Two-dimensional density of states in the extreme quantum limit

Smith, Thor L.; Wang, W. I.; Stiles, P. J.

doi:10.1103/physrevb.34.2995

Cited by 107 publications

(33 citation statements)

References 17 publications

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“…Similar conclusions were reached on the basis of a number of calculations [43,44] and experiments on heat capacity [45] and cyclotron resonance [46]. Smith et al [47,48] modelled magnetocapacitance data using a field-independent Gaussian DOS, but a field-dependent width (Γ ∼ √ B) has also been reported experimentally from dHvA [9] and magnetocapacitance [49] measurements, the latter requiring in addition a constant background DOS. Other experiments though indicate a Lorentzian DOS [50,51].…”

Section: Theory Of the Dhva Effect In 2d Systemssupporting

confidence: 55%

Magnetometry of low-dimensional electron and hole systems

Usher¹,

Elliott²

2009

J. Phys.: Condens. Matter

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Abstract. The high magnetic field, low-temperature magnetic properties of lowdimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance.

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Section: Theory Of the Dhva Effect In 2d Systemssupporting

confidence: 55%

Magnetometry of low-dimensional electron and hole systems

Usher¹,

Elliott²

2009

J. Phys.: Condens. Matter

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“…There, the capacitance (and thus the DOS) is increased and grows only weakly with increasing V g . The weak increase of C with jV g j, is ascribed to an increase of C gt at higher jV g j since the carriers' wave function is "pressed" towards the interface, an effect neglected in our description [20,21]. Reducing V g below 2.2 V shifts E F below the valence band edge so that surface electrons and bulk holes coexist.…”

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confidence: 99%

“…Capacitance spectroscopy allows us to directly probe the thermodynamic DOS dn=dμ (n ¼ carrier density, μ ¼ electrochemical potential), denoted as D, of a 3D TI. The total capacitance measured between a metallic top gate and a 2DES depends, besides the geometric capacitance, on the quantum capacitance e 2 D, connected in series and reflecting the finite density of states D of the 2DES [18][19][20][21][22]; e is the elementary charge. Below, the quantum capacitance of the top surface is denoted as e 2 D t , the one of the bottom layer by e 2 D b .…”

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confidence: 99%

“…Therefore, the measured capacitance reflects primarily the top surface's DOS, D t . In the limit C tb → 0 or e 2 D b → 0 the total capacitance C is given by the expression usually used for conventional 2DES: 1=C ¼ 1=C gt þ 1=Ae 2 D with the geometric capacitance C gt ¼ ε gt ε 0 A=d gt , where ε gt is the dielectric constant of the layers between gate and top 2DES, d gt is the corresponding thickness [20,21]. Note that C gt ≪ e 2 D t ; therefore, variations of the DOS cause only small changes of C. First quantum capacitance measurements have been reported for Bi 2 Se 3 , but the experiments were carried out at high frequencies at which resistive effects prevail [26].…”

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confidence: 99%

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Probing Quantum Capacitance in a 3D Topological Insulator

et al. 2016

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We measure the quantum capacitance and probe thus directly the electronic density of states of the high mobility, Dirac type two-dimensional electron system, which forms on the surface of strained HgTe. Here we show that observed magnetocapacitance oscillations probe-in contrast to magnetotransportprimarily the top surface. Capacitance measurements constitute thus a powerful tool to probe only one topological surface and to reconstruct its Landau level spectrum for different positions of the Fermi energy. DOI: 10.1103/PhysRevLett.116.166802 Three-dimensional topological insulators (3D TI) represent a new class of materials with insulating bulk and conducting two-dimensional surface states [1][2][3][4]. The properties of these surface states are of particular interest as they have a spin degenerate, linear Dirac-like dispersion with spins locked to their electrons' k vectors [4,5]. Strained HgTe, examined here, constitutes a 3D TI with high electron mobilities allowing the observation of Landau quantization and quantum Hall steps down to low magnetic fields [6,7]. While unstrained HgTe is a zero gap semiconductor with inverted band structure [8,9], the degenerate Γ8 states split and a gap opens at the Fermi energy E F if strained. This system is a strong topological insulator [10], explored by transport [6,7,11], angleresolved photoemission spectroscopy [12], photoconductivity, and magneto-optical experiments [13][14][15][16]; also, the proximity effect has been investigated [17]. Since these two-dimensional electron states (2DES) have high electron mobilities of several 10 5 cm 2 =V s, pronounced Shubnikov-de Haas (SdH) oscillations of the resistivity and quantized Hall plateaus commence in quantizing magnetic fields [6,7,11], stemming from both top and bottom 2DES. The oscillations stem from Landau quantization which strongly modifies the density of states (DOS). Capacitance spectroscopy allows us to directly probe the thermodynamic DOS dn=dμ (n ¼ carrier density, μ ¼ electrochemical potential), denoted as D, of a 3D TI. The total capacitance measured between a metallic top gate and a 2DES depends, besides the geometric capacitance, on the quantum capacitance e 2 D, connected in series and reflecting the finite density of states D of the 2DES [18][19][20][21][22]; e is the elementary charge. Below, the quantum capacitance of the top surface is denoted as e 2 D t , the one of the bottom layer by e 2 D b . We show that capacitance measures, in contrast to transport, the properties of a single Dirac cone in a 3D TI.The experiments are carried out on strained 80 nm thick HgTe films, grown by molecular beam epitaxy on CdTe (013). For details, see [16]. The Dirac surface electrons have high electron mobilities of order 4 × 10 5 cm 2 =V s. The cross section of the structure is sketched in Fig. 1(a). For transport and capacitance measurements, carried out on one and the same device, the films were patterned into Hall bars with metallic top gates. Several devices from the same wafer have been studied. The measurement...

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“…This is termed the quantum capacitance [26] in the zero temperature limit and electron compressibility [27] when the density of states is smeared out at finite temperature. The effect has important consequences in capacitors formed from 2D systems such as semiconductor hetereostructures [28] and graphene [29], 1D systems such as carbon nanotubes [30] and 0D systems such as quantum dots [31,32], where changes in the density of states have been measured through the effect on the measured capacitance. These measurements were possible through the ability of some external parameter to change the density of states, which then allows the separation of the contributions to capacitance which would be otherwise indistinguishable.…”

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Anisotropic magnetocapacitance in ferromagnetic-plate capacitors

et al. 2015

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The capacitance of a parallel plate capacitor can depend on applied magnetic field. Previous studies have identified capacitance changes induced via classical Lorentz force or spin-dependent Zeeman effects. Here we measure a magnetization direction dependent capacitance in parallel-plate capacitors where one plate is a ferromagnetic semiconductor, gallium manganese arsenide. This anisotropic magneto-capacitance is due to the anisotropy in the density of states dependent on the magnetization through the strong spin-orbit interaction.Capacitance, the ability of a body to retain charge is defined by the relation 1/C g = dV e /dq, the ratio of the change in electrostatic potential to the amount of charge added. In a simple parallel plate capacitor one normally calculates this capacitance through the change in electrostatic potential by integrating the electric field E due to charges on the surface of two metallic plates over the separating distance d. However, corrections to this electrostatic picture can be important, and other contributions to the change in potential when additional charge is added must be taken into account. It is often helpful to reformulate these corrections as effective series capacitances in series with a geometrical capacitance expected from the classical picture [1][2][3]. In particular, the effect of change in chemical potential due to the finite density of states can be important in low dimensional systems. This has been exploited for example in two-dimensional electron gases where the additional chemical contribution to the potential, the electron compressibility, allows probing of Landau levels in the density of states in the quantum Hall regime [2].In this Letter, we exploit this kind of capacitance correction to demonstrate an anisotropic magnetocapacitance (AMC). This is analogous to anisotropic magneto-resistance (AMR) [4], an important technology in magnetic field sensing applications [5] and of a similarly relativistic magnetic origin, but in this different fundamental electrical circuit element.In general, magnetic effects on transport properties such as AMR can be ascribed to three different categories: ordinary (orbital), due to the Lorentz force; spindependent, due to splitting of spin sub-bands through ferromagnetism or the Zeeman effect; and extraordinary, relativistic in origin through the spin-orbit interaction. Some well known examples of these effects in resistance are Lorentz magneto-resistance, giant magnetoresistance (GMR) [6], and AMR [7] respectively. Classifying magneto-capacitance along similar lines, both ordinary and spin-dependent effects have been observed previously. Changes in capacitance as a function of in-plane magnetic field have been measured in two-dimensional electron gases and attributed to combined Lorentz force and quantum confinement effects [8,9]; spin dependent effects have been considered theoretically [10], and experimentally measured due to the Zeeman splitting in Pd plate capacitors [11] and in magnetic tunnel junctions several measurements ...

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Two-dimensional density of states in the extreme quantum limit

Cited by 107 publications

References 17 publications

Magnetometry of low-dimensional electron and hole systems

Magnetometry of low-dimensional electron and hole systems

Probing Quantum Capacitance in a 3D Topological Insulator

Anisotropic magnetocapacitance in ferromagnetic-plate capacitors

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