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Bitan Roy

Publications and source records attributed to Bitan Roy.

At least 109 records · Page 6Linked to original sources
arXiv2016

Dirty Weyl semimetals: Stability, phase transition and quantum criticality

We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetal and the phase diagram of dirty double Weyl semimetal at finite energies.

cond-mat.dis-nn↗
arXiv2016

Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions

We study the renormalization group flow of the velocities in the field theory describing the coupling of the massless quasi-relativistic fermions to the bosons through the Yukawa coupling, as well as with both bosons and fermions coupled to a fluctuating $U(1)$ gauge field in two and three spatial dimensions. Different versions of this theory describe quantum critical behavior of interacting Dirac fermions in various condensed-matter systems. We perform an analysis using one-loop $ε-$expansion about three spatial dimensions, which is the upper critical dimension in the problem. In two dimensions, we find that velocities of both charged fermions and bosons ultimately flow to the velocity of light, independently of the initial conditions, the number of fermionic and bosonic flavors, and the value of the couplings at the critical point. In three dimensions, due to the analyticity of the gauge field propagator, both the $U(1)$ charge and the velocity of light flow, which leads to a richer behavior than in two dimensions. We show that all three velocities ultimately flow to a common terminal velocity, which is non-universal and different from the original velocity of light. Therefore, emergence of the Lorentz symmetry in the ultimate infrared regime seems to be a rather universal feature of this class of theories in both two and three dimensions.

hep-th↗
arXiv2016

Half vortex and fractional electrical charge in two dimensions

Despite fermion doubling, a two-dimensional quasi-relativistic spin-1/2 system can still lead to true fractionalization of electrical charge, when a massive ordered phase supports a "half-vortex". Such topological defect is possible when the order parameter in form of Dirac mass is described by two $U(1)$ angles, and each of them winds by an angle $π$ around a point. We demonstrate that such a mass configuration in an eight-dimensional Dirac Hamiltonian exhibits only a single bound zero mode, and therefore binds the charge of $e/2$. In graphene, for example, such an ordered phase is provided by the easy-plane spin-triplet Kekule valence bond solid. We argue that an application of an in-plane magnetic field can cause an excitonic instability toward such ordered phase, even for weak repulsion, when the on-site, nearest-neighbor and second neighbor components of it are of comparable strengths.

cond-mat.mes-hall↗
arXiv2015

Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides

A number of strongly correlated heavy fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions near certain (three) points of the surface Brillouin zone, hereafter referred to as the valleys. In strong perpendicular magnetic fields, the conical Dirac dispersions of these surface states quench onto three sets of Landau levels and we predict various possible hierarchies of incompressible quantum Hall states on the surface of hexaborides. In addition, we address the effects of strong electron-electron interaction within the surface zeroth Landau levels. Specifically, we show that depending on the relative strength of the long-range (Coulomb-type) and the finite-range (Hubbard-type) interactions the ground state can display either a valley-polarized or a valley-coherent distribution of electronic density. We also show that the transition between two valley-polarized states is always discontinuous, while that between a valley-polarized and a valley-coherent phase is continuous. The Zeeman splitting and/or an applied uniaxial strain on the surface can drive the system through various quantum phase transitions and place it in different broken-symmetry phases. Application of uniaxial strain is also shown to considerably modify the precise sequence of quantum Hall states. We also highlight the role of topology in determining the broken symmetry phases, disorder on the surface of topological hexaborides in strong magnetic fields.

cond-mat.mes-hall↗
arXiv2015

Magnetic catalysis and axionic charge-density-wave in Weyl semimetals

Three-dimensional Weyl and Dirac semimetals can support a chiral-symmetry-breaking, fully gapped, charge-density-wave order even for sufficiently weak repulsive electron-electron interactions, when placed in strong magnetic fields. In the former systems, due to the natural momentum space separation of Weyl nodes the ordered phase lacks the translational symmetry and represents an axionic phase of matter, while that in a Dirac semimetal (neglecting the Zeeman coupling) is only a trivial insulator. We present the scaling of this spectral gap for a wide range of subcritical (weak) interactions as well as that of the diamagnetic susceptibility with the magnetic field. A similar mechanism for charge-density-wave ordering at weak coupling is shown to be operative in double and triple-Weyl semimetals, where the dispersion is linear (quadratic and cubic, respectively) for the z (planar) component(s) of the momentum. We here also address the competition between the charge-density-wave and a spin-density-wave orders, both of which breaks the chiral symmetry and leads to gapped spectrum, and show that at least in the weak coupling regime the former is energetically favored. The anomalous surface Hall conductivity, role of topological defects such as axion strings, existence of one-dimensional gapless dispersive modes along the core of such defects, and anomaly cancellation through the Callan-Harvey mechanism are discussed.

cond-mat.mes-hall↗
arXiv2015

Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators

We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac nodes on the surface, but only two of them are energetically degenerate and exhibit an energy offset relative to the third one. With a tunable chemical potential, when the surface states host electron and hole pockets of comparable size, strong interactions may drive this system into rotational symmetry breaking nematic and translational symmetric breaking excitonic spin- or charge-density-wave phases, depending on the relative chirality of the Dirac cones. Taking a realistic surface band structure into account we analyze the associated Ginzburg-Landau theory and compute the mean field phase diagram for interacting surface states. Beyond mean field theory, this system can be described by a two-component isotropic Ashkin-Teller model at finite temperature, and we outline the phase diagram of this model. Our theory provides a possible explanation of recent measurements which detect a two-fold symmetric magnetoresistance and an upturn in surface resistivity with tunable gate voltage in SmB$_6$. Our discussion can also be germane to other cubic topological insulators, such as ytterbium hexaboride (YbB$_6$), plutonium hexaboride (PuB$_6$).

cond-mat.mes-hall↗
arXiv2015

Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals

Three dimensional Dirac semimetals are stable against weak potential disorder, but not against strong disorder. In the language of renormalization group, such stability stems from the irrelevance of weak disorder in the vicinity of the noninteracting Gaussian fixed point. However, beyond a threshold, potential disorder can take Dirac semimetals into a compressible diffusive metallic phase through a quantum phase transition (QPT), where density of states at zero energy, quasiparticle lifetime and metallic conductivity at $T=0$, are finite. Universal behavior of such unconventional QPT is described within the framework of an $ε(=d-2)$-expansion near the lower critical dimension. Various exponents near this QCP are obtained after performing a two loop perturbative expansion in the vanishing replica limit and we demonstrate that the theory is renormalizable at least to two loop order.We argue that such QPT is always continuous in nature, share same university class with a similar transition driven by odd-parity disorder, critical exponents are independent of flavor number of Dirac femrions and thus can be germane to disordered Cd$_3$As$_2$, Na$_3$Bi. Scaling behaviors of various measurable quantities, such as specific heat, density of states across such QPT are proposed.

cond-mat.dis-nn↗
arXiv2014

Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $ν= 0$ and $ν= \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|ν|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $ν= 0$ and $|ν| = 1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.

cond-mat.mes-hall↗
arXiv2014

Surface Theory of a Family of Topological Kondo Insulators

A low-energy theory for the helical metallic states, residing on the surface of cubic topological Kondo insulators, is derived. Despite our analysis being primarily focused on a prototype topological Kondo insulator, Samarium hexaboride (SmB$_6$), the surface theory derived here can also capture key properties of other heavy fermion topological compounds with a similar underlying crystal structure. Starting from an effective mean-field eight-band model in the bulk, we arrive at a low-energy description of the surface states, pursuing both analytical and numerical approaches. In particular, we show that helical Dirac excitations occur near the $\barΓ$ point and the two $\bar{X}$-points of the surface Brillouin zone and generally the energies of the Dirac points display {\it offset} relative to each other. We calculate the dependence of several observables (such as bulk insulating gap, energies of the surface Dirac fermions, their relative position to the bulk gap, etc.) on various parameters in the theory. We also investigate the effect of a spatial modulation of the chemical potential on the surface spectrum and show that this band bending generally results in "dragging down" of the Dirac points deep into the valence band and strong enhancement of Fermi velocity of surface electrons. Comparisons with recent ARPES and quantum oscillation experiments are drawn.

cond-mat.mes-hall↗
arXiv2014

Disordered and interacting parabolic semimetals in two and three dimensions

A clean noninteracting parabolic semimetal is characterized by quadratic band touching between the conduction and the valence bands at isolated diabolic points in the Brillouin zone and describes a fermionic quantum critical system with dynamic exponent z=2. We consider the stability of such a semimetal against electronic interaction and quenched disorder using a perturbative renormalization group analysis for two and three spatial dimensions. For the noninteracting problem infinitesimally weak disorder leads to an Anderson insulator and a diffusive metal respectively in two and three dimensions. On the other hand, the long range Coulomb interaction causes an excitonic instability for the clean interacting problem towards a broken symmetry ground state in both dimensions. Our weak coupling analysis of the combined effects of disorder and interaction suggests the competition between a broken symmetry and a disorder controlled metallic or insulating states, but is inadequate for describing the quantum phase transitions among them. We discuss the relevance of our results for bilayer graphene and some 227 iridate compounds, and identify these materials as promising candidates for exploring novel disorder and interaction controlled quantum critical phenomena.

cond-mat.str-el↗
arXiv2014

Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields

In the presence of axial magnetic fields that can be realized in deliberately buckled monolayer graphene, quasi-relativistic Dirac fermions may find themselves in a variety of broken symmetry phases even for weak interactions. Through a detailed Hartree self-consistent numerical calculation in finite strained graphene with cylindrical and open boundaries we establish the possibility of realizing a charge-density-wave order for the spinless fermions in the presence of weak nearest-neighbor repulsion. Such an instability gives rise to a staggered pattern of average fermionic density between bulk and boundary of the system as well as among two sublattices of graphene, due to the spatial separation of the zero energy states localized on opposite sublattices. Although with fermions spin restored, an unconventional magnetic order driven by the onsite repulsion, possibly leads to the dominant instability at the Dirac point, the proposed charge-density-wave order can nevertheless be realized at finite doping, which is always accompanied by a finite ferromagnetic moment. Additionally, the charge-density-wave phase supports a quantized charge or spin Hall conductivity when its formation away from the Dirac point is further preceded by the appearance of topological anomalous or spin Hall insulator respectively. The topological orders in strained graphene can be supported by weak second neighbor repulsion, for example. Therefore, depending on the relative strength of various short-range components of the Coulomb interaction a number of broken symmetry phases can be realized within the zero energy manifold in strained graphene.

cond-mat.mes-hall↗
arXiv2014

Axionic superconductivity in three dimensional doped narrow gap semiconductors

We consider the competition between the conventional s-wave and the triplet Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the two contending channels are comparable, we find a simultaneously time-reversal and parity violating $p + is$ state at low temperatures, which provides an example of dynamic axionic state of matter. In contradistinction to the time-reversal invariant, topological B-phase, the $p + is$ state possesses gapped Majorana fermions as the surface Andreev bound states, which give rise to an anomalous surface thermal Hall effect. The anomalous gravitational and electrodynamic responses of the $p+is$ state can be described by the $θ$ vacuum structure, where $θ\neq 0$ or $π$.

cond-mat.supr-con↗
arXiv2014

Strain-induced time-reversal odd superconductivity in graphene

Time-reversal symmetry breaking superconductors are exotic phases of matter with fascinating properties, which are, however, encountered rather sparsely. Here we identify the possibility of realizing such a superconducting ground state that exhibits an $f+is$ pairing symmetry in strained graphene. Although the underlying attractive interactions need to be sufficiently strong and comparable in pristine graphene to support such pairing state, we argue that strain can be conducive for its formation even for weak interactions. We show that quantum-critical behavior near the transition is controlled by a multicritical point, characterized by various critical exponents computed here in the framework of an $ε$-expansion near four spacetime dimensions. Furthermore, a vortex in this mixed superconducting state hosts a pair of Majorana fermions supporting a quartet of insulating and superconducting orders, among which topologically nontrivial quantum spin Hall insulator. These findings suggest that strained graphene could provide a platform for the realization of exotic superconducting states of Dirac fermions.

cond-mat.mes-hall↗
arXiv2014

Theory of integer quantum Hall effect in insulating bilayer graphene

A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $ν=0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling $ν=\pm 2$, whereas the remote hopping in BLG yields $ν=\pm 1$ Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at $ν=2$, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.

cond-mat.mes-hall↗
arXiv2014

Zero-modes and global antiferromagnetism in strained graphene

A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Néel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Néel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization this way vanishes, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and non-uniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling), which is exclusively Néel ordered, with zero local magnetization everywhere in the system.

cond-mat.mes-hall↗
arXiv2014

$Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions

We consider the gapless modes along the vortex line of the fully gapped, momentum independent paired states of three-dimensional Dirac fermions. For this, we require the solution of fermion zero modes of the corresponding two-dimensional problem in the presence of a point vortex, in the plane perpendicular to the vortex line. Based on the spectral symmetry requirement for the existence of the zero mode, we identify the appropriate generalized Jackiw-Rossi Hamiltonians for different paired states. A four-dimensional generalized Jackiw-Rossi Hamiltonian possesses spectral symmetry with respect to an antiunitary operator, and gives rise to a single zero mode only for the {\em odd vorticity}, which is formally described by a $Z_2$ index. In the presence of generic perturbations such as chemical potential, Dirac mass, and Zeeman couplings, the associated two-dimensional problem for the odd parity topological superconducting state maps onto {\em two} copies of generalized Jackiw-Rossi Hamiltonian, and consequently an odd vortex binds two Majorana fermions. In contrast, there are no zero energy states for the topologically trivial $s$-wave superconductor in the presence of any chiral symmetry breaking perturbation in the particle-hole channel, such as regular Dirac mass. We show that the number of one-dimensional dispersive modes along the vortex line is also determined by the index of the associated two-dimensional problem. For an axial superfluid state in the presence of various perturbations, we discuss the consequences of the $Z_2$ index on the anomaly equations.

cond-mat.mes-hall↗
arXiv2014

Migdal's theorem and electron-phonon vertex corrections in Dirac materials

Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound ($v_s$) to Fermi ($v_F$) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as $η=v_s/v_F$ as $η\rightarrow 0$, is, however, enhanced by an ultraviolet \emph{logarithmic divergent correction}, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as $v_s/v^0_F$, where $v^0_F$ is the bare Fermi velocity, and small when $v_s \ll v^0_F$. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.

cond-mat.mes-hall↗