Thermal conductivity at a disordered quantum critical point

A generic two-dimensional disordered topological superconductor in symmetry class D exhibits rich phenomenology and multiple phases: diffusive thermal metal (DTM), Anderson insulator (AI), and thermal quantum Hall (TQH) phase (a topological superconductor). We numerically investigate the phase diagram of a lattice model of such class-D superconductor, specifically focusing on transitions between the phases and the associated universal critical behaviors. We confirm the existence of a tricritical point and its repulsive nature at the point on the phase diagram where the three phases meet. We characterize the critical behaviors at various critical points and the tricritical point using numerical evaluation of the localization length, the conductance (or conductivity), and the density of states. We conclude that the two metal-insulator transitions (DTM-TQH and DTM-AI) belong to the same universality class, whereas the tricritical point represents a distinct universality class.A generic two-dimensional disordered topological superconductor in symmetry class D exhibits rich phenomenology and multiple phases: diffusive thermal metal (DTM), Anderson insulator (AI), and thermal quantum Hall (TQH) phase (a topological superconductor). We numerically investigate the phase diagram of a lattice model of such class-D superconductor, specifically focusing on transitions between the phases and the associated universal critical behaviors. We confirm the existence of a tricritical point and its repulsive nature at the point on the phase diagram where the three phases meet. We characterize the critical behaviors at various critical points and the tricritical point using numerical evaluation of the localization length, the conductance (or conductivity), and the density of states. We conclude that the two metal-insulator transitions (DTM-TQH and DTM-AI) belong to the same universality class, whereas the tricritical point represents a distinct universality class.

arXiv:2108.12133Physical review. B./Physical review. BNov 1, 202115 citations

Disordered systems near quantum critical points

Heiko Rieger

Computer Physics CommunicationsSep 1, 19990 citations

Signatures of the nematic ordering transitions in the thermal conductivity of d -wave superconductors

Lars Fritz, Subir Sachdev A

We study experimental signatures of the Ising nematic quantum phase transition in $d$ -wave superconductors, associated with the change of lattice symmetry from tetragonal to orthorhombic in the superconducting state. The characteristic feature of this transition is that the ratio between the Fermi velocity ${v}_{F}$ and gap velocity ${v}_{\ensuremath{\Delta}}$ flows to a maximally anisotropic fixed point; i.e., the renormalization-group fixed point is situated at ${({v}_{\ensuremath{\Delta}}/{v}_{F})}^{\ensuremath{\ast}}=0$. Our main point is that the logarithmic approach to this fixed point has visible signatures in the thermal transport. The analysis of the quasiparticle contribution to the thermal transport is carried out in the framework of a kinetic approach, which shows that the thermal conductivity is enhanced near the nematic critical point. Another aspect of our study is the interplay of dilute disorder and electronic interactions in the measured thermal transport coefficients.We study experimental signatures of the Ising nematic quantum phase transition in $d$-wave superconductors, associated with the change of lattice symmetry from tetragonal to orthorhombic in the superconducting state. The characteristic feature of this transition is that the ratio between the Fermi velocity ${v}_{F}$ and gap velocity ${v}_{\ensuremath{\Delta}}$ flows to a maximally anisotropic fixed point; i.e., the renormalization-group fixed point is situated at ${({v}_{\ensuremath{\Delta}}/{v}_{F})}^{\ensuremath{\ast}}=0$. Our main point is that the logarithmic approach to this fixed point has visible signatures in the thermal transport. The analysis of the quasiparticle contribution to the thermal transport is carried out in the framework of a kinetic approach, which shows that the thermal conductivity is enhanced near the nematic critical point. Another aspect of our study is the interplay of dilute disorder and electronic interactions in the measured thermal transport coefficients.

arXiv:0901.3530Physical Review BOct 5, 200923 citations

Estimating critical disorder strength of an AAH system via thermal response

Nandi, Sanchita, Santanu K. Maiti

The Aubry-André-Harper (AAH) model provides a paradigmatic platform to study localization phenomena, where a transition from a conducting to an insulating phase occurs at a critical disorder strength equal to twice the nearest-neighbor hopping amplitude, $2t$ . While this transition has been explored extensively through various probes, here we propose a fundamentally new approach based on thermal response. Specifically, we demonstrate that the electronic specific heat exhibits a distinctive signature across the transition, directly reflecting the anomalous evolution of the density of states with disorder strength. Our findings, supported by numerical analysis, establish specific heat measurement as a powerful and sensitive probe for detecting the critical point. This thermal characterization opens a new avenue for exploring disorder-induced phase transitions and paves the way for experimental realization in engineered quantum systems.The Aubry-André-Harper (AAH) model provides a paradigmatic platform to study localization phenomena, where a transition from a conducting to an insulating phase occurs at a critical disorder strength equal to twice the nearest-neighbor hopping amplitude, $2t$. While this transition has been explored extensively through various probes, here we propose a fundamentally new approach based on thermal response. Specifically, we demonstrate that the electronic specific heat exhibits a distinctive signature across the transition, directly reflecting the anomalous evolution of the density of states with disorder strength. Our findings, supported by numerical analysis, establish specific heat measurement as a powerful and sensitive probe for detecting the critical point. This thermal characterization opens a new avenue for exploring disorder-induced phase transitions and paves the way for experimental realization in engineered quantum systems.

arXiv:2505.07059May 11, 20250 citations

Disordered systems near quantum critical points

Heiko Rieger

Physica A Statistical Mechanics and its ApplicationsApr 1, 19991 citation

We study experimental signatures of the Ising nematic quantum phase transition in

d

-wave superconductors, associated with the change of lattice symmetry from tetragonal to orthorhombic in the superconducting state. The characteristic feature of this transition is that the ratio between the Fermi velocity

{v}_{F}

and gap velocity ${v}_{\ensuremath{\Delta}}$ flows to a maximally anisotropic fixed point; i.e., the renormalization-group fixed point is situated at ${({v}_{\ensuremath{\Delta}}/{v}_{F})}^{\ensuremath{\ast}}=0$. Our main point is that the logarithmic approach to this fixed point has visible signatures in the thermal transport. The analysis of the quasiparticle contribution to the thermal transport is carried out in the framework of a kinetic approach, which shows that the thermal conductivity is enhanced near the nematic critical point. Another aspect of our study is the interplay of dilute disorder and electronic interactions in the measured thermal transport coefficients.

2t

. While this transition has been explored extensively through various probes, here we propose a fundamentally new approach based on thermal response. Specifically, we demonstrate that the electronic specific heat exhibits a distinctive signature across the transition, directly reflecting the anomalous evolution of the density of states with disorder strength. Our findings, supported by numerical analysis, establish specific heat measurement as a powerful and sensitive probe for detecting the critical point. This thermal characterization opens a new avenue for exploring disorder-induced phase transitions and paves the way for experimental realization in engineered quantum systems.