Level curvature distribution and the structure of eigenfunctions in disordered systems

Basu, Chinmay; Canali, Carlo M.; Kravtsov, V. E.; Yurkevich, Igor V.

doi:10.1103/physrevb.57.14174

Cited by 8 publications

(12 citation statements)

References 37 publications

(62 reference statements)

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“…Within this method, the asymptotic "tails" of the distribution functions are obtained by finding a non-trivial saddle-point configuration of the supersymmetric σ-model. Further development and generalization of the method allowed one to calculate the asymptotic behavior of the distribution functions of relaxation times [29,30,31], eigenfunction intensities [32,33], local density of states [34], inverse participation ratio [35,36], level curvatures [37,38] etc. The saddle-point solution describes directly the spatial shape of the corresponding anomalously localized state [29,36].…”

Section: Introductionmentioning

confidence: 99%

Statistics of energy levels and eigenfunctions in disordered systems

2000

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The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on low-dimensional (quasi-1D and 2D) systems. Calculations are based on the supermatrix σ-model approach. The method reproduces, in so-called zero-mode approximation, the universal random matrix theory (RMT) results for the energy-level and eigenfunction fluctuations. Going beyond this approximation allows us to study system-specific deviations from universality, which are determined by the diffusive classical dynamics in the system. These deviations are especially strong in the far "tails" of the distribution function of the eigenfunction amplitudes (as well as of some related quantities, such as local density of states, relaxation time, etc.). These asymptotic "tails" are governed by anomalously localized states which are formed in rare realizations of the random potential. The deviations of the level and eigenfunction statistics from their RMT form strengthen with increasing disorder and become especially pronounced at the Anderson metal-insulator transition. In this regime, the wave functions are multifractal, while the level statistics acquires a scale-independent form with distinct critical features. Fluctuations of the conductance and of the local intensity of a classical wave radiated by a point-like source in the quasi-1D geometry are also studied within the σ-model approach. For a ballistic system with rough surface an appropriately modified ("ballistic") σ-model is used. Finally, the interplay of the fluctuations and the electron-electron interaction in small samples is discussed, with application to the Coulomb blockade spectra.

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Section: Introductionmentioning

confidence: 99%

Statistics of energy levels and eigenfunctions in disordered systems

2000

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“…In that case, neither the statistical mechanical model Eq. (1.10) can be introduced, nor are the nontrivial periodic configurations of the Q-matrix available in associated nonlinear σ-model [18]. This signals of a topological origin of the discovered oscillations.…”

Section: )mentioning

confidence: 97%

Topological universality of level dynamics in quasi-one-dimensional disordered conductors

Kanzieper

Kravtsov

1999

Phys. Rev. B

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Nonperturbative, in inverse Thouless conductance g −1 , corrections to distributions of level velocities and level curvatures in quasi-one-dimensional disordered conductors with a topology of a ring subject to a constant vector potential are studied within the framework of the instanton approximation of nonlinear σ-model. It is demonstrated that a global character of the perturbation reveals the universal features of the level dynamics. The universality shows up in the form of weak topological oscillations of the magnitude ∼ e −g covering the main bodies of the densities of level velocities and level curvatures. The period of discovered universal oscillations does not depend on microscopic parameters of conductor, and is only determined by the global symmetries of the Hamiltonian before and after the perturbation was applied. We predict the period of topological oscillations to be 4/π 2 for the distribution function of level curvatures in orthogonal symmetry class, and √ 3/π for the distribution of level velocities in unitary and symplectic symmetry classes.PACS number(s): 05.45.+b, 72.15.Rn

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“…where A 1 = 1,A 2 = (4/π). Corrections to this distribution, which are especially notable at low values of k as result of non-universal features have also been discussed [45,47]. Since here one normalizes the curvature by its absolute averaged value, the dependence on δ disappears.…”

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confidence: 94%

“…Keeping track of all the influences of magnetic field on the vortex motion is a rather herculean task. Nevertheless, we can exploit the theory developed for correlations [40][41][42][43] and curvature distribution [44][45][46][47] of the spectral response to external parameters which show universal behavior of the derivative of the energies of the system with respect to an external parameter. Specifically, for the ith eigenvalue i (x) (where x is the value of the external parameter) of the Hamiltonian one may define a "velocity" j i = ∂ x i (x)/δ (where δ is the mean level spacing, i.e.…”

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confidence: 99%

“…This leads to an unusual correlation curve since the correlation should be maximum at δX = 0, and approaches zero from below an large δX, which means that there is a negative minimum of the correlation at some intermediate value of δX. For the curvature, a universal distribution is expected [44][45][46][47]. Defining k = K i /| K i |, one obtains the distribution…”

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Universal Voltage Fluctuations in Disordered Superconductors

Roy,

Wu,

Berkovits

et al. 2020

Preprint

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The Aharonov-Casher effect is the analogue of the Aharonov-Bohm effect that applies to neutral particles carrying a magnetic moment. This can be manifested by vortices or fluxons flowing in trajectories that encompass an electric charge. These have been predicted to result in a persistent voltage which fluctuates for different sample realizations. Here we show that disordered superconductors exhibit reproducible voltage fluctuation, antisymmetrical with respect to magnetic field, as a function of various parameters such as magnetic field amplitude, field orientations and gate voltage. These results are interpreted as the vortex equivalent of the universal conductance fluctuations typical of mesoscopic disordered metallic systems. We analyze the data in the framework of random matrix theory and show that the fluctuation correlation functions and curvature distributions exhibit behavior which is the fingerprint of Aharonov-Casher physics. The results demonstrate the quantum nature of the vortices in highly disordered superconductors both above and below Tc.

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Level curvature distribution and the structure of eigenfunctions in disordered systems

Cited by 8 publications

References 37 publications

Statistics of energy levels and eigenfunctions in disordered systems

Statistics of energy levels and eigenfunctions in disordered systems

Topological universality of level dynamics in quasi-one-dimensional disordered conductors

Universal Voltage Fluctuations in Disordered Superconductors

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