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Register a new userQuantum criticality and the metal-insulator transition in 2D: a critical test
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Using recent insights obtained in heavy fermion physics on the thermodynamic singularity structure associated with quantum phase transitions, we present here an experimental strategy to establish if the zero-temperature transition in the disordered two dimensional gas is a real quantum phase transition. We derive a overcomplete set of scaling laws relating the density and temperature dependence of the chemical potential and the effective mass, which are in principle verifyable by experiment.
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In contrast to the seminal weak localization prediction of a non-critical Hall constant ($R_{H}$) at the Anderson metal-insulator transition (MIT), $R_{H}$ in quite a few real disordered systems exhibits both, a strong $T$-dependence and critical scaling near their MIT. Here, we investigate these issues in detail within a non-perturbative strong localization regime using cluster-dynamical mean field theory (CDMFT). We uncover $(i)$ clear and unconventional quantum-critical scaling of the $gamma$-function, finding that $gamma(g_{xy})simeq$ log$(g_{xy})$ over a wide range spanning the continuous MIT, very similar to that seen for the longitudinal conductivity, $(ii)$ strongly $T$-dependent and clear quantum critical scaling in both transverse conductivity and $R_{H}$ at the MIT. We find that these surprising results are in comprehensive and very good accord with signatures of a novel kind of localization in disordered NbN near the MIT, providing substantial support for our strong localization view.
We study the stability of the Wilson-Fisher fixed point of the quantum $mathrm{O}(2N)$ vector model to quenched disorder in the large-$N$ limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-$epsilon$ expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when $N=1$.
It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. We find that when the exchange coupling J is smaller than a certain value J*, the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states. The width of this critical region increases with a power of the concentration of magnetic impurities.
Quantum-mechanical fluctuations between competing phases at $T=0$ induce exotic finite-temperature collective excitations that are not described by the standard Landau Fermi liquid framework. These excitations exhibit anomalous temperature dependences, or non-Fermi liquid behavior, in the transport and thermodynamic properties in the vicinity of a quantum critical point, and are often intimately linked to the appearance of unconventional Cooper pairing as observed in strongly correlated systems including the high-$T_c$ cuprate and iron pnictide superconductors. The presence of superconductivity, however, precludes direct access to the quantum critical point, and makes it difficult to assess the role of quantum-critical fluctuations in shaping anomalous finite-temperature physical properties. Here we report temperature-field scale invariance of non-Fermi liquid thermodynamic, transport, and Hall quantities in a non-superconducting iron-pnictide, Ba(Fe$_{1/3}$Co$_{1/3}$Ni$_{1/3}$)$_{2}$As$_{2}$, indicative of quantum criticality at zero temperature and zero applied magnetic field. Beyond a linear in temperature resistivity, the hallmark signature of strong quasiparticle scattering, we find the scattering rate that obeys a universal scaling relation between temperature and applied magnetic fields down to the lowest energy scales. Together with the dominance of hole-like carriers close to the zero-temperature and zero-field limits, the scale invariance, isotropic field response, and lack of applied pressure sensitivity suggests a unique quantum critical system that does not drive a pairing instability.
The physical properties of rare-earth (RE) dodecaborides, characterized by a cage-glass crystal structure with loosely bound RE ions, are reviewed. These compounds are strongly correlated electron systems with simultaneously active charge, spin, orbital, and lattice degrees of freedom, which explains the complexity of all $Rmathrm{B}_{12}$ compounds including antiferromagnetic (TbB$_{12}$-TmB$_{12}$) and nonmagnetic (LuB$_{12}$) metals, on one side, and the so-called Kondo insulator compound YbB$_{12}$ and Yb-based Yb$_{x}R_{1-x}$B$_{12}$ solid solutions, on the other. The development of the cooperative dynamic Jahn-Teller instability of the covalent boron network produces trigonal and tetragonal distortions of the rigid cage and results in the symmetry lowering of the fcc lattice in the dodecaborides. The ferrodistortive dynamics in the boron sub-lattice generates both the collective modes and quasilocal vibrations (rattling modes) of the heavy RE ions, causing a modulation in the charge-carrier density and the emergence of dynamic charge stripes. We consider their manifestations both in the properties of the nonmagnetic reference compound LuB$_{12}$ and in the phase diagrams of the $Rmathrm{B}_{12}$ antiferromagnets that exhibit multiple magnetic phases with anisotropic field-angular phase diagrams in the form of the Maltese cross. We also discuss the metal-insulator transitions in YbB$_{12}$ and Yb-based dodecaborides in terms of the instability of the Yb 4$f$-electron configuration, which appears in addition to the Jahn-Teller instability of the boron cage, providing one more mechanism of the charge and spin fluctuations. The experimental results challenge the established Kondo-insulator scenario in YbB$_{12}$, providing arguments in favor of the appearance of Yb-Yb vibrationally coupled pairs which should be considered as the main factor responsible for the charge- and spin-gap formation.
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