# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 35: Poster 2

### Q 35.8: Poster

### Mittwoch, 14. März 2012, 16:30–19:00, Poster.I+II

**Perfect conducting channel in two-dimensional random lattices with XY-disorder and engineered hopping amplitudes** — •Alberto Rodriguez^{1}, Arunava Chakrabarti^{2}, and Rudolf A. Römer^{3} — ^{1}Phisikalisches Institut, Albert-Ludwigs Universität Freiburg, Hermann-Herder Strasse 3, D-79104, Freiburg, Germany — ^{2}Department of Physics, University of Kalyani, Kalyani, West Bengal-741 235, India — ^{3}Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom

We study the spectral and transport properties of two-dimensional lattices with random on-site energies є_{x,y}, and random vertical hopping amplitudes γ_{(x,y)→ (x,y+1)}. The disorder in the system is defined by three independent random sequences {α_{x}}, {β_{y}}, {ξ_{y}}, in the following way: є_{x,y}=α_{x}β_{y}, and γ_{(x,y)→ (x,y+1)}=α_{x}ξ_{y}. By engineering the random distribution ξ_{y}, a full band of Bloch states emerges in the spectrum, and a perfect conducting channel in the *x* direction is induced in the system. We describe how to create the conductance channel in finite systems, and we study its robustness against deviations from the ideal requested values for ξ_{y}. Remarkably, we demonstrate that the channel persists in the thermodynamic limit —for the infinite two-dimensional system—. Furthermore, we also discuss how to modify the localization of the eigenstates almost at will in the *x* and *y* directions. Our results are constructed analytically and supported by extensive numerical calculations of localization lengths, conductance and density of states.