Interlayer Coherence Research Articles

Effect of interlayer bare tunneling on electron-hole coherence in graphene bilayers

The influence of single-particle interlayer coupling on the many-body electron-hole condensation between two graphene monolayers separated by a thin dielectric film is studied. This work extends prior work by treating interlayer coupling, which controls critical interlayer tunneling currents, nonperturbatively. As before, a \ensuremath{\pi}-band tight-binding model of the graphene bilayer is combined with Fock mean-field theory. Our results demonstrate that both the strength and the sublattice distribution of interlayer coupling play essential roles. We consider both Bernal-like and quasi-hexagonal forms, and self-consistently solve for the condensate. We find that stronger bare coupling can considerably affect the nature of the condensate state itself, selecting a preferred pattern of interlayer coherence among the atomic sublattices. When this occurs, the sensitivity of the critical current to the nature of the bare coupling decreases substantially. Because condensate control via gated charge imbalance has been proposed for beyond Complementary Metal-Oxide Semiconductor (CMOS) switching, we also examine the effect of increasing charge imbalance between layers on the condensate strength as well as the critical current.

Two-Dimensional Superconducting Properties of the Organic Superconductor κL-(DMEDO-TSeF)2[Au(CN)4](THF) with Domain Structures

The anisotropy of superconducting coherence lengths of the layered organic superconductor κ L -(DMEDO-TSeF) 2 [Au(CN) 4 ](THF) with domain structures has been investigated, where DMEDO-TSeF is dimethyl(ethylenedioxy)tetraselenafulvalene and THF is tetrahydrofuran. The field angle dependence of the upper critical field and the short interlayer coherence length indicate that the present compound is a two-dimensional superconductor. Although this compound has domain walls parallel to the conducting layer depending on the orientation of the THF molecules, the interlayer coherence length shorter than the structural correlation length shows that the domain walls parallel to the conducting layers do not affect the superconductivity.

Breakdown of Counterflow Superfluidity in a Disordered Quantum Hall Bilayer

We present a theory for the regime of coherent interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. We find that the system consists of domains of polarized superfluid phase. Injected currents introduce phase slips between the polarized domains which are pinned by disorder. We present a model of saturated tunneling domains that predicts a critical current for the breakdown of coherent tunneling that is extensive in the system size. This theory is supported by numerical results from a disordered phase model in two dimensions. We also discuss how our picture might be used to interpret experiments in the counterflow geometry and in two-terminal measurements.

Nondispersive RamanDband activated by well-ordered interlayer interactions in rotationally stacked bilayer graphene

Raman measurements on monolayer graphene folded back upon itself as an ordered but skew-stacked bilayer (i.e. with interlayer rotation) presents new mechanism for Raman scattering in sp2 carbons that arises in systems that lack coherent AB interlayer stacking. Although the parent monolayer does not exhibit a D-band, the interior of the skewed bilayer produces a strong two-peak Raman feature near 1350 cm-1; one of these peaks is non-dispersive, unlike all previously observed D-band features in sp2 carbons. Within a double-resonant model of Raman scattering, these unusual features are consistent with a skewed bilayer coupling, wherein one layer imposes a weak but well-ordered perturbation on the other. The discrete Fourier structure of the rotated interlayer interaction potential explains the unusual non-dispersive peak near 1350 cm-1.

Spontaneous interlayer superfluidity in bilayer systems of cold polar molecules

Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up possibilities for realizing quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable broken-symmetry states with spontaneous interlayer coherence in cold polar molecule bilayers. These exotic states, which are manifestations of collective bilayer quantum entanglement, appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets, and excitonic condensates.

Coherence and Disorder in Bilayer Quantum Hall Systems

The quantum Hall bilayer at total filling factor displays a number of properties akin to superfluidity, most clearly apparent in its very low dissipation in tunneling and counterflow transport. Theoretical descriptions in terms of quantum Hall ferromagnetism or thin-film superfluidity can be developed to explain these phenomena. In either case, merons can be identified as important low energy excitations. We demonstrate that a model in which puddles of merons induced by disorder, separated by narrow regions of interlayer coherence—a coherence network—can naturally explain many of the imperfect superfluid finite temperature properties that are observed in these systems. The periodic realization of this model shows that there can be low energy excitations beyond the superfluid mode. These are associated with transitions between states of different meron number in the puddles, where we argue that merons should be unbound atanytemperature, and which can have important implications for the effect of quantum fluctuations on the system.

Electron-electron interactions in decoupled graphene layers

Multilayer graphene on the carbon face of silicon carbide is an intriguing electronic system which typically consists of a stack of ten or more layers. Rotational stacking faults in this system dramatically reduce interlayer coherence. In this paper we report on the influence of interlayer interactions, which remain strong even when coherence is negligible, on the Fermi-liquid properties of charged graphene layers. We find that interlayer interactions increase the magnitudes of correlation energies and decrease quasiparticle velocities, even when remote-layer carrier densities are small, and that they lessen the influence of exchange and correlation on the distribution of carriers across layers.

Impurity-Induced Bound States and Proximity Effect in a Bilayer Exciton Condensate

The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single-fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity-induced single-fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single-impurity states, we predict that a finite concentration of such impurities will increase the critical temperature for exciton condensation.

Commensuration and interlayer coherence in twisted bilayer graphene

The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a fault and preempts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully gapped systems due to a pseudospin-orbit coupling appearing in their effective low energy Hamiltonians.

First observation of angle-dependent Stark cyclotron resonance in bulk crystals: High-electric-field interlayer magnetotransport in a layered organic conductor

We report a novel angle-dependent magnetotransport phenomenon in layered conductors under strong interlayer electric fields. Interlayer conduction shows the Stark cyclotron resonance (SCR) when electron orbital motion becomes periodic in k-space. The SCR amplitude oscillates depending on magnetic field orientations. The conventional angle-dependent magnetoresistance oscillation (AMRO) switches to the angle-dependent SCR in high electric fields. We predict angle-dependent SCR due to electron orbital motion in layered conductors with coherent interlayer coupling. In addition, we demonstrate the expected switching from conventional AMRO to angle-dependent SCR in high electric fields using an organic conductor α-(BEDT-TTF) 2NH 4Hg(SCN) 4. This is the first observation of the SCR with orbital origin in bulk crystals.

The phase diagram of quantum disordered superconducting networks

I review the low energy dynamics and the phase diagram of two parallel coupled Josephson junction arrays (JJA) in the presence of charge and magnetic frustration. Starting from the quantum phase model known to capture the relevant physics of JJA, the system is mapped in the self-dual limit into an Abelian gauge theory with a mixed Chern-Simons term. The low energy dynamics is shown to be governed by Higgs fields associated with disordering effects due to electric charges and magnetic excitations minimally coupled to gauge fields related to the currents of Cooper pairs and vortices. A rich phase diagram not attainable by standard mean field theories emerges as a result of the condensation of disorder fields. The interplay between Hall quantization and interlayer coherence displays appealing features resulting into quantized Hall states coexisting with interlayer coherence, quantized Hall states without interlayer coherence, and interlayer coherent states without Hall quantization.

A boomerang-shaped reduction in interlayer phase coherence in Bi2Sr2CaCu208+y with splayed columnar defects

We present evidence for entangled solid vortex matter in a glassy state in a layered superconductor Bi2Sr2CaCu2O8+y containing randomly splayed linear defects. The interlayer phase coherence(IPC)—probed by the Josephson plasma resonance—is enhanced at high temperatures, reflecting the recoupling of vortex liquid by the defects. At low temperatures in the vortex solid state, the interlayer coherence follows a boomerang-shaped reentrant temperature path with an unusual low field decrease in coherence, indicative of meandering vortices. This behavior suggests strongly suppressed IPC in this system, which may be explained by the vortex entanglement induced by the columnar defects in the "splayed-glass" state.

Entanglement of Solid Vortex Matter: A Boomerang-Shaped Reduction Forced by Disorder in Interlayer Phase Coherence inBi2Sr2CaCu2O8+y

We present evidence for entangled solid vortex matter in a glassy state in a layered superconductor Bi2Sr2CaCu2O8+y containing randomly splayed linear defects. The interlayer phase coherence--probed by the Josephson plasma resonance--is enhanced at high temperatures, reflecting the recoupling of vortex liquid by the defects. At low temperatures in the vortex solid state, the interlayer coherence follows a boomerang-shaped reentrant temperature path with an unusual low-field decrease in coherence, indicative of meandering vortices. We uncover a distinct temperature scaling between in-plane and out-of-plane critical currents with opposing dependencies on field and time, consistent with the theoretically proposed "splayed-glass" state.

Quantum disordering and the phase diagram of bilayer Josephson junction arrays

I present a theoretical analysis of the phase diagram of bilayer Josephson junction arrays in the presence of charge and magnetic frustration. Using a dual description I show that the fundamental constituents of this theory are electric and magnetic excitations and that their condensations lead to a plethora of possible phases. The new formulation points out to the emergence of a rich phase diagram not attainable by standard mean field theory approaches. In addition to the usual superconducting and insulating states in the bilayer system, I find states exhibiting Hall quantization coexisting with interlayer coherence, states with Hall quantization without interlayer coherence and interlayer coherent states without Hall quantization.

Atomic structure and formation mechanism of (301) rutile twins from Diamantina (Brazil)

Rutile (TiO 2 ) twins from Diamantina in Brazil were investigated using analytical transmission electron microscopy methods. High-resolution transmission electron microscopy (HRTEM) imaging of (301) twinned rutile revealed the existence of a coherent interlayer at the twin boundary. The interface lamella, with a lateral width of a few nanometers, consists of ilmenite (FeTiO 3 ) containing some Al. The orientation relationship between the ilmenite lamella and the epitaxial rutile crystals is (0110)[0001] 1 || (301)[010] R . The ilmenite-rutile interfaces are atomically sharp and devoid of misfit dislocations that would compensate for the lattice mismatch between the two structures. The Ti/Fe concentration ratios, as measured in the twin lamella by means of the variable-beam-diameter energy-dispersive spectroscopy (VBD/EDS) technique, correspond to ilmenite. The valence-sensitive features in electron energy-loss spectra (EELS) revealed that the Fe in the twin lamella adopts a divalent oxidation state (Fe 2+ ), which is characteristic of ilmenite. The lattice mismatch between the ilmenite and rutile appears to be compensated by the incorporation of Al into the ilmenite. The presence of goethite-related reflections and the existence of nanotwins in the ilmenite lamella imply that it formed via a thermally induced dehydration process from an oxyhydroxide precursor mineral with a tivanite-type structure. This lamella subsequently served as a nucleation site for the epitaxial growth of rutile domains in a (301) twin configuration.

Collective modes ofCP3skyrmion crystals in quantum Hall ferromagnets

The two-dimensional electron gas (2DEG) in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor $\ensuremath{\nu}=1$ even in the absence of tunneling between the layers. This system, which can be described as a quantum Hall pseudospin ferromagnet, has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor $\ensuremath{\nu}=1$, a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling $({\ensuremath{\Delta}}_{SAS})$, Zeeman coupling $({\ensuremath{\Delta}}_{Z})$, or electrical bias $({\ensuremath{\Delta}}_{b})$, these textured crystal states can involve spin, pseudospin, or both intertwined. This last case is a ``$C{P}^{3}$ skyrmion crystal.'' In this paper, we present a comprehensive numerical study of the collective excitations of these textured crystals using the generalized random-phase approximation. For the pure spin case, at finite Zeeman coupling the state is a skyrmion crystal with a gapless phonon mode and a separate goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent skyrmions break up, and the resulting state is a meron crystal with four gapless modes. In contrast, a pure pseudospin-skyrme crystal at finite tunneling has only the phonon mode. For ${\ensuremath{\Delta}}_{SAS}\ensuremath{\rightarrow}0$, the state evolves into a meron crystal and supports an extra gapless [U(1)] mode in addition to the phonon. For a $C{P}^{3}$ skyrmion crystal, we find a U(1) gapless mode in the presence of nonvanishing symmetry-breaking fields ${\ensuremath{\Delta}}_{SAS}$, ${\ensuremath{\Delta}}_{Z}$, and ${\ensuremath{\Delta}}_{b}$. In addition, a second mode with a very small gap is present in the spectrum. We present dispersion relations for the different low-energy modes of these various crystals as well as their physical interpretations.

Persistence to High Temperatures of Interlayer Coherence in an Organic Superconductor

The interlayer magnetoresistance rho(zz) of the organic metal kappa-(BEDT-TTF)(2)Cu(NCS)(2) is studied in fields of up to 45 T and at temperatures T from 0.5 to 30 K. The peak in rho(zz) seen in in-plane fields, a definitive signature of interlayer coherence, remains to Ts exceeding the Anderson criterion for incoherent transport by a factor approximately 30. Angle-dependent magnetoresistance oscillations are modeled using an approach based on field-induced quasiparticle paths on a 3D Fermi surface, to yield the T dependence of the scattering rate tau(-1). The results suggest that tau(-1) does not vary strongly over the Fermi surface, and that it has a T(2) dependence due to electron-electron scattering.

Interlayer coherence in Bi2Sr2CaCu2O8+y with splayed columnar defects

By using the Josephson plasma resonance, we investigate the interlayer phase coherence (IPC) in the vortex states of GeV-proton-irradiated Bi2Sr2CaCu2O8+y crystals containing splayed columnar defects, which are introduced by Bi fission. At high temperatures in the vortex liquid state, we observe an enhancement of IPC in a field range beginning well below the matching field BΦ, in close correspondence with the recoupling crossover observed near BΦ/3 in the heavy-ion irradiated Bi2Sr2CaCu2O8+y. At low temperatures in the vortex solid state, a reentrant behavior of the resonance field is found in the zero-field-cooling condition, which has not been observed in pristine samples. This behavior suggests strongly suppressed IPC in this system, which may be explained by the vortex entanglement induced by the columnar defects in the splayed glass state.

Dynamic equation for quantum Hall bilayers with spontaneous interlayer coherence: The low-density limit

The bilayer systems exhibit the Bose-Einstein condensation of excitons that emerge due to Coulomb pairing of electrons belonging to one layer with the holes belonging to the other layer. Here we present the microscopic derivation of the dynamic equation for the condensate wave function at a low density of electron-hole $(e\text{\ensuremath{-}}h)$ pairs in a strong magnetic field perpendicular to the layers and an electric field directed along the layers. From this equation we obtain the dispersion law for collective excitations of the condensate and calculate the electric charge of the vortex in the exciton condensate. The critical interlayer spacing, the excess of which leads to a collapse of the superfluid state, is estimated. In bilayer systems with curved conducting layers, the effective mass of the $e\text{\ensuremath{-}}h$ pair becomes the function of the $e\text{\ensuremath{-}}h$ pair coordinates; the regions arise, where the energy of the $e\text{\ensuremath{-}}h$ pair is lowered (exciton traps); and lastly $e\text{\ensuremath{-}}h$ pairs can gain the polarization in the basal plane. This polarization leads to the appearance of quantized vortices even at zero temperature.

High-field studies of the slow thermal death of interlayer coherence in quasi-two-dimensional metals

The interlayer magnetoresistance ρzz of the organic metal κ-(BEDTTTF)2Cu(NCS)2 has been studied in fields B of up to 45 T and at temperatures T from 0.5 K to 50 K. The peak in ρzz seen in exactly in-plane fields, a definitive signature of interlayer coherence, remains to Ts exceeding the Anderson criterion for incoherent transport by a factor ∼ 25. Angle-dependent magnetoresistance oscillations (AMROs) due to Fermi-surface orbits are suppressed by rising T, with a T2dependence suggesting electron-electron scattering.