Metallic island array as synthetic quantum matter: fractionalized entropy and thermal transport

TL;DR

The paper analyzes a one-dimensional array of floating metallic islands connected by quantum Hall edge channels and demonstrates that, in the regime where charging energy dominates, the system exhibits charge fractionalization and a novel heat transport behavior. Using a bosonic scattering formalism and a boundary sine-Gordon perspective, the authors derive a universal finite-entropy quench upon partitioning the chain with a quantum point contact, $\Delta S = \frac{1}{2}k_B \log(N+1)$, and predict a heat flow $J$ that can persist with negligible internal temperature differences at filling factor $\nu=1$. They show that the chain supports a flat temperature profile for $\nu=1$ with $T_{\Omega,n}^2 = (T_1^2+T_2^2)/2$ and a conductance scaling as $G_N = \frac{1}{N+1} \frac{e^2}{h}$, and they connect the observed entropy change to emergent parafermion-like excitations via $\Delta = 1/(N+1)$. The work generalizes to higher integer fillings, where neutral modes modify transport and entropy in a controllable way, suggesting a route to engineering synthetic quantum matter with nontrivial topological features.

Abstract

The surprisingly rich physics of a single Coulomb-blockaded metallic island, when coupled to quantum Hall edge channels, is now well established -- giving rise to charge fractionalization and multi-channel quantum impurity behavior. Here, we show that qualitatively new physics emerges in arrays of such elements. We consider a 1D chain of $N$ metallic islands, focusing on thermodynamic signatures such as quantized entropy and anomalous thermal conductance. Universal and robust behavior emerges for energy scales smaller than the charging energy of the islands. In particular, we demonstrate that for the bulk filling factor of $ν=1$, the islands could support a finite heat flow without temperature difference between them. Upon pinching the array with a quantum point contact, we predict an entropy change that scales with the number of islands as $ΔS = \frac{1}{2}k_B \log (N+1)$, which can be measured using charge detection. This fractional entropy suggests the emergence of a novel type of excitations in the array.

Figures (5)

• Figure 1: (a) 1D array of metallic islands connected by quantum Hall edge states. (b) Each island describes a scattering matrix Eq. (\ref{['eq:S']}) connecting outgoing and incoming modes. Importantly, the channels extending into the island also act as either incoming $(I_{3,4})$ or outgoing $(O_{1,2})$ modes. (c) The properties of the array are obtained by combining many such scattering matrices.
• Figure 2: Top: schematic of $N$ islands connected to microscopic reservoirs at temperatures $T_1$ and $T_2$. Bottom: temperature profile along the 1D array displaying constant temperature profile for $\nu=1$, which is a consequence of the heat Coulomb blockade. As the filling factor is increased, the temperature profile approaches that without the charging energy (see the $\nu=100$ curve), however for small $\nu$ it remains essentially flat in the middle of the array.
• Figure 3: Chain disconnection due to reflection at a QPC and associated entropy difference.
• Figure 4: 1D array of metallic islands with 2 QPCs and schematic conductance and entropy curves. The conductance displays interference versus the gate voltage, and the entropy shows peaks scaling logarithmically with the number of islands.
• Figure 5: (a) We illustrate explicitly the 10 components of the incoming current vector $\vec{I} = \{I_\mu \}$ for the case of 4 islands. (b) Rather than talking about currents $j_\mu = -\frac{e}{2\pi} \partial_t \phi_{\mu}$, one can equivalently distinguish incoming and outgoing components of the bosonic fields $\{ \phi_{\mu} \}$. We draw all the boson fields as right movers propagating from the incoming- to the outgoing-region, and depict the interactions due to the separate charging energy terms. The QPC acts at an intermediate stage within the scattering process. (c) The particular combination of incoming fields $\tilde{\phi}_1 = \frac{1}{\sqrt{2(N+1)}}\sum_{\mu=1}^{2(N+1)} (-1)^\mu \phi_\mu$, corresponding to Eq. (\ref{['eq:L_R']}), is a globally neutral scattering eigenmode to which the QPC uniquely couples at any link.