Abstract
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate. Our experiments probe deeply into the regime where theory has long predicted an interaction-driven charge density wave or Wigner crystal state. A number of interesting features arise in the transport in this regime, including a striking re-entrant nonlinearity in the current–voltage characteristics. We discuss these features in the context of possible correlated electron states, and present an alternative picture based on magnetic-field induced puddling of electrons.
Highlights
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities
This heating process is known to produce oxygen vacancies within the sample volume, which act as electron donors27–30. (In principle, a single oxygen vacancy acts stoichiometrically as a double-donor, but it is generally accepted that one of the two electron states remains tightly bound to the doubly-charged oxygen ion, so that the vacancy donates only a single electron to the conduction band31–34.) The heating temperature was varied from one sample to another in order to produce samples with different doping levels
Strong nonlinearity in the transport is expected when electrons form a spatially-correlated state, such as a charge density wave (CDW) or Wigner crystal, that can be pinned by a disorder potential[50]
Summary
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities. Low-temperature electron gas, such a dimensionally reduced dispersion implies a number of potentially competing instabilities, including spin or valley density wave, charge density wave (CDW) and Wigner crystallization[1,2,3,4]. Such a high-field situation, is difficult to realize experimentally. STO has a static, long-wavelength dielectric constant e that reaches E24,000 at low temperatures (with a weak directional dependence[15]) One implication of this enormous dielectric constant is that the effective Bohr radius aB 1⁄4 4pe0e:2/me[2] associated with shallow donor states becomes extremely large: aBE760 nm. As we discuss below, this large dielectric constant implies a significant robustness against localization by charge disorder
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