Disordered topological quantum critical points in three-dimensional systems

Ryuichi Shindou, Ryota Nakai, Shuichi Murakami

Generic non-magnetic disorder effects on topological quantum critical points (TQCP), which intervene between the three-dimensional (3D) topological insulator and an ordinary insulator, are investigated in this work. We first show that, in such 3D TQCP, any backward-scattering process mediated by chemical-potential-type impurity is always cancelled by its time-reversal ( -reversal) counter-process because of the nontrivial Berry phase supported by these two processes in the momentum space. However, this cancellation can be generalized into only those backward-scattering processes that conserve a certain internal degree of freedom, i.e. the parity density, while the 'absolute' stability of the TQCP against any non-magnetic disorders is required by the bulk-edge correspondence. Motivated by this, we further derive the self-consistent Born-phase diagram and the quantum conductivity correction in the presence of generic non-magnetic disorder potentials. The distinctions and similarities between the case with only the chemical-potential-type disorder and that with the generic non-magnetic disorders are summarized.

Bohm‐Jung Yang, Eun-Gook Moon, Hiroki Isobe +1 more

Heiko Rieger

Vaitheeswaran Gnanaraj, Balakrishanan Vellaikannan, P Balamanikandan

Abstract The interplay between disorder, topology, and many-body interactions in two-dimensional superconducting systems continues to reveal unexpected critical phenomena beyond the reach of conventional universality theory. We propose and characterize a novel universality class — the Discrete Scale Invariance Multicritical Point (DSI-MCP) — emerging from Efimov-type discrete scale invariance at the tricritical point of a two-dimensional disordered Class D topological superconductor. Using a two-loop renormalization group analysis within the replica framework, we demonstrate that when disorder and three-body couplings simultaneously exceed their critical thresholds, the renormalization group flow bypasses the conventional tricritical point and spirals into a new stable fixed point with complex eigenvalues. The imaginary component of these eigenvalues — absent at any conventional critical point with real scaling exponents — encodes log-periodic scaling and generates an infinite geometric tower of bound states, establishing the condensed matter analogue of the atomic Efimov effect. The DSI-MCP is distinguished from the tricritical point of Pan et al. by three independent criteria: a localization exponent that is fixed by symmetry and independent of the dimensional regularization parameter, a two-parameter multicritical threshold requiring simultaneous supercriticality in both disorder and three-body coupling, and the presence of log-periodic oscillations in the correlation length that are strictly forbidden at any conventional critical point. We further identify a competition between the DSI mechanism and Quantum Griffiths Singularity physics, governed by the statistical character of the disorder distribution, and construct a unified phase diagram delineating three experimentally distinguishable regimes: activated scaling, log-periodic power-law modulation, and a coexistence corridor exhibiting a doubled oscillation frequency with no precedent in the existing literature on disordered topological systems. All predictions are parameter-free once the operating point in coupling space is specified, and are directly accessible to STM spectroscopy, mesoscopic transport, and cold-atom platforms simulating Class D symmetry. These findings establish the DSI-MCP as a new entry in the classification of critical phenomena in disordered topological matter, bridging Efimov physics, quantum Griffiths singularities, and multicritical disorder-driven phase transitions into a unified theoretical framework.

Heiko Rieger

Koji Kobayashi, Tomi Ohtsuki, Ken‐Ichiro Imura +1 more

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of a disordered Z2 topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent ν and the dynamical critical exponent z are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.