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Takeshi Saito

Publications and source records attributed to Takeshi Saito.

At least 37 records · Page 2Linked to original sources
arXiv2017

Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by 13C NMR

The electronic states in isolated single-wall carbon nanotubes (SWCNTs) have been considered as an ideal realization of a Tomonaga-Luttinger liquid (TLL). However, it remains unclear whether one-dimensional correlated states are realized under local environmental effects such as the formation of a bundle structure. Intertube effects originating from other adjacent SWCNTs within a bundle may drastically alter the one-dimensional correlated state. In order to test the validity of the TLL model in bundled SWCNTs, low-energy spin excitation is investigated by nuclear magnetic resonance (NMR). The NMR relaxation rate in bundled mixtures of metallic and semiconducting SWCNTs shows a power-law temperature dependence with a theoretically predicted exponent. This demonstrates that a TLL state with the same strength as that for effective Coulomb interactions is realized in a bundled sample, as in isolated SWCNTs. In bundled metallic SWCNTs, we found a power-law temperature dependence of the relaxation rate, but the magnitude of the relaxation rate is one order of magnitude smaller than that predicted by theory. Furthermore, we found an almost doubled magnitude of the Luttinger parameter. These results indicate suppressed spin excitations with reduced Coulomb interactions in bundled metallic SWCNTs, which are attributable to intertube interactions originating from adjacent metallic SWCNTs within a bundle. Our findings give direct evidence that bundling reduces the effective Coulomb interactions via intertube interactions within bundled metallic SWCNTs.

cond-mat.str-el↗
arXiv2016

Characteristic cycle of the exterior product of constructible sheaves

We show that the characteristic cycle of the exterior product of constructible complexes is the exterior product of the characteristic cycles of factors. This implies the compatibility of characteristic cycles with smooth pull-back which is a first step in the proof of the index formula.

math.AG↗
arXiv2016

The characteristic cycle and the singular support of a constructible sheaf

We define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula a la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler-Poincare characteristic, generalizing the Grothendieck-Ogg-Shafarevich formula to higher dimension. An essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi-continuity of the Swan conductor due to Deligne-Laumon. We prove the index formula by establishing certain functorial properties of characteristic cycles.

math.AG↗
arXiv2015

Observation of the intrinsic magnetic susceptibility of highly purified single-wall carbon nanotubes

We report the observation of the intrinsic magnetic susceptibility of highly purified SWCNT samples prepared by a combination of acid treatment and density gradient ultracentrifugation (DGU). We observed that the diamagnetic susceptibility of SWCNTs increases linearly with increasing nanotube diameter. We found that the magnetic susceptibility divided by the diameter is a universal function of the scaled temperature. Furthermore, the estimated magnetic susceptibilities of pure semiconducting and pure metallic SWCNT samples suggest that they respond differently to changes in carrier density, which is consistent with theory. These findings provide experimental verification of the theoretically predicted diameter, temperature, and metallicity dependence of the magnetic susceptibility.

cond-mat.mes-hall↗
arXiv2014

Wild Ramification and the Cotangent Bundle

We define the characteristic cycle of a locally constant étale sheaf on a smooth variety in positive characteristic ramified along boundary as a cycle in the cotangent bundle of the variety, at least on a neighborhood of the generic point of the divisor on the boundary. The crucial ingredient in the definition is an additive structure on the boundary induced by the groupoid structure of multiple self products. We prove a compatibility with pull-back and local acyclicity in non-characteristic situations. We also give a relation with the characteristic cohomology class under a certain condition and a concrete example where the intersection with the 0-section computes the Euler-Poincaré characteristic.

math.AG↗
arXiv2014

Characteristic cycle and the Euler number of a constructible sheaf on a surface

We define the characteristic cycle of a constructible sheaf on a smooth surface in the cotangent bundle. We prove that the intersection number with the 0-section equals the Euler number and that the total dimension of vanishing cycles at an isolated characteristic point is also computed as an intersection number.

math.AG↗
arXiv2012

Ramification theory for varieties over a local field

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification locus. We prove a formula of Riemann-Roch type for the Swan conductor of cohomology together with its relative version, assuming that the local field is of mixed characteristic. We also prove the integrality of the Swan class for curves over a local field as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture of Serre on the Artin character for a group action with an isolated fixed point on a regular local ring, assuming the dimension is 2.

math.NT↗
arXiv2012

The second Stiefel-Whitney classes of l-adic cohomology

For a proper smooth variety of even dimension over a field of characteristic different from 2 or l, the second Stiefel-Whitney class of the l-adic cohomology and the second Hasse-Witt class of the de Rham cohomology are both defined in the second Galois homology. We state a conjecture on their relation and give several evidences.

math.AG↗
arXiv2011

Ramification and cleanliness

This article is devoted to studying the ramification of Galois torsors and of $\ell$-adic sheaves in characteristic $p>0$ (with $\ell\not=p$). Let $k$ be a perfect field of characteristic $p>0$, $X$ be a smooth, separated and quasi-compact $k$-scheme, $D$ be a simple normal crossing divisor on $X$, $U=X-D$, $Λ$ be a finite local ${\mathbb Z}_\ell$-algebra, $F$ be a locally constant constructible sheaf of $Λ$-modules on $U$. We introduce a boundedness condition on the ramification of $F$ along $D$, and study its main properties, in particular, some specialization properties that lead to the fundamental notion of cleanliness and to the definition of the characteristic cycle of $F$. The cleanliness condition extends the one introduced by Kato for rank one sheaves. Roughly speaking, it means that the ramification of $F$ along $D$ is controlled by its ramification at the generic points of $D$. Under this condition, we propose a conjectural Riemann-Roch type formula for $F$. Some cases of this formula have been previously proved by Kato and by the second author (T.S.).

math.AG↗
arXiv2010

Semiconductor-enriched single wall carbon nanotube networks applied to field effect transistors

Substantial progress on field effect transistors "FETs" consisting of semiconducting single wall carbon nanotubes "s-SWNTs" without detectable traces of metallic nanotubes and impurities is reported. Nearly perfect removal of metallic nanotubes is confirmed by optical absorption, Raman measurements, and electrical measurements. This outstanding result was made possible in particular by ultracentrifugation (150 000 g) of solutions prepared from SWNT powders using polyfluorene as an extracting agent in toluene. Such s-SWNTs processable solutions were applied to realize FET, embodying randomly or preferentially oriented nanotube networks prepared by spin coating or dielectrophoresis. Devices exhibit stable p-type semiconductor behavior in air with very promising characteristics. The on-off current ratio is 10^5, the on-current level is around 10 $μ$A, and the estimated hole mobility is larger than 2 cm2 / V s.

cond-mat.mtrl-sci↗
arXiv2009

Local Fourier transform and epsilon factors

Laumon introduced the local Fourier transform for $\ell$-adic Galois representations of local fields, of equal characteristic $p$ different from $\ell$, as a powerful tool to study the Fourier-Deligne transform of $\ell$-adic sheaves over the affine line. In this article, we compute explicitly the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon's formula relating the epsilon factor to the determinant of the local Fourier transform under the same condition.

math.AG↗
arXiv2008

Wild ramification and the characteristic cycle of an l-adic sheaf

We propose a geometric method to measure the wild ramification of a smooth etale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of positive characteristic with arbitrary residue field. We also define the characteristic cycle of an l-adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number. Definition 2.1.1 is corrected in v2.

math.AG↗
arXiv2006

Hilbert modular forms and p-adic Hodge theory

We consider the p-adic Galois representation associated to a Hilbert modular form. We show the compatibility with the local Langlands correspondence at a place divising p under a certain assumption. We also prove the monodromy-weight conjecture. The prime-to-p case is established by Carayol.

math.NT↗