Electromagnetic Response of a Half-Filled Chern Band near Topological Criticality

TL;DR

The paper analyzes electromagnetic response across a continuous CFL–FL transition in a half-filled Chern band using a parton construction with three species ($f,d_1,d_2$) coupled to gauge fields $a_\mu,b_\mu$ and the Ioffe-Larkin rule to obtain the electronic response, i.e., $\rho_e=\rho_\text{CF}+\rho_1+\rho_2$. It shows the sharp gapped plasmon of the CFL is damped near criticality due to inter-band transitions of emergent Dirac fermions, with damping controlled by the Dirac mass $m_1$ and persisting over a finite range across the transition. The Drude weight and the $q$-dependent conductivity evolve across the transition, with $\mathcal{D}_e^{-1}=\mathcal{D}^{-1}+\Delta_1^{-1}$ on the FL side and a linear-$q$ conductivity in the CFL regime, plus an $f$-sum rule $\lim_{q\to 0}\int d\omega\,\Re[\sigma_{xx}(\omega)]=\pi\mathcal{D}$ at criticality. The work extends the framework to bosonic Laughlin–to–superfluid transitions and insulator* phases, showing plasmon damping is a robust feature of deconfined TPTs and suggesting THz probes to detect these signatures.

Abstract

We evaluate electromagnetic-response observables in a half-filled Chern band, across a topological phase transition between a composite Fermi liquid (CFL) and a Fermi liquid (FL) phase. While a sharp gapped plasma mode exists deep in the CFL phase, we demonstrate that it is damped near the proposed continuous phase transition between CFL and FL. This plasmon-damping phenomenon originates from emergent gauge fields and a Dirac-fermion-like spectrum. Similar features also occur in other continuous deconfined topological phase transitions, such as the Laughlin to superfluid transition in a bosonic system. In particular, this damping behavior extends over a finite range across the phase boundary, and, hence, we expect it to persist even when the transition is weakly first-order. Furthermore, we analyze the behavior of the Drude weight, the wavevector-dependent conductivity, and the chiral mirror effect across these topological phase transitions.

Figures (3)

• Figure 1: Damping of the plamon mode near a CFL-FL topological phase transition. (a) Absolute value of the real part of the conductivity $\sigma_{xx}(\omega)$ in the vicinity of the CFL ($m_1<0$) to FL ($m_1>0$) transition in the long wavelength limit, $q\to 0$. The plasma mode has a long lifetime at large $\abs{m_1}$ but is damped when it enters the particle-hole continuum of the emergent Dirac fermions near the deconfined topological phase transition (the fan is determined by $\omega> 2\abs{m_1}$). (b) Line cuts at different masses $m_1$. The energies are measured in units of the parton Drude weight $\cal D$.
• Figure 2: Dissipative part of conductivity at finite momentum. (a) Electron conductivity at $\omega=0.01 {\cal D}$ in CFL ($m_1<0$) phase near the phase transition at different wave vectors. The region with a linear in $q$ conductivity (approximately equal distant contours) is bounded by $|m_1|$ when $|m_1|$ is small. (b) Line cuts at different $m_1$. The inset shows the behavior at small $q$ indicated by the green box. When the mass of the Dirac fermion $m_1$ goes below $\omega/2$, we also get a real conductivity at small $q$ due to the dissipation events from the particle-hole continuum of the almost gapless Dirac fermion parton.
• Figure 3: Plasmon damping for different deconfined TPTs. Near the deconfined TPTs, the plasma mode gets damped when entering the particle-hole continuum of the Dirac fermions (fan defined by $\omega> 2\abs{m_1}$), similar to the CFL-FL transition. (a) CFL-insulator* transition, where one of the Dirac fermions ($m_1'$) flips the sign of the mass, while the other retains a negative mass, $m_1"<0$. (b) Insulator*-FL transition, where $m_1'$ remains positive while $m_1"$ flips its sign. (c) Laughlin state ($m_1<0$) to superfluid ($m_1>0$) transition. There is no sharp plasma mode for the Laughlin state.