and collective excitations in an anisotropic two-dimensional system undergoing a quantum phase transition with merging of two Dirac points. Analytical results for the one-loop polarization function are obtained at the finite momentum, frequency, and chemical potential. The evolution of the plasmon dispersion across the phase transition is then analyzed within the random phase approximation. Read More

We have analyzed the crucial role the Coulomb interaction strength plays on the even and odd denominator fractional quantum Hall effects in a two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system, the Landau level gaps are much smaller than those in conventional GaAs systems. The Coulomb interaction is also very large compared to the Landau level gap even in very high magnetic fields. Read More

We have investigated the possible presence of Majorana fermions in a semiconductor quantum ring containing a few interacting electrons, and a strong spin-orbit interaction, proximity coupled to an s-wave superconductor. We have found that for rings with sizes of a few hundred angstroms and for certain values of the chemical potential and the entire range of the magnetic field, there are strong indications of the presence of Majorana fermions. In particular, the ground state energies and the average electron numbers for the states with even and odd electron numbers are almost identical. Read More

We have analyzed the effects of the anisotropic energy bands of phosphorene on magnetoroton branches for electrons and holes in the two Landau levels close to the band edges. We have found that the fractional quantum Hall effect gap in the lowest (highest) Landau level in conduction (valance) band is slightly larger than that for conventional semiconductor systems and therefore experimentally observable. We also found that the magnetoroton mode for both electrons and holes consists of two branches with two minima due to the anisotropy. Read More

We study the ground states and low-energy excitations of a generic Dirac material with spin-orbit coupling and a buckling structure in the presence of a perpendicular magnetic field. The ground states can be classified into three types under different conditions: SU(2), easy-plane, and Ising quantum Hall ferromagnets. For the SU(2) and the easy-plane quantum Hall ferromagnets there are goldstone modes in the collective excitations, while all the modes are gapped in an Ising-type ground state. Read More

We have investigated the effects of long-range Coulomb interaction on the topological superconducting phase in a quasi-one dimensional semiconductor wire, proximity coupled to a s-wave using the exact diagonalization approach. We find that in accordance with previous studies the addition of Coulomb interaction results in an enlargement of the region of parameter values where topological superconductivity can be observed. However, we also find that although the interaction decreases the bulk gap for values of the magnetic field close to the phase transition point, for moderate magnetic fields away from the transition point, the interaction actually enhances the bulk gap which can be important for observation of topological superconductivity in this system. Read More

We study theoretically the properties of buckled graphene-like materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influences the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in magnetic flux quantum is a rational number, ? = p/q, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. Read More

In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, in which we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. Read More

We report on our studies of fractal butterflies in biased bilayer graphene in the fractional quantum Hall effect (FQHE) regime. We have considered the case when the external periodic potential is present in one layer and have illustrated the effect of varying both the periodic potential strength and the bias voltage on the FQHE and the butterfly energy gaps. Interestingly, the butterfly spectra exhibits remarkable phase transitions between the FQHE gap and the butterfly gap for chiral electrons in bilayer graphene, by varying either the periodic potential strength or the bias voltage. Read More

The magnetization of anisotropic quantum dots in the presence of the Rashba spin-orbit interaction has been studied for three interacting electrons in the dot. We observe unique behaviors of magnetization that are direct reflections of the anisotropy and the spin-orbit interaction parameters independently or concurrently. In particular, there are saw-tooth structures in the magnetic field dependence of the magnetization, as caused by the electron-electron interaction, that are strongly modified in the presence of large anisotropy and high strength of the spin-orbit interactions. Read More

Recent experiments on the role of electron-electron interactions in fractal Dirac systems have revealed a host of interesting effects, in particular, the unique nature of the magnetic field dependence of butterfly gaps in graphene. The novel gap structure observed in the integer quantum Hall effect is quite intriguing [Nat. Phys. Read More

We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic properties of monolayer and bilayer graphene that helped to detect experimentally the fractal nature of the energy spectrum. We have discussed the theoretical background on the Moir\'e pattern in graphene. Read More

We report on the influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene. We have shown that for two values of the magnetic flux per unit cell (one-half and one-third flux quantum) an increase of the periodic potential strength results in a closure of the FQHE gap and appearance of gaps due to the periodic potential. In the case of one-half flux quantum this causes a change of the ground state and consequently the change of the momentum of the system in the ground state. Read More

We report on the fractional quantum Hall states of germanene and silicene where one expects a strong spin-orbit interaction. This interaction causes an enhancement of the electron-electron interaction strength in one of the Landau levels corresponding to the valence band of the system. This enhancement manifests itself as an increase of the fractional quantum Hall effect gaps compared to that in graphene and is due to the spin-orbit induced coupling of the Landau levels of the conduction and valence bands, which modifies the corresponding wave functions and the interaction within a single level. Read More

We have studied the exciton states in a CdTe quantum ring in an external magnetic field containing a single magnetic impurity. We have used the multiband approximation which includes the heavy hole - light hole coupling effects. The electron-hole spin interactions and the s, p-d interactions between the electron, hole and the magnetic impurity are also included. Read More

The intrinsic geometric degree of freedom that was proposed to determine the optimal correlation energy of the fractional quantum Hall states, is analyzed for quantum confined planar electron systems. One major advantage in this case is that the role of various unimodular metrics resulting from the absence of rotational symmetry can be investigated independently or concurrently. For interacting electrons in our system, the confinement metric due to the anisotropy shifts the minimum of the ground state and the low-lying excited states from the isotropic case much more strongly than the corresponding shift due to the unimodular Galilean metric. Read More

**Affiliations:**

^{1}Georgia State University,

^{2}University of Manitoba

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum have been studied. Our studies indicate that the effects of the interaction depend strongly on the amplitude of the periodic potential. For large amplitudes the interaction effects are small and the properties of the system are primarily determined by the periodic potential but for small amplitudes the interaction greatly influences the band gap. Read More

Coulomb interaction among electrons is found to have profound effects on the electronic properties of anisotropic quantum dots in a perpendicular external magnetic field, and in the presence of the Rashba spin-orbit interaction. This is more evident in optical transitions, which we find in this system to be highly anisotropic and super-intense, in particular, for large values of the anisotropy parameter. Read More

We report on the properties of incompressible states of Dirac fermions in graphene in the presence of anisotropic interactions and a quantizing magnetic field. We introduce the necessary formalism to incorporate the anisotropy in the system. The incopmpressible state in graphene is found to survive the anisotropy upto a critical value of the anisotropy parameter. Read More

The relativistic-like behavior of electrons in graphene significantly influences the interaction properties of these electrons in a quantizing magnetic field, resulting in more stable fractional quantum Hall effect states as compared to those in conventional (non-relativistic) semiconductor systems. In bilayer graphene the interaction strength can be controlled by a bias voltage and by the orientation of the magnetic field. The finite bias voltage between the graphene monolayers can in fact, enhance the interaction strength in a given Landau level. Read More

We have studied the tachyonic excitations in the junction of two topological insulators in the presence of an external magnetic field. The Landau levels, evaluated from an effective two-dimensional model for tachyons, and from the junction states of two topological insulators, show some unique properties not seen in conventional electrons systems or in graphene. The $\nu=1/3$ fractional quantum Hall effect has also a strong presence in the tachyon system. Read More

We have considered a system of two topological insulators and have determined the properties of the surface states at the junction. Here we report that these states, under certain conditions exhibit superluminous (tachyonic) dispersion of the Dirac fermions. Although superluminal excitations are known to exist in optical systems, this is the first demonstration of possible tachyonic excitations in a purely electronic system. Read More

The effect of mispair on charge transport in a DNA of sequence (GC)(TA)_N(GC)_3 connected to platinum electrodes is studied using the tight-binding model. With parameters derived from ab initio density functional result, we calculate the current versus bias voltage for DNA with and without mispair and for different numbers of (TA) basepairs N between the single and triple (GC) basepairs. The current decays exponentially with $N$ under low bias but reaches a minimum under high bias when a multichannel transport mechanism is established. Read More

We have investigated the electronic properties of elliptical quantum dots in a perpendicular external magnetic field, and in the presence of the Rashba spin-orbit interaction. Our work indicates that the Fock-Darwin spectra display strong signature of Rashba spin-orbit coupling even for a low magnetic field, as the anisotropy of the quantum dot is increased. An explanation of this pronounced effect with respect to the anisotropy is presented. Read More

From our theoretical studies of resonant Raman transitions in two-electron quantum dots (artificial helium atoms) we show that in this system, the singlet-triplet Raman transitions are allowed (in polarized configuration) only in the presence of spin-orbit interactions. With an increase of the applied magnetic field this transition dominates over the singlet-singlet and triplet-triplet transitions. This intriguing effect can therefore be utilized to tune Raman transitions as well as the spin-orbit coupling in few-electron quantum dots. Read More

**Affiliations:**

^{1}Georgia State University,

^{2}University of Manitoba

Trilayer graphene in the fractional Quantum Hall Effect regime displays a set of unique interaction-induced transitions that can be tuned entirely by the applied bias voltage. These transitions occur near the anti-crossing points of two Landau levels. In a large magnetic field ($> 8$ T) the electron-electron interactions close the anti-crossing gap, resulting in some unusual transitions between different Landau levels. Read More

**Affiliations:**

^{1}Georgia State University,

^{2}University of Manitoba

We have studied the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently. Our studies indicate that the fractional quantum Hall states should indeed be observable in the surface Landau levels of a topological insulator. The strength of the effect will however be different, compared to that in graphene, due to the finite thickness of the topological insulator film and due to the admixture of Landau levels of the two surfaces of the film. Read More

With the help of the quantum chemistry methods we have investigated the nature of interlayer interactions between graphene fragments in different stacking arrangements (AA and AB). We found that the AB stacking pattern as the ground state of the system, is characterized by the effective inter-band orbital interactions which are barely present in the AA. Their vanishing induces electronic decoupling between the graphene layers, so that the bonding interaction $\Delta E_{oi}$ between the flakes is drastically reduced from -0. Read More

We demonstrate theoretically that hydrogenation and annealing applied to nanoscale carbon structures play a crucial role in determining the final shape of the system. In particular, graphene flakes characterized by the linear and non-hydrogenated zigzag or armchair edges have high propensity to merge into a bigger flake or a nanotube (the formation of a single carbon-carbon bond lowers the total energy of the system by up to 6.22 eV). Read More

Here we show that the Pfaffian state proposed for the $\frac52$ fractional quantum Hall states in conventional two-dimensional electron systems can be readily realized in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. Read More

We have explored the electronic properties of stacked graphene flakes with the help of the quantum chemistry methods. We found that the behavior of a bilayer system is governed by the strength of the repulsive interactions that arise between the layers as a result of the orthogonality of their $\pi$ orbitals. The decoupling effect, seen experimentally in AA stacked layers is a result of the repulsion being dominant over the orbital interactions and the observed layer misorientation of 2$^{\circ}-5^{\circ}$ is an attempt by the system to suppress that repulsion and stabilize itself. Read More

Misoriented bilayer graphene with commensurate angles shows unique magneto-optical properties. The optical absorption spectra of such a system strongly depend on the angle of rotation. For a general commensurate twist angle the absorption spectra has a simple single-peak structure. Read More

The quantum Hall effects, discovered about thirty years ago have remained one of the most spectacular discoveries in condensed matter physics in the past century. Those discoveries triggered huge expansion in the field of low-dimensional electronic systems, the area grew at an unprecedented rate and continues to expand. Novel and challenging observations, be it theoretical or experimental, have been reported since then on a regular basis. Read More

We describe the gated bilayer graphene system when it is subjected to intense terahertz frequency electromagnetic radiation. We examine the electron band structure and density of states via exact diagonalization methods within Floquet theory. We find that dynamical states are induced which lead to modification of the band structure. Read More

Graphene, a single atomic layer of graphite, first isolated in 2004, has made a quantum leap in the exploration of the physics of two-dimensional electron systems. Since the initial report of its discovery, many thousands of papers have been published, attempting to explain every aspect of the exotic electronic properties of this system. The graphene euphoria has culminated with the 2010 Nobel Prize in physics being awarded jointly to Andre Geim and Konstantin Novoselov of the University of Manchester, UK, "for groundbreaking experiments regarding the two-dimensional material graphene". Read More

The nature of electron correlations in bilayer graphene has been investigated. An analytic expression for the radial distribution function is derived for an ideal electron gas and the corresponding static structure factor is evaluated. We also estimate the interaction energy of this system. Read More

Here we report from our theoretical studies that in biased bilayer graphene, one can induce phase transitions from an incompressible fractional quantum Hall state to a compressible state by tuning the bandgap at a given electron density. The nature of such phase transitions is different for weak and strong inter-layer coupling. Although for strong coupling more levels interact there are lesser number of transitions than for the weak coupling case. Read More

The electron and hole states in a CdTe quantum dot containing a single magnetic impurity in an external magnetic field are investigated, using the multiband approximation which includes the heavy hole-light hole coupling effects. The electron-hole spin interactions and s,p-d interactions between the electron, the hole and the magnetic impurity are also included. The exciton energy levels and optical transitions are evaluated using the exact diagonalization scheme. Read More

Discoveries of graphene and graphane possessing unique electronic and magnetic properties offer a bright future for carbon based electronics, with future prospects of superseding silicon in the semiconductor industry. Read More

Here we report from our theoretical studies that in biased bilayer graphene, one can induce phase transitions from an incompressible state to a compressible state by tuning the bandgap at a given electron density. Likewise, variation of the density with a fixed bandgap results in a transition from the FQHE states at lower Landau levels to compressible states at intermediate Landau levels and finally to FQHE states at higher Landau levels. This intriguing scenario of tunable phase transitions in the fractional quantum Hall states is unique to bilayer graphene and never before existed in conventional semiconductor systems. Read More

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. Read More

We have investigated the Coulomb screening properties and plasmon spectrum in a bilayer graphene under a perpendicular electric bias. The bias voltage applied between the two graphene layers opens a gap in the single particle energy spectrum and modifies the many-body correlations and collective excitations. The energy gap can soften the plasmon modes and lead to a crossover of the plasmons from a Landau damped mode to being undamped. Read More

The electronic and magnetic properties of graphane with H-vacancies are investigated with the help of quantum-chemistry methods. The hybridization of the edges is found to be absolutely crucial in defining the size of the bandgap, which is increased from 3.04 eV to 7. Read More

We have theoretically investigated the electronic and magnetic properties of graphene whose zigzag edges are oxidized. The alteration of these properties by adsorption of $\mathrm{H_{2}O}$ and $\mathrm{NH_3}$ molecules have been considered. It was found that the adsorbed molecules form a cluster along the oxidized zigzag edges of graphene due to interaction with the electro-negative oxygen. Read More

The effect of Rashba spin-orbit (SO) interaction on the hole states in a quantum dot is studied in the presence of an external magnetic field. We demonstrate here that the Rashba SO coupling has a profound effect on the energy spectrum of the holes revealing level repulsions between the states with the same total momentum. We also show that the resulting spin-orbit gap is much larger than the corresponding one for the electron energy levels in a quantum dot. Read More

We propose a unique way to control both bandgap and the magnetic properties of nanoscale graphene, which might prove highly beneficial for application in nanoelectronic and spintronic devices. We have shown that chemical doping by nitrogen along a single zigzag edge breaks the sublattice symmetry of graphene. This leads to the opening of a gap and a shift of the molecular orbitals localized on the doped edge in such a way that the spin gap asymmetry, which can lead to half-metallicity under certain conditions, is obtained. Read More