Application of Random-Matrix Theory to Quantum Electron Transport
| Project/Area Number |
16540291
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Condensed matter physics I
|
|---|
| Research Institution | Hiroshima University |
|---|
Principal Investigator |
TAKANE Yositake Hiroshima University, Graduate School of Advanced Sciences of Matter, Associate Professor, 大学院先端物質科学研究科, 助教授 (40254388)
|
|---|
| Project Period (FY) |
2004 – 2006
|
| Project Status |
Completed (Fiscal Year 2006)
|
| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
|
|---|
| Keywords | quantum electron transport / quantum wire / conductance / symplectic class / Anderson localization / perfectly conducting channel / ランダム行列理論 / シンブレクティック・クラス / ジョセフソン効果 / シンプレクティック・クラス / 超行列理論 |
|---|
| Research Abstract |
We have studied conductance of disordered wires with symplectic symmetry at zero temperature. In the symplectic universality class, the parity of conducting channel number N plays an essential role in electron transport. In contrast to the ordinary case of an even N, a perfectly conducting channel without backscattering is stabilized in the odd-N case. The purpose of this study is to clarify the even-odd difference arising in the behavior of conductance. To accomplish this purpose, we have adapted the random-matrix theory to our problem, and formulated the scaling theory by which we can consider both the even-and odd-channel cases within a unified manner. Based on the scaling theory, we have shown that in the ordinary even-channel case, the averaged dimensionless conductance vanishes in the long-wire limit, while it approaches to unity in the odd-channel case. We have also shown that the localization length for the odd channel case is much shorter than that for the even-channel case. We observe that these even-odd differences are attributed to the perfectly conducting channel that exists only in the odd-channel case. To confirm the validity of the scaling theory, we have performed large-scale numerical simulations. We have presented a simple tight-binding model on the square lattice for disordered wires with symplectic symmetry, and studied the behavior of the conductance focusing on the even-odd difference. We have obtained numerical results that strongly support our theory.
|
Report
(4 results)
Research Products
(15 results)
