Conductance and multifractality at integer quantum Hall transitions with dissipation

Hideaki Obuse

Karlsruhe Institute of Technology, Institute of Nanotechnology, Karlsruhe, Germany

The integer quantum Hall (IQH) effect has been the exciting area of research of condensed matter physics for more than two decades, although the conductance distributions at the plateau transition are not fully understood. On the other hand, it is known that wave functions at critical point show scale-invariant multifractal structures. Multifractality is quite important because exponents characterizing multifractality are universal exponents and related to scaling dimensions of underlying conformal field theories in two dimensions. Since, the wave functions are difficult to observe in experiments, a relation between multifractality and the conductance should be clarified. In this work, we theoretically investigate multifractality of the conductance at the IQH transition in two dimensions with and without dissipation. Dissipation is taken into account by introducing absorbing boundaries where the current can flow out from the system. In the dissipationless case, we show that exponents calculated from the point-contact conductance are related to the multifractality calculated from the wave function. On the other hand, in the system with dissipation where multifractality of wave functions are not understood due to non-Hermiticity, we find that this system shows the different critical behavior from the dissipationless system and is characterized by new multifractality. Finally, we show that these results are obtained even for the two-terminal conductance in the quasi-one dimension, like Hall bars, due to conformal invariance.

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