Characterization of the quantized Hall insulator phase in the quantum critical regime

Abstract

The conductivity σ and resistivity ρ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy EF and temperature T in the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors are eliminated by using the noncommutative Kubo-formula. The results reproduce all the key experimental characteristics of this transition in Integer Quantum Hall (IQHE) systems. In particular, the Quantized Hall Insulator (QHI) phase is detected and analyzed. The presently accepted characterization of the QHI phase in the quantum critical regime, based entirely on experimental data, is fully supported by our theoretical investigation.

Antilevitation of Landau levels in vanishing magnetic fields

“…Similar disorder-driven anti-levitation scenario was already hinted in earlier numerical calculations [13,14].…”

Mapping the current–current correlation function near a quantum critical point

“…Numerical applications of the Kubo-formula with dissipation can be found in Refs. [27,48,54,55], which focused on the critical behavior of the transport coefficients of disorder topological insulators.…”

“…As we have seen above, this is absolutely necessary in order to understand the quantum critical regime. More specifically, the simulations reported in [27] were based on the finite-temperature Kubo-formula written in Eq. (30) and simplified to the so called relaxation time approximation.…”

Disordered crystals from first principles I: Quantifying the configuration space

“…Given these inputs, a controlled and exponentially fast (w.r.t. crystal's size) converging numerical implementation of the formalism has been developed in [11,12] and, for simple models of disordered crystals, applications can be found in [13,14,15,16]. The transport formalism and its numerical implementation has been extended in [17] to other aperiodic systems, such as incommensurately layered materials.…”