--Why are we doing STM?
--Some technical aspects of STS/STM
--Why STM/STS on topological insulator
--Landau level spectroscopy on topological insulator
Strategy to find exotic phenomena
One way we search for exotic phenomena is to build up "boring" electrons to find new emergent macroscopic phenomena.
Alternatively, lets break down "boring" materials, analyze them thoroughly to find quantum structure and interference around impurities and otherwise microscopic properties that show it wasn't as "boring" as we thought.
Background to STM
- STM is a tool to explore the electronic states - measures the local density of states (LDOS), and can make topographical scans of material surfaces.
- At any certain point, can measure current as function of bias, and to a good approximation, the LDOS of the material is given by dI/dV.
- At any fixed bias, can then scan the surface, to get a "topograph conductance" map - this is spectroscopic imaging STM (SI-STM). Then can obtain these images at different biases, V (or in other words, energy, epsilon). Putting these together and taking a Fourier transform gives momentum space information.
Why is STM so powerful?
--Atomic spatial resolution: 0.1nm laterally and ~pm vertically giving very precise local information
--Momentum space accessible, from FT SI-STM (Fourier-Transform Spectroscopic Imaging Scanning Tunneling Microscopy)
--Very high energy resolution, as high as micro-eV
--can do experiments under a wide range of external conditions.
To get good results, one needs a few target specifications of the SI-STM machine:
--Ultra-high vacum (of order 10^-10 Torr), as the surface must be kept clean for a long time.
--High magnetic field >10T to control the spin and Landau orbits
--very low temperature <1k in order to reduce the thermal broadening [ Typical energy scales in materials we want to see: Mott gap ~ eV, Thermal 1K~0.1meV, SC gap (HTC) ~ 10meV, impurity resonances ~ 1meV, Zeeman energy ~ 0.06meV/T ] --variable temperature (in order to study phase transitions) Typical scans (of space and energy) will take of order 36 hours, and require even nm drift forbidden during this timescale. In RIKEN, have a multi-extreme STM, satisfying all of these requirements, including sub-pm noise. How small is sub-pm noise? 0.5pm/2cm = 0.1 micro meter / 4000m (height of Mt. Fuji) [bloggers note: wow! this is serious resolution!]
Now onto main topic of talk
published recently in: Hanaguri et al PRB 82, 081305(R) (2010)
Also see similar recent work in: Cheng et al PRL 105, 076801 (2010)
Introduction to Topological insulators: Topological insulators are (band) insulators with a robust gapless edge or surface state. How can this be true? Need a band structure with a specific "topology".
What about 3D case? [see e.g. Fu, Kane and Mele PRL 98, 106803 (2007)] In 2D, we have gapless edge states with linear dispersion. In 3D, this will map into gapless surface states with a linear dispersion - i.e. Dirac Fermions (with an added helical structure).
In fact, in solid state, one finds that Dirac cones are everywhere!
--Graphene [ see e.g. Castro Neto et al, RMP (2009) ]
--Organic conductors
--d-wave SC
--Surface states of 3D topological insulators (TI).
Usually, the Dirac cones come in pairs. However, in the TI, find an odd number of cones centered at time-reversal invariant momenta. This is due to the TR invariance, one of the conditions of a topological insulator. We also find that in the TI (unlike other cases) there is no spin degeneracy in the surface states. This is related to the spin-orbit coupling necessary to make this state.
Experimental verifications of 3D TI: First, Bi-Sb -- ARPES revealed an odd number of Dirac cones [ Hsieh et al, Nature 452, 970 (2008) ]
Since then, we have found some other cases:
--Bi2Se3 - single isotropic Dirac cone [Zhang et al, Nat. Phys. 5, 438 (2009) ]
--Bi2Te3 - which is anisotropic [ Chen et al, Science, 178 (2009) ]
An odd number of Dirac cones is good evidence for TI states. But what more can we do?
Next, spin-resolved ARPES revealed the helical spin structure.
So ARPES is great! There is a helical Dirac cone in these materials no doubt.
But what else can we do?
Let's look a little close at the helical spin-structure: one of the properties is that it gives suppressed back scattering. Now, scattering interference may generate electronic standing waves (QPI), which should detect this interesting scattering properties of the helical Dirac fermions.
The helical structure can be modeled by a multi-band model with spin-selection rules. Can also include certain FS distortions -- many of these have been calculated, and give nice agreement with QPI patterns.
What about Landau levels?
First, take some lessons from Graphene, [Castro Neto et al, RMP 81, 109 (2009) ]
--Find that the LL (Landau level) energies E_n are proportional to \sqrt{nB}
--Also find a B-independent LL with n=0. This gives a half-integer QHE, and furthermore the large gap due to this n=0 state means that the QHE can even be observed at room temperature. [Novoselov et al, Science 315, 1379 (2007)]
We should compare this to the conventional 2D electron gas where E_n proportional to (n+1/2)B.
In a topological insulator: this should be easier to look at than graphene as you see the Dirac fermions at the surface of a large bulk material. Furthermore, in graphene, you get factors of 4 (from 2 Dirac cones, and 2-fold spin degeneracy). But in a TI, there is a single Dirac cone may give rise to true half-integer QHE. In other words, the TI should be great to look at the ususual QHE properties of the Dirac cone.
But there is a little problem - an unavoidable bulk contribution in Bi2Se3. For example, compare band calculations [Zhang et al, Nat. Phys. 5, 438 (2009)] to ARPES data [Xia et al, Nat. Phys. 5, 398 (2009)] and find that the experimental system looks e-doped. This bulk contribution dominates for example magneto-transport. A surface probe is necessary to study the Dirac cone; but ARPES is not magnetic-field compatible. So lets do STM.
Experiment on Bi2Se3, crystals grown by Igarashi and Sasagawa (TIT). Bulk electron density in range 10^18 to 10^20 for two different samples.
Basic tunneling conductance against sample bias agrees nicely with ARPES results (including e-doping level).
Question: Why is there a sharp kink seen at 0 sample bias?
Answer: Don't know (although I didn't quite catch the slightly more extended answer)
Search for QPI : see almost nothing!!! QPI is very weak in single, isotropic and helical Dirac cone, as compatible with the theory of forbidden backscattering.
Now, LL spectroscopy: Increase B, and measure tunneling conductance against sample bias. We see clearly the development of the Landau levels, including the n=0 level at the Dirac point. E_n is definitely sub-linear in n, and is furthermore consistent with square root behavior of LL of single helical Dirac cone. [T. Hanaguri et al, PRB 82, 081305(R) (2010)].
However, as compared to the perfectly square root behavior seen in Graphene, we find in Bi2Se3 slight deviations from this. A short analysis shows us that in fact plotting E_n against sqrt(nB) is in fact an energy/momentum like relation - showing the slight bending away from linear behavior in the Dirac cones of Bi2Se3. This can be nicely compared to the dispersion seen in ARPES. This is new momentum-resolved spectroscopy using STM!
--missing n<0 LLs - maybe due to coupling with bulk band. --Enhanced amplitude of LL oscillations near E_F. This can be interpreted as an E-dependent QP lifetime. --Also find anomalous fine features near E_F. The fine structures shift in the same manner as LL's. --There is also an extra amplitude enhancement suddenly at |E|<~20meV. This is a new energy scale in the problem. [What is this energy scale?]
Summary
--Studied Helical Dirac fermions at surface of topological insulator.
--Clearly identified unusual LL structure expected for Dirac fermions
--Anomalous fine structures identified near E_F.
--Spectroscopic STM is now ready to explore exotic electronic phenomena.
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