Critical conductance of two-dimensional chiral systems with random magnetic flux

Markoš, Peter; Schweitzer, L.

doi:10.1103/physrevb.76.115318

Cited by 16 publications

(28 citation statements)

References 44 publications

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“…We mention that our result does not satisfy the Harris criterion, 39 which states that d −2 Ն 0. There are similar results also for other models [40][41][42][43][44][45] with chiral critical exponents Ͻ 1. In the absence of a constant magnetic field, we observed that the value of the conductance at E = 0 depends considerably on the size of the system, g͑L͒ = 2.62-11.48/ L. Even worse, the scaling behavior is fulfilled only in a very narrow interval of conductance values.…”

Section: ͑7͒supporting

confidence: 81%

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Schweitzer

Markoš

2008

Phys. Rev. B

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The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong perpendicular magnetic field. We found a disorder-driven splitting of the longitudinal conductance peak within the narrow lowest Landau band near the Dirac point. The energy splitting follows a relation which is proportional to the square root of the magnetic field and linear in the disorder strength. We calculate the scale invariant peaks of the two-terminal conductance and obtain the critical exponents as well as the multifractal properties of the chiral and quantum Hall states. We found approximate values Ϸ 2.5 for the quantum Hall states but = 0.33Ϯ 0.1 for the divergence of the correlation length of the chiral state at E = 0 in the presence of a strong magnetic field. Within the central n = 0 Landau band, the multifractal properties of both the chiral and the split quantum Hall states are the same, showing a parabolic f͓␣͑s͔͒ distribution with ␣͑0͒ = 2.27Ϯ 0.02. In the absence of the constant magnetic field, the chiral critical state is determined by ␣͑0͒ = 2.14Ϯ 0.02.

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Section: ͑7͒supporting

confidence: 81%

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Schweitzer

Markoš

2008

Phys. Rev. B

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“…The broadening of LLs in graphene due to nondiagonal disorder has been studied numerically in Refs. [20][21][22][23][24][25][26][27]. The results of simulations in all the above papers are consistent with each other.…”

Section: Introductionsupporting

confidence: 81%

“…Under the assumption adopted above, that the disorder h 2 (x, y) is weak, the shape of the density of states de-velops a sharp feature at small energies, as illustrated in Fig. 2, which is somewhat reminiscent of the numerical data [20][21][22][23][24][25][26][27] , but does not capture the robust low-energy behavior revealed in these papers. We argue that the reason of the discrepancy lies in the fact that we disregarded the energy dependence of the matrix element (h 2 ) ν,ν .…”

Section: Density Of Statesmentioning

confidence: 85%

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Shape of the zeroth Landau level in graphene with nondiagonal disorder

Malla

Raǐkh

2019

Phys. Rev. B

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Non-diagonal (bond) disorder in graphene broadens Landau levels (LLs) in the same way as random potential. The exception is the zeroth LL, n = 0, which is robust to the bond disorder, since it does not mix different n = 0 states within a given valley. The mechanism of broadening of the n = 0 LL is the inter-valley scattering. Several numerical simulations of graphene with bond disorder had established that n = 0 LL is not only anomalously narrow but also that its shape is very peculiar with three maxima, one at zero energy, E = 0, and two others at finite energies ±E. We study theoretically the structure of the states in n = 0 LL in the presence of bond disorder. Adopting the assumption that the bond disorder is strongly anisotropic, namely, that one type of bonds is perturbed much stronger than other two, allowed us to get an analytic expression for the density of states which agrees with numerical simulations remarkably well. On the qualitative level, our key finding is that delocalization of E = 0 state has a dramatic back effect on the density of states near E = 0. The origin of this unusual behavior is the strong correlation of eigenstates in different valleys.PACS numbers:

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“…In the chiral unitary class, the critical resistance depends on the strength of the magnetic field. The critical resistance is maximum; h/1.49e 2 = 17.3 kΩ for the strongest field [27] Fig. 2 (a) and (b), it is considered that doped iron brings decline of mobility of electrons rather than carrier doping.…”

Section: Resultsmentioning

confidence: 95%

Chiral Unitary Quantum Phase Transition in 2H-Fe $$_x$$ x TaSe $$_2$$ 2

et al. 2016

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We have observed a metal-insulator transition of a quasi-two dimensional electronic system in transition metal dichalcogenide 2H-TaSe 2 caused by doping iron. The sheet resistance of 2H-Fe x TaSe 2 (0 ≤ x ≤ 0.120) single crystals rises about 10 6 times with the increasing of x at the lowest temperature. We investigated the temperature dependence of the resistance and found a metal-insulator transition with a critical sheet resistance 11.7 ± 5.4 kΩ. The critical exponent of the localization length ν is estimated 0.31 ± 0.18. The values of the critical sheet resistance and ν are accordant to those of the chiral unitary class (less than h/1.49e 2 = 17.3 kΩ and 0.35 ± 0.03, respectively). We suggest that 2H-Fe x TaSe 2 is classified as the chiral unitary class, not as standard unitary class.

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Critical conductance of two-dimensional chiral systems with random magnetic flux

Cited by 16 publications

References 44 publications

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Shape of the zeroth Landau level in graphene with nondiagonal disorder

Chiral Unitary Quantum Phase Transition in 2H-Fe $$_x$$ x TaSe $$_2$$ 2

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