Novel Electric Field Effects on Landau Levels in Graphene

Lukose, Vinu; Shankar, Ravi; Baskaran, G.

doi:10.1103/physrevlett.98.116802

Cited by 319 publications

(352 citation statements)

References 31 publications

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“…This transformation shows that the spectrum at k = 0 is affected by the electric field in the presence of the magnetic field. An alternative approach based on Lorentzboosted Landau levels was developed in Lukose et al (2007). Both approaches yield the same spectrum and eigenvalues,…”

Section: (D) Criss-crossed Electric and Magnetic Fieldsmentioning

confidence: 99%

Graphene nanoribbons in criss-crossed electric and magnetic fields

Roslyak

Gumbs

Huang

2010

Phil. Trans. R. Soc. A.

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Graphene nanoribbons (GNRs) in mutually perpendicular electric and magnetic fields are shown to exhibit dramatic changes in their band structure and electron-transport properties. A strong electric field across the ribbon induces multiple chiral Dirac points, closing the semiconducting gap in armchair GNRs. A perpendicular magnetic field induces partially formed Landau levels as well as dispersive surface-bound states. Each of the applied fields on its own preserves the even symmetry E k = E −k of the sub-band dispersion. When applied together, they reverse the dispersion parity to be odd, which gives E e,k = −E h,−k , and mix the electron and hole sub-bands within the energy range corresponding to the change in potential across the ribbon. This leads to oscillations of the ballistic conductance within this energy range. The broken time-reversal symmetry provides dichroism in the absorption of the circularly polarized light. As a consequence, one can observe electrically enhanced Faraday rotation, since the edges of the ribbon provide formation of the substantial density of states.

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Section: (D) Criss-crossed Electric and Magnetic Fieldsmentioning

confidence: 99%

Graphene nanoribbons in criss-crossed electric and magnetic fields

Roslyak

Gumbs

Huang

2010

Phil. Trans. R. Soc. A.

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“…Рассмотрим ре-лятивистскую задачу об энергетическом спектре двумерного заряженного фермиона в скрещенных магнитном и электрическом полях. В режиме скрещенных полей дираков-ские материалы проявляют интересные свойства [5][6][7][8][9][10]. В двумерном случае в качестве матриц Дирака достаточно взять матрицы Паули: …”

Section: общая структура методаunclassified

“…Для случая графена этот метод был использован в работе [5]. Чтобы ре-шить волновое уравнение (39), перейдем в систему отсчета, движущуюся со скоростью , cE H совпадающей со скоростью дрейфа электронов в направлении, перпендикуляр-ном электрическому и магнитному полям.…”

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“…Чтобы ре-шить волновое уравнение (39), перейдем в систему отсчета, движущуюся со скоростью , cE H совпадающей со скоростью дрейфа электронов в направлении, перпендикуляр-ном электрическому и магнитному полям. Этот переход необходимо осуществить с по-мощью следующих преобразований Лоренца [5,11]: …”

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A simple method of "partial" diagonalization of an operator matrix and its application to a real physical problem

Alisultanov¹,

Abdullaev²,

Khizriev³

2017

HDSU

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“…Large V 0 leads to large E in the region between BG and TG region which modifies the LLs locally. It has been shown by Lukose et al [28] and later extended by Gu et al [18] for the case of a topgate geometry that the LL spectrum and the wavefunctions in crossed E and B are fundamentally modified in graphene, an aspect that is not observable in conventional 2DEGS semiconductors. LL wavefunction is modified in two ways.…”

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Tuning equilibration of quantum Hall edge states in graphene – Role of crossed electric and magnetic fields

Dubey

Deshmukh

2016

Solid State Communications

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We probe quantum Hall effect in a tunable 1-D lateral superlattice (SL) in graphene created using electrostatic gates. Lack of equilibration is observed along edge states formed by electrostatic gates inside the superlattice. We create strong local electric field at the interface of regions of different charge densities. Crossed electric and magnetic fields modify the wavefunction of the Landau Levels (LLs) -a phenomenon unique to graphene. In the region of copropagating electrons and holes at the interface, the electric field is high enough to modify the Landau levels resulting in increased scattering that tunes equilibration of edge states and this results in large longitudinal resistance.Magnetotransport across one-dimensional superlattice (SL) had been studied in two-dimensional electron gas in semiconductor heterostructures (2DEGS) [1][2][3][4][5][6], reporting dissipationless transport across high potential barriers [1] and magnetic commensurability oscillations in longitudinal resistance [3]. The motivation was to study various competing length scales and energy scales between tunable SL potential and quantum Hall system. Graphene offers the advantage of large cyclotron gap allowing quantum Hall effect to be observed at room temperature [7][8][9]. Substrate induced SL in graphene in the presence of magnetic field led to the experimental observation of Hofstadter butterfly physics [10][11][12]. The ability to create abrupt (∼ 10 nm) tunable barriers in graphene allows new aspects to be explored. In addition, new physics, due to the role of crossed electric and magnetic field, that cannot be seen in conventional 2DEGS can be studied in SL structures based on graphene.In this letter, we study magneto transport in an electrostatically defined 1D lateral SL in graphene [13]. In our device we apply a perpendicular magnetic field and periodically modulate the charge carrier density in adjacent "ribbons" of graphene, tuning from an array of p-p' (or n-n' ) to an array of p-n' junctions. Changing the magnetic field allows us to vary l B relative to λ; and changing the gate voltage allows us to tune the SL potential strength relative to LL spacing. The relative abruptness, bipolarity of charge carriers, large modulation and unequally spaced LLs distinguishes the present work from the previous work on 1D SL using 2DEGS systems [1][2][3][4]14].Apart from the length scales, we also study the energy scales involved. The competition between SL amplitude (V 0 ) and LL spacing (hω c , whereh = h/2π, h being the Planck's constant, and ω c is the cyclotron frequency) gives rise to three regimes. When V 0 >>hω c , SL effect dominates giving rise to extra Dirac points [15]. In the other extreme when V 0 <

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Novel Electric Field Effects on Landau Levels in Graphene

Cited by 319 publications

References 31 publications

Graphene nanoribbons in criss-crossed electric and magnetic fields

Graphene nanoribbons in criss-crossed electric and magnetic fields

A simple method of "partial" diagonalization of an operator matrix and its application to a real physical problem

Tuning equilibration of quantum Hall edge states in graphene – Role of crossed electric and magnetic fields

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