Electronic transport in a Cantor stub waveguide network

We theoretically investigate the character of electronic eigenstates and transmission properties of a one-dimensional array of stubs with Cantor geometry. Within the framework of real space renormalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical, or acoustic waves in such hierarchical geometries.

[1]  D. Kaharudin,et al.  Microwave and Optical Technology Letters , 1988 .

[2]  A. Chakrabarti,et al.  Electronic properties of a Cantor lattice , 2004 .

[3]  A. Chakrabarti,et al.  Electronic transmission in quasiperiodic serial stub structures , 2004 .

[4]  Z. Hou,et al.  Quantum waveguide properties of a comb structure with a ring , 2003 .

[5]  J. Cerveró,et al.  Simple model for a quantum wire II. Statistically correlated disorder , 2003 .

[6]  F. Domínguez-Adame,et al.  Transport through a quantum wire with a side quantum-dot array , 2002, cond-mat/0210589.

[7]  V. Pouthier,et al.  Electronic transmission through a set of metallic clusters randomly attached to an adsorbed nanowire: Localization-delocalization transition , 2002 .

[8]  J. Cerveró,et al.  Infinite chain of different deltas: A simple model for a quantum wire , 2002, cond-mat/0206486.

[9]  H. Aubert,et al.  Use of variable lacunarity, multigap, Cantor slabs in waveguides for the design of microwave filters , 2001 .

[10]  R. Peng,et al.  Electronic transport in k-component Fibonacci quantum waveguides , 2000 .

[11]  Kiev,et al.  Ballistic electron transport in stubbed quantum waveguides: experiment and theory , 2000, cond-mat/0002284.

[12]  S. Jiang,et al.  Quantum waveguide theory of serial stub structures , 1999 .

[13]  J. Vasseur,et al.  Electronic band gaps in one-dimensional comb structures of simple metals , 1998 .

[14]  R. Riklund,et al.  Solitonlike states in a nonlinear asymmetric Cantor lattice , 1997 .

[15]  B. Gu,et al.  QUANTUM WAVEGUIDE TRANSPORT WITH SIDE-BRANCH STRUCTURES : A RECURSIVE ALGORITHM , 1997 .

[16]  M. W. Cole,et al.  Physical Adsorption: Forces and Phenomena , 1997 .

[17]  Deo,et al.  Quantum waveguide transport in serial stub and loop structures. , 1994, Physical review. B, Condensed matter.

[18]  Chakrabarti,et al.  Renormalization-group analysis of extended electronic states in one-dimensional quasiperiodic lattices. , 1994, Physical review. B, Condensed matter.

[19]  Molinari,et al.  Vibrational properties of a continuous self-similar structure. , 1994, Physical review. B, Condensed matter.

[20]  Datta,et al.  Nonscattered states in a random-dimer model. , 1993, Physical review. B, Condensed matter.

[21]  N. Sano,et al.  Electron propagation through a fibonacci lattice , 1993 .

[22]  Molinari,et al.  Direct experimental observation of fracton mode patterns in one-dimensional Cantor composites. , 1992, Physical review letters.

[23]  Xia.  Quantum waveguide theory for mesoscopic structures. , 1992, Physical review. B, Condensed matter.

[24]  S. A. Chalmers,et al.  New Quantum Structures , 1991, Science.

[25]  Severin,et al.  Transmission of light through deterministic aperiodic non-Fibonaccian multilayers. , 1990, Physical review. B, Condensed matter.

[26]  Kouwenhoven,et al.  Transport through a finite one-dimensional crystal. , 1990, Physical review letters.

[27]  Wu,et al.  Absence of localization in a random-dimer model. , 1990, Physical review letters.

[28]  Karl Hess,et al.  Theory for a quantum modulated transistor , 1989 .

[29]  Karl Hess,et al.  On the possibility of transistor action based on quantum interference phenomena , 1989 .

[30]  J. Sokoloff.  Unusual band structure, wave functions and electrical conductance in crystals with incommensurate periodic potentials , 1985 .

[31]  Chao Tang,et al.  Localization Problem in One Dimension: Mapping and Escape , 1983 .