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arXiv:2510.20491

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

Nitay Hurvitz, Gleb Finkelstein, Eran Sela

Published Oct 23, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2510.20491

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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 NNN 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=1ν=1ν=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=12kBlog⁡(N+1)ΔS = \frac{1}{2}k_B \log (N+1)ΔS=21​kB​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.
Unconventional quantum states defying the ubiquitous Fermi-liquid paradigm can emerge in the presence of strong electronic correlations. Among these, non-Abelian anyons - such as Majorana zero modes and Fibonacci anyons - are of particular interest for topological quantum computing due to their non-integer quantum dimensions d>1, which allows for protected non-local encoding and processing of quantum information. However, despite considerable efforts, the unambiguous characterisation of such anyons via transport measurements has proved challenging. Instead, here we provide experimental evidence for the low-temperature fractional entropy Delta S associated with a single anyon, which directly implies its non-Abelian character through the relation Delta S = kB ln(d). This thermodynamic signature is measured in metal-semiconductor quantum circuits engineered to realize quantum-critical states from frustrated interactions. Using a micrometre-scale metallic island coupled to two or three electronic leads, we tune the system to two-channel and three-channel Kondo critical points. By measuring the island charge and exploiting a thermodynamic Maxwell relation, we estimate the entropy associated with the anyons that emerge in these critical states. Our observations reveal fractional values, exposing non-Abelian anyons. The corresponding scaling dimensions are consistent with theoretical predictions for a Majorana zero mode Delta S = kB ln(sqrt(2)) and a Fibonacci anyon Delta S = kB ln(1 +sqrt(5))/2 for two and three channels. These findings establish entropy measurements as a powerful tool for characterizing exotic quantum states.
We show that it is possible and rather efficient to compute at non-zero temperature the thermoelectric characteristics of Coulomb blockaded fractional quantum Hall islands, formed by two quantum point contacts inside of a Fabry–Pérot interferometer, using the conformal field theory partition functions for the chiral edge excitations. The oscillations of the thermopower with the variation of the gate voltage as well as the corresponding figure-of-merit and power factors, provide finer spectroscopic tools which are sensitive to the neutral multiplicities in the partition functions and could be used to distinguish experimentally between different universality classes sharing the same electric properties. We also propose a procedure for measuring the ratio r=vn/vc of the Fermi velocities of the neutral and charged edge modes for filling factor νH=5/2 from the power-factor data in the low-temperature limit.
We study the influence of many-body interactions on the transport properties in a two-site charge Kondo circuit recently implemented in a hybrid metal-semiconductor double-quantum dot device [W. Pouse et al., Nat. Phys. 19, 492 (2023)]. There emerge two principal types of interactions: (i) an intrinsic one, described by the Luttinger liquid model, and (ii) an induced one, which appears due to the coupling of the system to an Ohmic environment. Case (i) could be achieved if the charge Kondo circuit operates in the fractional quantum Hall regime, while case (ii) can be implemented via a finite number of open ballistic channels coupled to both the quantum dots. We demonstrate that the conductance scaling for the case of strong and weak interdot coupling is fully determined by the effective interaction parameter, which is the combination of the fractional filling factor $\ensuremath{\nu}=1/m$ and the number of transmitting channels. Furthermore, we predict that the fractional filling factor $\ensuremath{\nu}$ defines a universal Kondo scaling in the vicinity of a special triple-quantum critical point featured by the emergence of a Z3{\mathbb{Z}}_{3}Z3​ parafermion.
Measuring entropy in highly correlated systems extends beyond simply counting accessible microstates in the ground state, offering key insights where traditional observables, such as conductance, may be insufficient. However, traditional entropy measurements, which often rely on bulk properties, lack the sensitivity required for systems with only a few particles.In this study, we investigate the entropy evolution in a non-Fermi liquid by examining aKondo impurity. This impurity mediates strong electron-electron interactions, and reflects theexotic properties of heavy fermions and the non-Fermi liquids behavior that may arise inquantum phase transitions.Specifically, by mapping the Kondo impurity onto the charge degrees of freedom of a metallic island, its state can be measured non-invasively through a capacitively coupledcharge sensor. By linking charge and entropy through a Maxwell relation, we observe a reduction in the impurity's residual entropy. This reduction aligns with Kondo universal renormalization flows, illustrating a transition from a free spin-1/2 state with entropy kᵦ ln(2) to a screened singlet state with zero entropy. Additionally, coupling the impurity to multiple leads, we identify a quantum critical regime where the fractional impurity entropy suggests the emergence of anyons.
We study the thermoelectric transport properties of fractional quantum Hall systems based on an exact diagonalization calculation. Based on the relation between the thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ has power-law scaling ${\ensuremath{\alpha}}_{xy}\ensuremath{\propto}{T}^{\ensuremath{\eta}}$ for gapless composite Fermi-liquid states at filling numbers $\ensuremath{\nu}=1/2$ and 1/41/41/4 at low temperatures (TTT), with an exponent $\ensuremath{\eta}\ensuremath{\sim}0.5$ distinctly different from Fermi liquids. The power-law scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior of these interacting systems at low TTT. In contrast, for the 1/31/31/3 fractional quantum Hall state, ${\ensuremath{\alpha}}_{xy}$ vanishes at low TTT with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish another manifestation of the non-Fermi-liquid nature of quantum Hall fluids at a finite temperature.
We study the influence of many-body interactions on the transport properties in a two-site charge Kondo circuit recently implemented in a hybrid metal-semiconductor double-quantum dot device [W. Pouse {\it et al.}, Nat. Phys. {\bf 19}, 492 (2023)]. There emerge two principal types of interactions: (i) an intrinsic one, described by the Luttinger liquid model, and (ii) an induced one, which appears due to the coupling of the system to an Ohmic environment. Case (i) could be achieved if the charge Kondo circuit operates in the fractional quantum Hall regime, while case (ii) can be implemented via a finite number of open ballistic channels coupled to both the quantum dots. We demonstrate that the conductance scaling for the case of strong and weak interdot coupling is fully determined by the effective interaction parameter, which is the combination of the fractional filling factor ν=1/mν=1/mν=1/m and the number of transmitting channels. Furthermore, we predict that the fractional filling factor ννν defines a universal Kondo scaling in the vicinity of a special triple quantum critical point featured by the emergence of a Z3\mathbb{Z}_3Z3​ parafermion.