Multi-flavor quantum criticality

In a quantum critical metal, the electronic density of states, or quasiparticle mass on the Fermi surface, is strongly enhanced through electronic correlations. The density of states in the quantum critical unconventional superconductor CeCoIn$_5$, can be readily accessed in the normal state because all energy scales are small. However, the experimental challenges associated with large nuclear specific heat and long nuclear spin-lattice relaxation times have impeded unveiling a more detailed physical picture. Here we report an extensive thermal impedance spectroscopy study of CeCoIn$_5$ that assesses the density of states in two independent ways, via the nuclear spin-lattice relaxation rate and via the specific heat. We establish that the temperature- and magnetic field dependence of the nuclear spin-lattice relaxation rate is determined entirely by the energy-scale competition near the quantum critical point. In particular, mass enhancement is cut off at finite magnetic fields. However, the specific heat measurements reveal excess entropy in addition to that associated with the density of states on the Fermi surface. This excess entropy is direct thermodynamic evidence for a "second flavor" of fluctuating boson in CeCoIn$_5$. The electronic nature of this excess entropy is evidenced by its suppression in the superconducting state. We suggest such a multi-flavour character for a broader class of quantum critical metals.Comment: 39 page

Element-specific probe of quantum criticality in CeCoIn5\mathrm{CeCoIn_{5}}

Employing the elemental sensitivity of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), we study the valence and magnetic order in the heavy fermion superconductor CeCoIn$_5$. We probe spin population of the f-electrons in Ce and d-electrons in Co as a function of temperature (down to 0.1 K) and magnetic field (up to 6 T). From the XAS we find a pronounced contribution of Ce$^{4+}$ component at low temperature and a clear temperature dependence of the Ce valence below 5 K, suggesting enhanced valence fluctuations, an indication for the presence of a nearby quantum critical point (QCP). We observe no significant corresponding change with magnetic field. The XMCD displays a weak signal for Ce becoming clear only at 6 T. This splitting of the Kramers doublet ground state of Ce$^{3+}$ is significantly smaller than expected for independent but screened ions, indicating strong antiferromagnetic pair interactions. The unconventional character of superconductivity in CeCoIn$_5$ is evident in the extremely large specific heat step at the superconducting transition.Comment: 5 pages, 5 figures. Supplementary information (4 pages, 5 figures

Probing quantum criticality in heavy fermion CeCoIn5

Understanding the low-temperature properties of strongly correlated materials requires accurate measurement of the physical properties of these systems. Specific heat and nuclear spin-lattice relaxation are two such properties that allow the investigation of the electronic behavior of the system.  In this thesis, nanocalorimetry is used to measure specific heat, but also as basis for new experimental approach, developed to disentangle the different contributions to specific heat at low temperatures. The technique, that we call Thermal Impedance Spectroscopy (TISP) allows independent measurement of the electronic and nuclear specific heat at low temperatures based on the frequency response of the calorimeter-sample assembly. The method also enables simultaneous measurements of the nuclear spin-lattice relaxation time (T1). The nuclear spin lattice relaxation, as 1/T1T, and electronic specific heat, as C/T, provide information about the same quantity, electronic density of states, in the system. By comparing these properties in strongly correlated systems, we can obtain insights of electronic interactions.  Metallic indium is studied using thermal impedance spectroscopy from 0.3 K to 7 K at 35 T. The magnetic field dependence of nuclear spin-lattice relaxation rate is measured. Indium is a simple metallic system and the expected behavior of the nuclear spin-lattice relaxation is similar to that of the electronic specific heat. The results of the measurement are matched with the expectation from a simple metallic system and Nuclear Magnetic Resonance (NMR) measurements. This demonstrates the effectiveness of the new technique.  The heavy-fermion superconductor CeCoIn5 is studied using thermal impedance spectroscopy and ac-calorimetry. This material is located near a quantum critical point (QCP) bordering antiferromagnetism, as evidenced by doping studies. The nature of its quantum criticality and unconventional superconductivity is still elusive. Contrasting specific heat and nuclear spin-lattice relaxation in this correlated system helps to reveal the character of its quantum criticality.  The quantum criticality in CeCoIn5 is also studied using X-ray Absorption Spectroscopy (XAS) across the superconducting transition and X-ray Magnetic Circular Dichroism (XMCD) at 0.1 K and 6 T. The element-specific probe zooming in on cerium in this material indicates two things, a mixed valence of Ce in the superconducting state and a very small magnetic moment, that implies resonance-bond like antiferromagnetic local ordering in the system.

Probing quantum criticality in heavy fermion CeCoIn5

Understanding the low-temperature properties of strongly correlated materials requires accurate measurement of the physical properties of these systems. Specific heat and nuclear spin-lattice relaxation are two such properties that allow the investigation of the electronic behavior of the system.  In this thesis, nanocalorimetry is used to measure specific heat, but also as basis for new experimental approach, developed to disentangle the different contributions to specific heat at low temperatures. The technique, that we call Thermal Impedance Spectroscopy (TISP) allows independent measurement of the electronic and nuclear specific heat at low temperatures based on the frequency response of the calorimeter-sample assembly. The method also enables simultaneous measurements of the nuclear spin-lattice relaxation time (T1). The nuclear spin lattice relaxation, as 1/T1T, and electronic specific heat, as C/T, provide information about the same quantity, electronic density of states, in the system. By comparing these properties in strongly correlated systems, we can obtain insights of electronic interactions.  Metallic indium is studied using thermal impedance spectroscopy from 0.3 K to 7 K at 35 T. The magnetic field dependence of nuclear spin-lattice relaxation rate is measured. Indium is a simple metallic system and the expected behavior of the nuclear spin-lattice relaxation is similar to that of the electronic specific heat. The results of the measurement are matched with the expectation from a simple metallic system and Nuclear Magnetic Resonance (NMR) measurements. This demonstrates the effectiveness of the new technique.  The heavy-fermion superconductor CeCoIn5 is studied using thermal impedance spectroscopy and ac-calorimetry. This material is located near a quantum critical point (QCP) bordering antiferromagnetism, as evidenced by doping studies. The nature of its quantum criticality and unconventional superconductivity is still elusive. Contrasting specific heat and nuclear spin-lattice relaxation in this correlated system helps to reveal the character of its quantum criticality.  The quantum criticality in CeCoIn5 is also studied using X-ray Absorption Spectroscopy (XAS) across the superconducting transition and X-ray Magnetic Circular Dichroism (XMCD) at 0.1 K and 6 T. The element-specific probe zooming in on cerium in this material indicates two things, a mixed valence of Ce in the superconducting state and a very small magnetic moment, that implies resonance-bond like antiferromagnetic local ordering in the system.

PDE-based deployment with communicating leaders for a large-scale multi-agent system

We study the deployment of a first-order multiagent system (MAS) onto a curve in Rn. The MAS has a chain topology and two types of agents: leaders and followers. The leaders know their positions relative to the target curve. Neighboring leaders can communicate with one another. Each follower is aware of the intended and existing differences between its state and the states of its two nearest neighbors. To solve the formation control problem, we derive a semilinear parabolic PDE describing the system when the number of agents is sufficiently large. We derive the stability condition in terms of linear matrix inequalities (LMIs). Using numerical simulations, we demonstrate that increased connectivity between the leaders improves the deployment speed of the MAS