3,711 research outputs found

### 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.Comment: 4 pages RevTeX, 3 jpg figure

### Electronic structure of turbostratic graphene

We explore the rotational degree of freedom between graphene layers via the
simple prototype of the graphene twist bilayer, i.e., two layers rotated by
some angle $\theta$. It is shown that, due to the weak interaction between
graphene layers, many features of this system can be understood by interference
conditions between the quantum states of the two layers, mathematically
expressed as Diophantine problems. Based on this general analysis we
demonstrate that while the Dirac cones from each layer are always effectively
degenerate, the Fermi velocity $v_F$ of the Dirac cones decreases as $\theta\to
0^\circ$; the form we derive for $v_F(\theta)$ agrees with that found via a
continuum approximation in Phys. Rev. Lett., 99:256802, 2007. From tight
binding calculations for structures with $1.47^\circ \le \theta < 30^\circ$ we
find agreement with this formula for $\theta \gtrsim 5^\circ$. In contrast, for
$\theta \lesssim 5^\circ$ this formula breaks down and the Dirac bands become
strongly warped as the limit $\theta \to 0$ is approached. For an ideal system
of twisted layers the limit as $\theta\to0^\circ$ is singular as for $\theta >
0$ the Dirac point is fourfold degenerate, while at $\theta=0$ one has the
twofold degeneracy of the $AB$ stacked bilayer. Interestingly, in this limit
the electronic properties are in an essential way determined \emph{globally},
in contrast to the 'nearsightedness' [W. Kohn. Phys. Rev. Lett., 76:3168,
1996.] of electronic structure generally found in condensed matter.Comment: Article as to be published in Phys. Rev B. Main changes: K-point
mapping tables fixed, several changes to presentation

### Liquid-crystal patterns of rectangular particles in a square nanocavity

Using density-functional theory in the restricted-orientation approximation,
we analyse the liquid-crystal patterns and phase behaviour of a fluid of hard
rectangular particles confined in a two-dimensional square nanocavity of side
length $H$ composed of hard inner walls. Patterning in the cavity is governed
by surface-induced order, capillary and frustration effects, and depends on the
relative values of particle aspect ratio $\kappa\equiv L/\sigma$, with $L$ the
length and $\sigma$ the width of the rectangles ($L\ge\sigma$), and cavity size
$H$. Ordering may be very different from bulk ($H\to\infty$) behaviour when $H$
is a few times the particle length $L$ (nanocavity). Bulk and confinement
properties are obtained for the cases $\kappa=1$, 3 and 6. In the confined
fluid surface-induced frustration leads to four-fold symmetry breaking in all
phases (which become two-fold symmetric). Since no director distorsion can
arise in our model by construction, frustration in the director orientation is
relaxed by the creation of domain walls (where the director changes by
$90^{\circ}$); this configuration is necessary to stabilise periodic phases.
For $\kappa=1$ the crystal becomes stable with commensuration transitions
taking place as $H$ is varied. In the case $\kappa=3$ the commensuration
transitions involve columnar phases with different number of columns. Finally,
in the case $\kappa=6$, the high-density region of the phase diagram is
dominated by commensuration transitions between smectic structures; at lower
densities there is a symmetry-breaking isotropic $\to$ nematic transition
exhibiting non-monotonic behaviour with cavity size.Comment: 31 pages, 15 figure

### Quantum interference at the twist boundary in graphene

We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the Î¸ â†’ 0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles

### Magnetic hour-glass dispersion and its relation to high-temperature superconductivity in iron-tuned Fe$_{1+y}$Te$_{0.7}$Se$_{0.3}$

High-temperature superconductivity remains arguably the largest outstanding
enigma of condensed matter physics. The discovery of iron-based
high-temperature superconductors has renewed the importance of understanding
superconductivity in materials susceptible to magnetic order and fluctuations.
Intriguingly they show magnetic fluctuations reminiscent of the superconducting
(SC) cuprates, including a 'resonance' and an 'hour-glass' shaped dispersion,
which provide an opportunity to new insight to the coupling between spin
fluctuations and superconductivity. Here we report inelastic neutron scattering
data on Fe$_{1+y}$Te$_{0.7}$Se$_{0.3}$ using excess iron concentration to tune
between a SC ($y=0.02$) and a non-SC ($y=0.05$) ground states. We find
incommensurate spectra in both samples but discover that in the one that
becomes SC, a constriction towards a commensurate hourglass shape develop well
above $T_c$. Conversely a spin-gap and concomitant spectral weight shift happen
below $T_c$. Our results imply that the hourglass shaped dispersion is most
likely a pre-requisite for superconductivity, whereas the spin-gap and shift of
spectral weight are consequences of superconductivity. We explain this
observation by pointing out that an inwards dispersion towards the commensurate
wave-vector is needed for the opening of a spin gap to lower the magnetic
exchange energy and hence provide the necessary condensation energy for the SC
state to emerge

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