Novel physical phenomena in proximity to quantum critical point

Abstract

The weakly interacting quasiparticle picture of a Fermi liquid proposed by Landau (the phonon-mediated electron-pairing theory of Bardeen-Cooper-Schrieffer) provided a coherent theoretical basis for understanding how the interactions between electrons affect the low-temperature properties of metals (metallic superconductors) for the past five decades. However, in recent years, strong departures from the predictions of these theories have been observed in an increasingly large number of systems, particularly in the vicinity of a quantum phase transition (QPT). This paper briefly reviews the current state of research in the areas of the non-Fermi liquid (NFL) state, spin-fluctuation-mediated anisotropic superconductivity, and Bose-Einstein condensation (BEC) of magnons (bosonic quasiparticle excitations) near a quantum critical point (QCP), which is induced by external pressure or doping or nanocrystallite size or magnetic fields. 1 Preamble Early theoretical proposition [1] that the ground state of a quantum system at T ¼ 0 changes from ordered to disordered when some control parameter (e.g., a coupling constant) in the Hamiltonian attains a critical value [the quantum critical point (QCP)], shifted the scientific focus away from the classical phase transitions, which occur at finite temperatures and are driven by thermal fluctuations of the order parameter with temperature as a control parameter. T ¼ 0 or T 6 ¼ 0 is not the only distinguishing feature between quantum and classical phase transitions. Unlike in classical phase transitions, the statics and dynamics in quantum systems at T ¼ 0 are inextricably linked with the result that a d-dimensional quantum system at T ¼ 0 can be considered [1, 2] as a (d þ z)-dimensional classical system, where z is the critical exponent that characterizes the dynamics in the vicinity of a quantum phase transition (QPT). Although a QPT occurs at zero temperature, the behavior of the system at temperatures sufficiently close to the QCP is still governed by quantum critical effects [1,2]. The underlying QCP effects can thus be studied experimentally at finite but low temperatures even though the QCP at T ¼ 0 is inaccessible to experiments. In practice, external pressure ( p) or doping (x, chemical pressure) or an external magnetic field (H) is used as a control parameter to tune the spin system to the QCP by bringing down the magnetic order-disorder transition temperature (i.e., Curie temperature, T C , for a ferromagnet or Néel temperature, T N , for an antiferromagnet) to almost zero when the control parameter approaches a threshold p c or x c or H c .In recent years, discovery of new physical phenomena near the QCP such as the non-Fermi liquid (NFL) state, unconventional superconductivity and Bose-Einstein condensation (BEC) of quasiparticle excitations necessitated a constant revision in our understanding of how interactions between electrons influence the low-temperature properties of metals, in particular and spin systems, in general. In the following sections, these phenome...

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“…Rare earth compounds occupy the center stage in condensed matter physics because they exhibit novel electronic and magn etic states, and the coupling between them gives rise to a new class of materials with exotic physical properties. Quantum critical point (QCP), which refers to a continuous phase trans ition at absolute zero driven by zero-point quantum spin fluctuations, has been realized at non-zero temperatures [1] in a wide variety of strongly correlated electron systems, including heavy Fermions. In experiments, a given system is tuned to the QCP by using either applied magnetic field (H) or pressure (p ) or chemical doping (x) to progressively bring down the antiferromagnetic (AFM) or ferromagnetic (FM) phase trans ition temperature, i.e., T N (Néel) or T c (Curie) temper ature, so that T N or T c approach absolute zero at a critical value of the control parameter H c or p c or x c .…”

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“…Recently, BEC of triplet and quintuplet excitations have also been observed above the critical fields 8.7 T, and 32.42 T, respectively, in the S = 1 dimer compound Ba 3 Mn 2 O 8 [14,15]. On the other hand, BEC of magnons has been observed in other class of materials with magnetic-LRO including, yttrium-iron-garnet films at room temperature via microwave pumping [16], Cs 2 CuCl 4 [17] and Gd nanocrystalline samples [18,19]. In the case of Cs 2 CuCl 4 , although the material undergoes a magnetic transition (T N ) at 0.595 K, the gap in the magnon spectrum closes at about 8.51 T and the three dimensional (3D) BEC phase boundary relation T N ∝ (H − H c ) 1/α with an exponent 1/α = 2/3 is observed, similar to other spin-gap materials [7][8][9][10][11][12][13][14][15].…”

“…In this context, the applied magnetic field (H) acts as a chemical potential in separating the spin-gap region and LRO region of the quantum phase diagram at T → 0 K [6]. Experimentally, the field-induced BEC of triplon behavior has been intensively studied for various spin-gap materials with S = 1/2 dimers TlCuCl 3 [7,8] [18,19]. In the case of Cs 2 CuCl 4 , although the material undergoes a magnetic transition (T N ) at 0.595 K, the gap in the magnon spectrum closes at about 8.51 T and the three dimensional (3D) BEC phase boundary relation T N ∝ (H − H c ) 1/α with an exponent 1/α = 2/3 is observed, similar to other spin-gap materials [7][8][9][10][11][12][13][14][15].…”