Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit
Zubair Iftikhar, A. Anthore, Andrew K. Mitchell, François D. Parmentier, U. Gennser, Abdelkarim Ouerghi, A. Cavanna, Christophe Mora, Pascal Simon, F. Pierre
Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.
Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.
This thesis explores several fundamental topics in mesoscopic circuitry that incorporates few electronic conduction channels. The first experiments address the quantized character (the discreteness) of charge in circuits. We demonstrate the charge quantization criterion, observe the predicted charge quantization scaling and demonstrate a crossover toward a universal behavior as temperature is increased. The second set of experiments addresses the unconventional quantum critical physics that arises in the multichannel Kondo model. By implementing a Kondo impurity with a pseudo-spin of ½ constituted by two degenerate charge states of a circuit, we explore the two- and three-channel Kondo physics. At the symmetric quantum critical point, we observe the predicted universal Kondo fixed points, scaling exponents and validate the full numerical renormalization group scaling curves. Away from the quantum critical point, we explore the crossover from quantum criticality: direct visualization of the development of a quantum phase transition, the parameter space for quantum criticality, as well as universality and scaling behaviors.
Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we resolve this regime for the three-channel charge Kondo device of Iftikhar et al. [Tunable quantum criticality and super-ballistic transport in a "charge" Kondo circuit, Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592], benchmarking against conformal field theory by reproducing the universal zero-frequency conductance and, crucially, going beyond it to obtain the full frequency crossover of the conductance and the full temperature crossover of the impurity entropy, together with a continuous line of fixed points for interacting leads. These results establish FRG as a powerful nonperturbative tool for quantum impurity problems in regimes inaccessible to conventional approaches, with direct implications for mesoscopic experiments.
The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its crossover to the one-channel counterpart, a Fermi liquid. Scaling up such a platform, we find a hierarchy of non-Fermi Liquids and their tunable crossovers based on a renormalization group analysis. Utilizing results from a conformal field theory, we further examine the universal conductances of this strongly correlated system and their finite temperature scaling, which elucidate the sharp distinctions between charge and spin Kondo physics.
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have made it possible to enhance the interaction between the electrons. Here we show that hitherto unexplained anticrossing between conduction energy subbands, observed in such experiments, can be explained through a simple yet effective discretized model which undergoes a second-order quantum phase transition within the Ising universality class. Accordingly, we observe how the charge distribution, transverse to the direction of the wire, will vary across the phase transition. We show that data coming from three different samples with differing electron densities and gate voltages show a remarkable universal scaling behavior, determined by the relevant critical exponent, which is only possible near a quantum phase transition.
The Kondo effect, deriving from a local magnetic impurity mediating electron-electron interactions, constitutes a flourishing basis for understanding a large variety of intricate many-body problems. Its experimental implementation in tunable circuits has made possible important advances through well-controlled investigations. However, these have mostly concerned transport properties, whereas thermodynamic observations - notably the fundamental measurement of the spin of the Kondo impurity - remain elusive in test-bed circuits. Here, with a novel combination of a 'charge' Kondo circuit with a charge sensor, we directly observe the state of the impurity and its progressive screening. We establish the universal renormalization flow from a single free spin to a screened singlet, the associated reduction in the magnetization, and the relationship between scaling Kondo temperature and microscopic parameters. In our device, a Kondo pseudospin is realized by two degenerate charge states of a metallic island, which we measure with a non-invasive, capacitively coupled charge sensor. Such pseudospin probe of an engineered Kondo system opens the way to the thermodynamic investigation of many exotic quantum states, including the clear observation of Majorana zero modes through their fractional entropy.
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/m and the number of transmitting channels. Furthermore, we predict that the fractional filling factor ν defines a universal Kondo scaling in the vicinity of a special triple quantum critical point featured by the emergence of a Z3 parafermion.