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arXiv:2208.05932 · Nature Physics

Critical slowing down near a magnetic quantum phase transition with fermionic breakdown

Chia‐Jung Yang, Kristin Kliemt, C. Krellner, Johann Kroha, M. Fiebig, Shovon Pal

Published Jul 31, 2023• 14 citations
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Abstract

Abstract When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.

DOI
10.1038/s41567-023-02156-7

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Abstract When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.
We generalize the dynamical large-NNN multichannel Schwinger-boson approach to study the quantum phase transition of a two-dimensional Kondo-Heisenberg model, relevant for heavy electron systems, close to an antiferromagnetic Kondo destruction quantum critical point. By breaking up a Kondo singlet into a charge fermion (holon) and a bosonic spinon, we identify and characterize the quantum phase transition from an antiferromagnetically ordered state to a Kondo-dominated paramagnetic state, and attribute a jump in the holon phase shift to Kondo breakdown. We calculate transport and thermodynamic quantities. The global finite-temperature phase diagram and the critical behavior of various physical observables therein show a close resemblance to experimental observations.
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Discontinuous quantum phase transitions besides their general interest are clearly relevant to the study of heavy fermions and magnetic transition metal compounds. Recent results show that in many systems belonging to these classes of materials the magnetic transition changes from second order to first order as they approach the quantum critical point (QCP). We investigate here some mechanisms that may be responsible for this change, specifically the coupling of the order parameter to soft modes and the competition between different types of order near the QCP. For weak first order quantum phase transitions general results are obtained. In particular, we describe the thermodynamic behaviour at this transition when it is approached from finite temperatures. This is the discontinuous equivalent of the non-Fermi-liquid trajectory close to a conventional QCP in a heavy-fermion material.
In this thesis, several cases of non-equilibrium phenomena and quantum phase transitions in strongly correlated electron systems are analyzed. The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals has triggered proposals on the breakdown of the Kondo effect at the critical point. In part I, we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling � this model displays both Kondo volume collapse and Kondo-breakdown transitions. Within a large-N treatment, we find that the Kondo breakdown transition remains of second order except for very soft lattices. Finally, we relate our findings to current heavy-fermion experiments. Using non-equilibrium Green�s functions, we derive transport equations for the degrees of freedom participating in the quantum critical region of the Kondo breakdown transition. We discuss conditions under which the transport of electrical charge is described by the independent motion of conduction electrons and auxiliary bosons. Under these conditions, we derive a semiclassical transport equation for the bosons and quantitatively discuss the electrical conductivity of the whole system. Motivated by pressure experiments on FeAs-122 superconductors, in part II we propose a scenario based on local-moment physics to explain salient features at the magnetic phase boundary of CaFe2As2. In this scenario, the low-pressure magnetic phase derives from Fe moments, which become screened in the paramagnetic high-pressure phase. The quantum phase transition can be described as an orbital-selective Mott transition, which is rendered first order by coupling to the lattice. These ideas are illustrated by a suitable mean-field analysis of an Anderson lattice model. An analytical description of non-equilibrium phenomena in interacting quantum systems is rarely possible. In part III we present one example where such a description can be achieved, namely the ferromagnetic Kondo model. In equilibrium, this model is tractable via perturbative renormalization-group techniques. We employ a recently developed extension of the flow-equation method to calculate the non-equilibrium decay of the local magnetization at zero temperature. The flow equations admit analytical solutions which become exact at short and long times, in the latter case revealing that the system always retains a memory of its initial state. Finally, in part IV we analyze the Nernst effect resulting from normal state quasiparticles in the cuprates in presence of various types of translational symmetry breaking. In the electron-doped cuprates, the Nernst signal resulting from a reconstruction of the Fermi surface due to spin density wave order is discussed. An order parameter consistent with the reconstruction of the Fermi surface detected in electron-doped materials is shown to sharply enhance the Nernst signal close to optimal doping. Within a semiclassical treatment, the obtained magnitude and position of the enhanced Nernst signal agrees with Nernst measurements in electron-doped cuprates. In the hole-doped cuprates, we discuss relations between the normal-state Nernst effect and stripe order. We find that Fermi pockets caused by translational symmetry breaking lead to a strongly enhanced Nernst signal with a sign depending on the modulation period of the ordered state and other details of the Fermi surface. This implies differences between antiferromagnetic and charge-only stripes. We compare our findings with recent data from La1.6−xNd0.4SrxCuO4 and YBa2Cu3Oy.
The authors introduce exactly solvable models of the quantum phase transition, marking the breakdown of the heavy Fermi liquid in heavy-fermion materials. The solutions capture the puzzling non-Fermi liquid transport with linear-in-temperature resistivity, as seen in experiments. Furthermore, they reveal a broad regime in which a ``Planckian'' strange metal is established, namely the quasiparticle lifetime in this regime is set only by fundamental constants and the temperature. The new large-NNN approach introduced in the paper may be useful for describing a broader class of quantum critical points in systems with strong electronic correlations.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.