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Register a new userCritical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities
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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.
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We study effects of classical magnetic impurities on the Anderson metal-insulator transition numerically. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{rm c}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $ u$ and enhances the multifractality parameter $alpha_0$. The new value of $ u$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.
Aging effects in the relaxations of conductivity of a two-dimensional electron system in Si have been studied as a function of carrier density. They reveal an abrupt change in the nature of the glassy phase at the metal-insulator transition (MIT): (a) while full aging is observed in the insulating regime, there are significant departures from full aging on the metallic side of the MIT, before the glassy phase disappears completely at a higher density $n_g$; (b) the amplitude of the relaxations peaks just below the MIT, and it is strongly suppressed in the insulating phase. Other aspects of aging, including large non-Gaussian noise and similarities to spin glasses, also have been discussed.
A wide range of disordered materials, including disordered correlated systems, show Universal Dielectric Response (UDR), followed by a superlinear power-law increase in their optical responses over exceptionally broad frequency regimes. While extensively used in various contexts over the years, the microscopics underpinning UDR remains controversial. Here, we investigate the optical response of the simplest model of correlated fermions, Falicov-Kimball model (FKM), across the continuous metal-insulator transition (MIT) and analyze the associated quantum criticality in detail using cluster extension of dynamical mean field theory (CDMFT). Surprisingly, we find that UDR naturally emerges in the quantum critical region associated with the continuous MIT. We tie the emergence of these novel features to a many-body orthogonality catastrophe accompanying the onset of strongly correlated electronic glassy dynamics close to the MIT, providing a microscopic realization of Jonschers time-honored proposal as well as a rationale for similarities in optical responses between correlated electronic matter and canonical glass formers.
We consider the orthogonality catastrophe at the Anderson Metal-Insulator transition (AMIT). The typical overlap $F$ between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size $L$ as $F sim exp (- langle I_Arangle /2)= exp(-c L^{eta})$, where $I_A$ is the so called Anderson integral, $eta $ is the power of multifractal intensity correlations and $langle ... rangle$ denotes the ensemble average. Thus, strong disorder typically increases the sensitivity of a system to an additional impurity exponentially. We recover on the metallic side of the transition Andersons result that fidelity $F$ decays with a power law $F sim L^{-q (E_F)}$ with system size $L$. This power increases as Fermi energy $E_F$ approaches mobility edge $E_M$ as $q (E_F) sim (frac{E_F-E_M}{E_M})^{- u eta},$ where $ u$ is the critical exponent of correlation length $xi_c$. On the insulating side of the transition $F$ is constant for system sizes exceeding localization length $xi$. While these results are obtained from the mean value of $I_A,$ giving the typical fidelity $F$, we find that $I_A$ is widely, log normally, distributed with a width diverging at the AMIT. As a consequence, the mean value of fidelity $F$ converges to one at the AMIT, in strong contrast to its typical value which converges to zero exponentially fast with system size $L$. This counterintuitive behavior is explained as a manifestation of multifractality at the AMIT.
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.
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