Chemistry Reference
In-Depth Information
collective mode is a
spin-1 zero sound
(SZS) of a 2+1 dimensional
massless
Dirac sea
, rather than a
Fermi sea
.
From an insulator point of view our collective mode defines a spin-triplet
exciton branch. Triplet excitons are well known in insulators, semiconduc-
tors and
pπ
bonded planar organic molecules; however, they usually have
a finite energy gap.
Our spin-1 collective mode may be also thought of as a manifestation
of Pauling's
[
7
]
RVB state of graphite: the spin-1 quanta is a delocal-
ized triplet bond in a sea of resonating singlets. The gaplessness makes it
a long range RVB rather than Pauling's short range RVB. Later we will
present an argument to suggest that at low energies the neutral spin-1 ex-
citation might undergo quantum number fractionization into two spin-
2
spinons.
Existence of our gapless spin-1 collective mode branch should influence
the spin part of the magnetic susceptibility, rather than the orbital part,
which for graphite is diamagnetic, large and anisotropic. Study of spin sus-
ceptibility by ESR, NMR and inelastic neutron scattering are good probes
to detect the low energy part of our collective modes over a limited energy
up to
. A recent observation of 'large internal fields' in oriented
pyrolitic graphite by Kopelevich and collaborators
[
15
]
, in their ESR stud-
ies could be due to our low energy spin-1 collective modes around the Γ
point in the BZ. Our mode could be probed over a large energy range, by
epithermal neutrons and spin polarized electron energy loss spectroscopy
(SPEELS) [16]. In view of a wide energy scale associated with the collective
modes, probes such as two magnon Raman scattering, ARPES, STM and
spin valves
[
17
]
should also be tried.
Importance of electron-electron interaction in graphite
[
18; 19
]
and re-
lated systems
[
20; 21; 22
]
has been realized recently and it has lead to several
interesting studies and predictions. 2d cuprates with Dirac cone spectrum
has been studied in the context of AFM order in the Mott insulating RVB-
flux phase, for spin-1 goldstone modes
[
23
]
and d-wave superconducting
phases, for spin-1 collective modes
[
24
]
.
Real graphite is a layered semimetal - stacked layer of graphene. The
coupling between graphite layers is van der Waals like. However, a small
'coherent' interlayer hopping has been invoked to explain the presence of
small electron and hole tubes and pockets, (with 10
−
4
carriers per carbon
atom, i.e., a Fermi energy
∼
50
meV
F
∼
100
−
200
K
), responsible for the semi
metallic character of graphite.
