arXiv subjects

M. V. Milovanović

Publications and source records attributed to M. V. Milovanović.

17 recordsLinked to original sources

arXiv2025

Pair density wave in the fractional quantum Hall effect at even denominator

The fractional quantum Hall effect (FQHE) at filling 5/2, which is usually understood as a $p$-wave paired state of underlying quasiparticles - composite fermions, transforms into a nematic phase under pressure \cite{csathy0, csathy}. A pair density wave (PDW) may be a precursor, underlying state for this behaviour, and such state(s) were proposed that maintain the weak-pairing feature of the uniform paired state \cite{frad}. Based on considerations in the weak-coupling regime of a microscopic description of the pairing phase (to mimic the phase as it gives way to a nematic phase in the experiments), we argue that the ensuing and relevant PDW state has a strong-pairing character. Furthermore, due to the existence of a single collective mode associated with the order parameter in the uniform paired phase, in the weak-coupling regime, the $p$-wave paired state, in general (for example, in the superconducting state of electrons), may be prone to a PDW instability.

cond-mat.str-el↗

arXiv2024

Topological pairing of composite fermions via criticality

The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator, 5/2, occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper pairing of underlying quasiparticles, composite fermions (CFs), leads to the explanation of this effect. Such a state should have a Pfaffian form of the BCS wave function (due to the absence of spin) and non-Abelian statistics of possible vortex-like excitations (due to the $p$-wave nature of the pairing). Here we expose the origin of pairing by using the effective dipole representation of the problem and show that pairing is encoded in a Hamiltonian that describes the interaction of the charge density with dipoles i.e. the current of CFs. The necessary condition for the paired state to exist is the effective dipole physics at the Fermi level as a consequence of the non-trivial topology of the ideal band in which electrons live - a Landau level (LL); the paired state is a resolution of the unstable, critical behaviour characterized by the distancing of correlation hole with respect to electron (and thus dipole) at the Fermi level due to the topology. We describe analytically this deconfined critical point, at which deconfinement of Majorana neutral fermions takes place. In the presence of large, short-range repulsive interaction inside a LL, the critical behavior may be stabilized into a regularized Fermi-liquid-like (FLL) state, like the one that characterizes the physics in the lowest LL (LLL), but in general, for an interaction with slowly decaying pseudopotentials, the system is prone to pairing.

cond-mat.str-el↗

arXiv2023

Dipole representation of half-filled Landau level

We introduce a variant of dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under exchange of particles and holes. This is implemented by a special constraint on composite fermion and composite hole degree of freedom (of an enlarged space), that makes the resulting composite particle, dipole, a symmetric object. We study an effective Hamiltonian, that commutes with the constraint on the physical space, and fulfills the requirement for boost invariance on the Fermi level. The calculated Fermi liquid parameter F2 is in a good agreement with numerical investigations in [Phys. Rev. Lett. 121, 147601 (2018)].

cond-mat.mes-hall↗

arXiv2019

Model interactions for Pfaffian paired states based on Chern-Simons field theory description

On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore - Read) state, and derive a general form of the model interaction in the case of PH Pfaffian. More than one Landau level is needed to establish the correlations of the PH Pfaffian, and we present the values of relevant three-body pseudo-potentials for two Landau levels.

cond-mat.str-el↗

arXiv2017

Excitonic physics in a Dirac quantum dot

We present a description of vacuum polarization in a circular Dirac quantum dot in two spatial dimensions assuming $α$ - the relative strength of the Coulomb interaction small enough to render an approximation with a single electron (hole) lowest energy level relevant. Applying this approximation, we find that for $ α_c \approx 1.05$ the lowest level is half-filled irrespective of the number of flavors that are present. The ground state can be represented as a superposition of particular (even number) excitonic states which constitute an excitonic cloud that evolves in a crossover manner. The ground state is degenerate with an intervalley excitonic state at $ α_c \approx 1.05$, a critical strength, that in our approximation marks a point with single electron and exciton resonances.

cond-mat.mes-hall↗

arXiv2017

Paired states in half-filled Landau levels

We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as {\em critical states} i.e. states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.

cond-mat.str-el↗

arXiv2015

Generalized Bloch theorem and topological characterization

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with translational group. Based on a group theory analysis we present generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

cond-mat.mes-hall↗

arXiv2014

Effective description of Chern insulators

The Berry curvature in Chern insulators appears to be a non-gauge-invariant quantity and does not immediately allow local length characterization. However, in two examples of 2- and 3-band models that we discuss, we find high-symmetry points in the Brillouin zone that have Berry curvature invariant under diagonal gauge transformations, and may serve as expansion points of geometrical description. On the basis of the geometrical description, in the case of Dirac based 2-band Chern insulators like Haldane model we conclude that the characteristic length based on the value of the Berry curvature at the expansion point plays the role of the magnetic length in the expression for the Hall viscosity. In the case of 2-band models the characteristic "cyclotron" spin is equal to 1/2, while in the 3-band kagome case this spin is likely non-quantized and non-universal.

cond-mat.mes-hall↗

arXiv2012

On the coexistence of antiferromagnetism and d + i d superconducting correlations in the graphene bilayer

We discuss t-J-U model on a honeycomb monolayer that has the same low-energy description of the kinetic term as graphene bilayer, and in particular study coexistence of antiferromagnetism and superconducting correlations that originate from Cooper pairs without phase coherence. We show that the model is relevant for the description of graphene bilayer and that the presence of the d + i d superconducting correlations with antiferromagnetism can lead to quadratic dependence in small magnetic fields of the gap of the effective monolayer consistent with the transport measurements of Velasco et al. on the graphene bilayer.

cond-mat.mes-hall↗

arXiv2011

p-wave superconductivity on monolayer and bilayer honeycomb lattice

We derive ground state wave functions of superconducting instabilities on the honeycomb lattice induced by nearest-neighbor attractive interactions. They reflect the Dirac nature of electrons in the low-energy limit. For the order parameter that is the same irrespective of the direction to any of the nearest neighbors we find weak pairing (slowly decaying) behavior in the orbital part of the Cooper pair with no angular dependence. At the neutrality point, in the spin-singlet case, we recover a strong pairing behavior. We also derive ground state wave functions for the superconductivity on the bilayer honeycomb lattice, with strong interlayer coupling, induced by attractive interactions between sites that participate in a low-energy description. Without these interactions, free electrons are described by a Dirac equation with a quadratic dispersion. This unusual feature, similarly to $^3$He - B phase, leads to the description with two kinds of Cooper pairs, with $p_x + i p_y$ and $p_x - i p_y$ pairing, in the presence of the attractive interactions. We discuss the edge modes of such a spin-singlet superconductor and find that it represents a trivial topological superconductor.

cond-mat.supr-con↗

arXiv2010

Towards the Hall viscosity of the Fermi-liquid-like phase at the filling factor of 1/2

We discuss the Berry curvature calculations of the Hall viscosity for the unprojected to the lowest Landau level wave function of the Fermi-liquid-like state. We conclude, within assumptions made, that in the linear response, with small deformation of the system and in the thermodynamic limit, the Hall viscosity takes the value characteristic for the Laughlin states. We present arguments that the value is the same even for general deformations in the same limit.

cond-mat.mes-hall↗

arXiv2010

Transition from two-component 332 Halperin state to one-component Jain state at filling factor ν=2/5

We study the transition induced by tunneling from the two-component 332 Halperin's state to the one-component Jain's state at the filling factor ν=2/5. In exact diagonalizations of small systems two possibilities for the transition are found: (a) avoided level crossing, and (b) level crossing i.e. first-order transition in the case of Coulomb interaction and short range interaction, respectively. An effective bosonic model with p-wave pairing for the transition is proposed. The relevance of the Gaffnian state for the transition is discussed as well as possible consequences of our model on the effective description of the Jain state.

cond-mat.mes-hall↗

arXiv2009

Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories

Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties like the Moore-Read Pfaffian for filling factor nu = 5/2. This wavefunction has been constructed by constructing correlation functions of a two-dimensional conformal field theory (CFT) involving a free boson and a Majorana fermion. By considering other CFTs many other clustered states have been proposed as candidate FQH states under appropriate circumstances. It is believed that the underlying CFT should be unitary if one wants to describe an incompressible i.e. gapped liquid state. We show that by changing the way one derives the wavefunction from its parent CFT it is possible to obtain an incompressible candidate state when starting from a non-unitary parent. The construction mimics a global change of parameters in the phase space of the electron system. We explicit our construction in the case of the so-called Gaffnian state (a state for filling factor 2/5) and also for the Haldane-Rezayi state (a spin-singlet state at filling 1/2).

cond-mat.mes-hall↗

arXiv2009

Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.

cond-mat.mes-hall↗

arXiv2009

Meron ground states of quantum Hall droplets

We argue that topological meron excitations, which are in a strong coupling phase (bound in pairs) in infinite quantum Hall ferromagnets, become deconfined in finite size quantum Hall systems. Although effectively for larger systems meron energy grows with the size of the system, when gyromagnetic ratio is small meron becomes the lowest lying state of a quantum Hall droplet. This comes as a consequence of the many-body correlations built in the meron construction that minimize the interaction energy. We demonstrate this by using mean field ansatzes for meron wave function. The ansatzes will enable us to consider much larger system sizes than in the previous work [A. Petkovic and M.V. Milovanovic, PRL 98, 066808 (2007)], where fractionalization into merons was introduced.

cond-mat.str-el↗

arXiv2009

Nonperturbative approach to the quantum Hall bilayer

We develop a nonperturbative approach to the quantum Hall bilayer (QHB) at ν=1 using trial wave functions. We predict phases of the QHB for arbitrary distance d and, our approach, in a dual picture, naturally introduces a new kind of quasiparticles - neutral fermions. Neutral fermion is a composite of two merons of the same vorticity and opposite charge. For small d (i.e. in the superfluid phase), neutral fermions appear as dipoles. At larger d dipoles dissociate into the phase of the two decoupled Fermi-liquid-like states. This scenario is relevant for the experimental situation where impurities lock charged merons. In a translation invariant (clean) system, continuous creation and annihilation of meron-antimeron pairs evolves the QHB toward a paired phase. The quantum fluctuations fix the form of the pairing function to g(z)=1/z^*. A part of the description of the paired phase is the 2D superconductor i.e. BF Chern-Simons theory. The paired phase is not very distinct from the superfluid phase.

cond-mat.mes-hall↗

arXiv2008

Fractionalization in dimerized graphene and graphene bilayer

We show that the fractional statistics of quasiparticles in dimerized graphene, in recent proposals for charge and statistics fractionalization, can have two realizations depending whether elementary objects can be considered as point-like or extended objects. Therefore, there are two phases of proposed excitations and we give their topological descriptions with their respective statistics. We propose that a natural setting for fractionalization are certain systems with excitonic instabilities and demonstrate this by an example of graphene bilayer.

cond-mat.mes-hall↗