Spatial Fluctuations of the Density of States in Magnetic Fields Observed with Scanning Tunneling Spectroscopy

Morgenstern, Markus; Wittneven, Chr.; Dombrowski, R.; Wiesendanger, R.

doi:10.1103/physrevlett.84.5588

Cited by 33 publications

(28 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…LLs correspond to quantized orbits in real and k-space [31]. In the semiclassical limit (large n), the Bohr-Sommerfeld quantization relation gives the area in k-space for the n th LL [32]:…”

Section: Landau Level Quantizationmentioning

confidence: 99%

See 1 more Smart Citation

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Soumyanarayanan

Hoffman

2015

Journal of Electron Spectroscopy and Related Phenomena

View full text Add to dashboard Cite

Topological materials host protected surface states with locked spin and momentum degrees of freedom. The helical Dirac character of the surface states, of tremendous scientific interest, stems from the interplay of the bulk band structure and surface Rashba spin-orbit interaction. The semimetal Sb offers a pristine platform to examine the Rashba origins of the Dirac-like topological surface states. Here we present an overview of our momentum-resolved scanning tunneling spectroscopy studies of Sb, over an extended (300 meV) energy range, revealing several features characteristic of the emergence of the Dirac-like surface states from a conventional Rashba-type parabolic dispersion. Our work provides a conceptual framework to create and investigate tunable Rashba states with topological properties.

show abstract

Section: Landau Level Quantizationmentioning

confidence: 99%

“…First, the application of a sufficiently large magnetic field B, quantizes the density of states into Landau levels (LLs), which manifest as oscillations in the STM conductance (dI/dV ) spectra [31]. LLs correspond to quantized orbits in real and k-space [31].…”

Section: Landau Level Quantizationmentioning

confidence: 99%

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Soumyanarayanan

Hoffman

2015

Journal of Electron Spectroscopy and Related Phenomena

View full text Add to dashboard Cite

show abstract

“…12,14,19 To acquire a detailed view of the LL variation in space, a complete mapping of LLs over the area in Fig. 3(a) was achieved by acquiring the conductance spectra on equally spaced grid points at 0 T and 9 T. Figure 3(b) shows the selected conductance spectra acquired at five different points in Fig.…”

mentioning

confidence: 99%

“…2,7-9 Microscopically, disorders induce potential variation that results in charge puddles and increased electron scattering, which has been observed in many two-dimensional electron systems including topological insulators. 4,[12][13][14][15] Bi 2Àx Sb x Te 3Ày Se y should have large local composition variation due to its non-stoichiometric structure and local potential fluctuation as a result, 2,6,7 but microscopic observation of charge puddle formation and information on their structure are absent in this material, which are essential for understanding the effects of composition variation on surface states.…”

mentioning

confidence: 99%

Local potential fluctuation of topological surface states in Bi1.5Sb0.5Te1.7Se1.3 observed by Landau level spectroscopy

Ko¹,

Park

Jeon³

et al. 2016

Applied Physics Letters

View full text Add to dashboard Cite

show abstract

“…This can be done by noting that these holes appear around the minima of σ(r) whose statistics is fixed by Eqs. (4)(5)(6)…”

mentioning

confidence: 99%

Nonlinear screening and percolative transition in a two-dimensional electron liquid

Fogler

2004

Phys. Rev. B

View full text Add to dashboard Cite

A variational method is proposed for calculating the percolation threshold, the real-space structure, and the ground-state energy of a disordered two-dimensional electron liquid. Its high accuracy is verified against exact asymptotics and prior numerical results. The inverse thermodynamical density of states is shown to have a strongly asymmetric minimum at a density that is approximately the triple of the percolation threshold. This implies that the experimentally observed metal-insulator transition takes place well before the percolation point is reached.The discovery that a two-dimensional (2D) electron liquid can be a metal at moderate electron density n e and an insulator at small n e was a major surprise that questioned our fundamental understanding of the role of disorder in such systems. Today, almost a decade later, it remains a subject of an intense debate. 1 One important reason why the conventional theory fails could be its flawed basic premise of the "good" metal, i.e., a uniform electron liquid slightly perturbed by impurities and defects. Indeed, modern nanoscale imaging techniques 2,3,4,5 unambiguously showed that low-density 2D electron systems are strongly inhomogeneous, "bad" metals, where effects of disorder are nonperturbatively strong. In particular, depletion regions (DR), i.e., regions where n(r) is effectively zero, exist. They appear when n e is too small to adequately compensate fluctuating charge density of randomly positioned impurities. As n e is reduced in the experiment, e.g., in order to approach the vicinity of the metal-insulator transition (MIT), the DRs are expected to grow in size and concentration and eventually merge below some percolation threshold n e = n p . An important and controversial issue is whether or not this percolation transition plays any role in the observed MIT. 1 To resolve it one needs to have a theory that is able to calculate n p and that can describe the inhomogeneous structure of the 2D metal at n e ∼ n p . A great progress in this direction has been achieved by Efros, Pikus, and Burnett, 6 whose paper is intellectually tied to earlier work on nonlinear screening by Efros and Shklovskii. 7 Still, analytical results remained scanty and numerical simulations 6,8 were the only known way to quantitatively study the n e ∼ n p regime. These simulations are very time consuming and redoing them in order to get any information beyond what is published 6,8 or to study novel experimental setups seems impracticable. Below I will show that a variational approach to the problem can be a viable alternative. Comparing it with the available numerical results for a typical model of the experimental geometry (Fig. 1), I establish that it correctly predicts the value of n p and accurately reproduces the energetics of the ground state, in particular, the density dependence of the electrochemical potential µ and of the inverse thermodynamical density of states (ITDOS), χ −1 = dµ/dn e , over a broad range of n e . The most striking feature of the resultant function χ −1 (n ...

show abstract

Spatial Fluctuations of the Density of States in Magnetic Fields Observed with Scanning Tunneling Spectroscopy

Cited by 33 publications

References 19 publications

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Momentum-resolved STM studies of Rashba-split surface states on the topological semimetal Sb

Local potential fluctuation of topological surface states in Bi1.5Sb0.5Te1.7Se1.3 observed by Landau level spectroscopy

Nonlinear screening and percolative transition in a two-dimensional electron liquid

Contact Info

Product

Resources

About