Phase Transition In Graphene Research Articles

Understanding Magnetic Phase Transitions in Graphene and Finding Ce2Ge2Mg

For 10 weeks, two projects were carried out at the University of Kentucky during the REU research project. The initial project was titled Understanding Magnetic Phase Transitions in Graphene. However, the latter project brought about more abundant results, which involved research based on the discovery of Ce2Ge2Mg crystals.

Monte Carlo exploration of magnetic properties: Graphene and borophene comparison

This study employs Monte Carlo simulations to investigate the magnetic characteristics of graphene and Borophene lattices, emphasizing various physical parameters. Temperature-dependent variations in magnetization and susceptibility reveal a transition from ferromagnetic to superparamagnetic states, characterized by the blocking temperature (TB). Borophene exhibits a higher TB than graphene, suggesting an easier phase transition in Graphene due to its distinct geometry. These findings provide valuable perspectives into the unique magnetic features of Graphene and Borophene lattices, guiding future advancements in materials and spintronics.

Effects of different 3D QED vertex Ansätze on the critical coupling

We study the semimetal-insulator phase transition in graphene using a Schwinger-Dyson approach. We consider various forms of vertex Ans\"atze to truncate the hierarchy of Schwinger-Dyson equations. We define a Ball-Chiu-type vertex that truncates the equations without violating gauge invariance. We show that there is a family of these vertices, parametrized by a continuous parameter that we call $a$, all of which satisfy the Ward identity. We have calculated the critical coupling of the phase transition using different values of $a$. We have also tested a common approximation in which only the first term in the Ball-Chiu Ansatz is included. This vertex is independent of $a$, and, although it is not gauge invariant, it has been used many times in the literature because of the numerical simplifications it provides. We have found that, with a one-loop photon polarization tensor, the results obtained for the critical coupling from the truncated vertex and the full vertex with $a=1$ agree very well, but other values of $a$ give significantly different results. We have also done a fully self-consistent calculation, in which the photons are backcoupled to the fermion degrees of freedom, for one choice $a=1$. Our results show that when photon dynamics are correctly taken into account, it is no longer true that the truncated vertex and the full Ball-Chiu vertex with $a=1$ agree well. The conclusion is that traditional vertex truncations do not really make sense in a system that does not respect Lorentz invariance, like graphene, and the need to include vertex contributions self-consistently is likely inescapable.

Phase transitions in anisotropic graphene

In this paper, we study the effects of anisotropy on phase transitions in graphene. We work with a low-energy effective field theory which is strongly coupled, and solves a coupled set of Schwinger–Dyson equations. We show that the effect of anisotropy is to reduce the critical coupling.

Effect of anisotropy on phase transitions in graphene

We study the effect of anisotropy (strain) on dynamical gap generation in graphene. We work with a low energy effective theory obtained from a tight-binding Hamiltonian expanded around the Dirac points in momentum space. We use a non-perturbative Schwinger-Dyson approach and calculate a coupled set of five momentum dependent dressing functions. Our results show that the critical coupling depends only weakly on the anisotropy parameter, and increases with greater anisotropy.

Numerical evidence of conformal phase transition in graphene with long-range interactions

Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.

Large N critical exponents for the chiral Heisenberg Gross-Neveu universality class

We compute the large $N$ critical exponents $\ensuremath{\eta}$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}$ and $1/\ensuremath{\nu}$ in $d$ dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of $1/N$. For instance, the large $N$ conformal bootstrap method is used to determine $\ensuremath{\eta}$ at $O(1/{N}^{3})$ while the other exponents are computed to $O(1/{N}^{2})$. Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behavior of the exponents in $2<d<4$ is in qualitative agreement with a functional renormalization group analysis. The $\ensuremath{\epsilon}$ expansion of each exponent near four dimensions is in exact agreement with recent four loop perturbation theory.

Observing a scale anomaly and a universal quantum phase transition in graphene

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ‘Efimov physics’. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.

The normal-auxeticity mechanical phase transition in graphene

When a solid object is stretched, in general, it shrinks transversely. However, the abnormal ones are auxetic, which exhibit lateral expansion, or negative Poisson ratio. While graphene is a paradigm 2D material, surprisingly, graphene converts from normal to auxetic at certain strains. Here, we show via molecular dynamics simulations that the normal-auxeticity mechanical phase transition only occurs in uniaxial tension along the armchair direction or the nearest neighbor direction. Such a characteristic persists at temperatures up to 2400 K. Besides monolayer, bilayer and multi-layer graphene also possess such a normal-auxeticity transition. This unique property could extend the applications of graphene to new horizons.

Controlling the bandgap in graphene/h-BN heterostructures to realize electron mobility for high performing FETs

Electric field induced field-effect mobility and nontrivial Z2 topological phase transition in graphene sandwiched by h-BN bilayers.

Four loop renormalization of the Gross-Neveu model

We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.

Edge states and quantum phase transition in graphene under in-plane effective exchange fields

We investigated the edge states and quantum phase transition in graphene under an in-plane effective exchange field. The result shows that the combined effects of the in-plane effective exchange field and a staggered sublattice potential can induce zero-energy flat bands of edge states. Such flat-band edge states can evolve into helical-like ones in the presence of intrinsic spin–orbit coupling, with a unique spin texture. We also find that the bulk energy gap induced by the spin–orbit coupling and staggered sublattice potential can be closed and reopened with the in-plane effective exchange field, and the reopened bulk gap can be even larger than that induced by only the spin–orbit coupling and staggered sublattice potential, which is different from the case of an out-of-plane effective exchange field. The calculated spin-dependent Chern numbers suggest that the bulk gap closing and reopening is accompanied by a quantum phase transition from a trivial insulator phase across a metal phase into a spin-dependent quantum Hall phase.

Edge states and phase diagram for graphene under polarized light

In this work, we investigate the topological phase transitions in graphene under the modulation of circularly polarized light, by analyzing the changes of edge states and its topological structures. A full phase diagram, with several different topological phases, is presented in the parameter space spanned by the driving frequency and light strength. We find that the high-Chern number behavior is very common in the driven system. While the one-photon resonance can create the chiral edge states in the π-gap, the two-photon resonance will induce the counter-propagating edge modes in the zero-energy gap. When the driving light strength is strong, the number and even the chirality of the edge states may change in the π-gap. The robustness of the edge states to disorder potential is also examined. We close by discussing the feasibility of experimental proposals.

Collective bulk and edge modes through the quantum phase transition in graphene atν=0

Undoped graphene in a strong, tilted magnetic field exhibits a radical change in conduction upon changing the tilt-angle, which can be attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor $\nu=0$. This behavior signifies a change in the nature of the collective ground state and excitations across the transition. Using the time-dependent Hartree-Fock approximation, we study the collective neutral (particle-hole) excitations in the two phases, both in the bulk and on the edge of the system. The CAF has gapless neutral modes in the bulk, whereas the FM state supports only gapped modes in its bulk. At the edge, however, only the FM state supports gapless charge-carrying states. Linear response functions are computed to elucidate their sensitivity to the various modes. The response functions demonstrate that the two phases can be distinguished by the evolution of a local charge pulse at the edge.

Magnetic field induced metal-insulator phasetransition in graphene

Magnetic field induced metal-insulator phasetransition in graphene

Phonon-supported pseudospin phase transition in graphene

The phonon-induced polarization of pseudospins in graphene is investigated in this work. On the basis of detailed quantum statistical calculations, it is found that the pseudospin average value always undergoes a sign change as the temperature is lowered through some critical value. This shows that the phonons not only induce a pseudospin polarization, but also lead to a phase transition of pseudospins. This phonon-induced pseudospin polarization is somewhat like the photon-induced polarization. If a circularly polarized light participates in pseudospin polarization besides the phonons, a refrigerating effect would occur.

SU(3) and SU(4) Singlet Quantum Hall States at ν=2/3.

We report on an exact diagonalization study of fractional quantum Hall states at a filling factor of ν=2/3 in a system with a fourfold degenerate n=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at a flux quantum shift 2 when a spherical geometry is employed and lie outside the established composite-fermion or multicomponent Halperin state patterns. We evaluate the two-particle correlation functions of these states and discuss quantum phase transitions in graphene between singlet states with a different number of components as the magnetic field strength is increased.

Zero-field and time-reserval-symmetry-broken topological phase transitions in graphene

We propose a quantum electronic device based on strained graphene nanoribbon. Mechanical strain, internal exchange field and spin-orbit couplings (SOCs) have been exploited as principle parameters to tune physical properties of the device. We predict a remarkable zero-field topological quantum phase transition between the time-reversal-symmetry broken quantum spin hall (QSH) and quantum anomalous hall (QAH) states, which was previously thought to take place only in the presence of finite magnetic field. We illustrate as intrinsic SOC is tuned, how two different helicity edge states located in the opposite edges of the nanoribbon exchange their locations. Our results indicates that pseudomagnetic field induced by the strain could be coupled to the spin degrees of freedom through the SOC responsible for the stability of QSH state. The controllability of this zero-field phase transition with strength and direction of the strain is also demonstrated. Our prediction offers a tempting prospect of strain, electric and magnetic manipulation of the QSH effect.

Ferroelectric phase transition in graphene with the Hubbard interaction

It has been revealed that, as an external dc electric field is applied to graphene with the Hubbard interaction between electrons, a spontaneous electric field perpendicular to the applied field can appear. This effect can be due to the nonequilibrium electron subsystem in graphene. The spontaneous field characteristics have been found as a function of the parameters of the problem.

Mean-field quantum phase transition in graphene and in general gapless systems

We study the quantum critical properties of antiferromagnetism in graphene at T=0 within mean-field (MF) theory. The resulting exponents differ from the conventional MF exponents, describing finite temperature transitions. Motivated by this, we have developed the MF theory of general gapless phases with density of states rho(E) |E|^r, r>-1, with the interaction as control parameter. For r>2, the conventional MF exponents \'a la Landau are recovered, while for -1<r<2, the exponents vary significantly with r. The critical interaction is finite for r>0, therefore no weak-coupling solution exists in this range. This generalizes the results on quantum criticality of the gapless Kondo systems to bulk correlated phases.