arXiv subjects

H. A. Fertig

Publications and source records attributed to H. A. Fertig.

At least 55 records · Page 3Linked to original sources

arXiv2012

Valley-kink in Bilayer Graphene at $ν=0$: A Charge Density Signature for Quantum Hall Ferromagnetism

We investigate interaction-induced valley domain walls in bilayer graphene in the $ν=0$ quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a double-gated suspended sample, where the electric field changes sign across a line in the middle. The non-interacting energy spectrum of the ground state is characterized by a sharp domain wall between two valley-polarized regions. Using the Hartree-Fock approximation, we find that the Coulomb interaction opens a gap between the two lowest-lying states near the Fermi level, yielding a smooth domain wall with a kink configuration in the valley index. Our results suggest the possibility to visualize the domain wall via measuring the charge density difference between the two graphene layers, which we find exhibits a characteristic pattern. The width of the kink and the resulting pattern can be tuned by the interplay between the magnetic field and gate electric fields.

cond-mat.str-el↗

arXiv2011

Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon

Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

cond-mat.mes-hall↗

arXiv2011

Transport in superlattices on single layer graphene

We study transport in undoped graphene in the presence of a superlattice potential both within a simple continuum model and using numerical tight-binding calculations. The continuum model demonstrates that the conductivity of the system is primarily impacted by the velocity anisotropy that the Dirac points of graphene develop due to the potential. For one-dimensional superlattice potentials, new Dirac points may be generated, and the resulting conductivities can be approximately described by the anisotropic conductivities associated with each Dirac point. Tight-binding calculations demonstrate that this simple model is quantitatively correct for a single Dirac point, and that it works qualitatively when there are multiple Dirac points. Remarkably, for a two dimensional potential which may be very strong but introduces no anisotropy in the Dirac point, the conductivity of the system remains essentially the same as when no external potential is present.

cond-mat.mes-hall↗

arXiv2010

Excitonic Effects in Two-Dimensional Massless Dirac Fermions

We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power law behavior at small wavevectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at $2k_F$, leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.

cond-mat.str-el↗

arXiv2010

Band topology and quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin orbit coupling, to assess its behavior as a topological insulator. The first Chern number $n$ for the energy bands of single and bilayer graphene is computed and compared. It is shown that for a given valley and spin, $n$ in a bilayer is doubled with respect to the monolayer. This implies that bilayer graphene will have twice as many edge states as single layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We also assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. Finally, we consider an intermediate situation in which only one of the two layers has spin orbit coupling, and find that although individual valleys have non-trivial Chern numbers, the spectrum as a whole is not gapped, so that the system is not a topological insulator.

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arXiv2010

Effective Magnetic Fields in Graphene Superlattices

We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We develop an effective theory that exploits a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential, to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.

cond-mat.mes-hall↗

arXiv2010

Critical Behavior in Graphene with Coulomb Interactions

We demonstrate that in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two dimensional systems, are discussed.

cond-mat.str-el↗

arXiv2010

Bilayer Quantum Hall Ferromagnet in a Periodic Potential

The bilayer quantum Hall system at a total filling of $ν_T=1$ has long resisted explanation in terms of a true counterflow superfluid, though many experimental features can be seen to be "almost" that of a superfluid. It is widely believed that quenched disorder is the root cause of this puzzle. Here we model the nonperturbative effects of disorder by investigating the $ν=1$ bilayer in a strong periodic potential. Our model assumes that fermions are gapped and real spins are fully polarized, and concentrates on the pseudospin variable (the layer index), with the external potential coupling to the topological (Pontryagin) density of the pseudospin. We find that as the potential strength increases, there are ground state transitions in which the topological content of the pseudospin configuration changes. These transitions are generically weakly first-order, with a new quadratically dispersing mode (in addition to the linearly dispersing Goldstone mode) sometimes becoming nearly gapless near the transition. We show that this leads to strong suppressions of both the Kosterlitz-Thouless transition temperature and the interlayer tunneling strength, which we treat perturbatively. We discuss how these results might extend to the case of true disorder.

cond-mat.str-el↗

arXiv2010

Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.

cond-mat.mes-hall↗

arXiv2009

Effective Time Reversal Symmetry Breaking and Energy Spectra of Graphene Armchair Rings

We study the energy spectra and wavefunctions of graphene rings formed from metallic armchair ribbons, near zero energy, to search for properties which may be identified with "effective broken time reversal symmetry" (EBTRS). Appropriately chosen corner junctions are shown to impose phase shifts in the wavefunctions that at low energies have the same effect as effective flux tubes passing near the ribbon surface. Closing the ribbon into a ring captures this flux and yields properties that may be understood as signatures of EBTRS. These include a gap in the spectrum around zero energy, which can be removed by the application of real magnetic flux through the ring. Spectra of five and seven sided rings are also examined, and it is shown these do not have particle-hole symmetry, which may also be understood as a consequence of EBTRS, and is connected to the curvature induced in the system when such rings are formed. Effects of deviations from the ideal geometries on the spectra are also examined.

cond-mat.mes-hall↗

arXiv2009

Onset of an Insulating Zero-Plateau Quantum Hall State in Graphene

We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by hybridization of two counter--propagating edge states of opposing spin due to interactions. The resulting non--chiral edge mode is a Luttinger liquid of parameter K, which enters a gapped, perfectly conducting state below a critical value K_c\approx 1/2. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates a finite resistivity R_{xx} via a "chiral Kondo effect". At finite temperatures T, R_{xx}(T) exhibits a crossover from metallic to insulating behavior as K is tuned across a threshold K_{MI}. For T->0, R_{xx} in the intermediate regime K_{MI}<K<K_c is finite, but diverges as K approaches K_c. This model provides a natural interpretation of recent experiments.

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arXiv2009

Linear Response and the Thomas-Fermi Approximation in Undoped Graphene

We analyze the range of validity of Thomas Fermi theory for describing charge density modulations induced by external potentials in neutral graphene. We compare exact results obtained from a tight-binding calculation with those of linear response theory and the Thomas Fermi approximation. For experimentally interesting ranges of size and density amplitudes (electron densities less than $\sim 10 ^{11} cm ^{-2}$, and spatial length scales below $\sim 20 nm$), linear response is significantly more accurate than Thomas Fermi theory.

cond-mat.mes-hall↗

arXiv2009

Majorana fermions of a two-dimensional Px+iPy superconductor

To investigate Majorana fermionic excitations of a $p_x+ip_y$ superconductor, the Bogoliubov-de-Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature, and is compared to the case of an {\it s}-wave superconductor. The zero bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order parameter symmetry, and as a direct measurement of the Majorana fermion.

cond-mat.supr-con↗

arXiv2009

Emerging Zero Modes for Graphene in a Periodic Potential

We investigate the effect of a periodic potential on the electronic states and conductance of graphene. It is demonstrated that for a cosine potential $V(x)=V_0\cos(G_0x)$, new zero energy states emerge whenever $J_0(\frac {2V_0}{\hbar v_F G_0})=0$. The phase of the wavefunctions of these states is shown to be related to periodic solutions of the equation of motion of an overdamped particle in a periodic potential, subject to a periodic force. Numerical solutions of the Dirac equation confirm the existence of these states, and demonstrate the chirality of states in their vicinity. Conductance resonances are shown to accompany the emergence of these induced Dirac points.

cond-mat.mes-hall↗

arXiv2008

Testing for Majorana Zero Modes in a Px+iPy Superconductor at High Temperature by Tunneling Spectroscopy

Directly observing a zero energy Majorana state in the vortex core of a chiral superconductor by tunneling spectroscopy requires energy resolution better than the spacing between core states $Δ^2/eF$. We show that nevertheless, its existence can be decisively tested by comparing the temperature broadened tunneling conductance of a vortex with that of an antivortex even at temperatures $T >> Δ^2/eF$.

cond-mat.str-el↗

arXiv2008

Skyrme and Wigner crystals in graphene

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $ν$ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.

cond-mat.mes-hall↗

arXiv2008

Phase diagram for quantum Hall states in graphene

We investigate integer and half-integer filling states (uniform and unidimensional stripe states respectively) for graphene using the Hartree-Fock approximation. For fixed filling factor, the ratio between the scales of the Coulomb interaction and Landau level spacing $g=(e^2/ε\ell)/(\hbar v_F/\ell)$, with $\ell$ the magnetic length, is a field-independent constant. However, when $B$ decreases, the number of filled negative Landau levels increases, which surprisingly turns out to decrease the amount of Landau level mixing. The resulting states at fixed filling factor $ν$ (for $ν$ not too big) have very little Landau level mixing even at arbitrarily weak magnetic fields. Thus in the density-field phase diagram, many different phases may persist down to the origin, in contrast to the more standard two dimensional electron gas, in which the origin is surrounded by Wigner crystal states. We demonstrate that the stripe amplitudes scale roughly as $B$, so that the density waves ``evaporate'' continuously as $B\to 0$. Tight-binding calculations give the same scaling for stripe amplitude and demonstrate that the effect is not an artifact of the cutoff procedure used in the continuum calculations.

cond-mat.mes-hall↗

arXiv2008

Conductance Through Graphene Bends and Polygons

We investigate the transmission of electrons between conducting nanoribbon leads oriented at multiples of 60 degrees with respect to one another, connected either directly or through graphene polygons. A mode-matching analysis suggests that the transmission at low-energies is sensitive to the precise way in which the ribbons are joined. Most strikingly, we find that armchair leads forming 120-degree angles can support either a large transmission or a highly suppressed transmission, depending on the specific geometry. Tight-binding calculations demonstrate the effects in detail, and are also used to study transmission at higher energies as well as for zigzag ribbon leads.

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