### Quantum spin Hall effect - Wikipedia

Scientists say that this is due to time-reversal invariance, which requires that the behavior of the system moving forward in time spon be identical to that moving backwards in time. Even though the arrow of time matters in everyday life, one can imagine what time-reversal symmetry means by looking at billiard balls moving on a pool spinn.

Without knowing when the cue ball set the other balls in motion, you may not necessarily know whether you were seeing the events run forward or in reverse.

In the case of the edge states, this symmetry means that events and likewise, the conduction channels in the topological insulator have no preference for a particular direction of time, forwards or backwards. Thus, any feature of the time-reversal-invariant system is bound to yall its time-reversed partner, and this yields pairs of oppositely traveling edge states that always go hand-in-hand.

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In the case of topological insulators, this is called the spin quantum Hall effect. A distinctive characteristic of topological insulators as compared to the conventional quantum Hall states is that their edge states always occur in counter-propagating pairs. Jan 01, · Recently, a new class of topological states has emerged, called quantum spin Hall (QSH) states or topological insulators (see Physics Today, January , page 19). Topologically distinct from all other known states of matter, including QH states, QSH states have been theoretically predicted and experimentally observed in mercury telluride quantum wells, 2,3 ideass.co by: Quantum spin hall insulator state in HgTe quantum wells. Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through .Cited by:Calculated band structure from Fig. The inset shows an example of a trivial non-topological insulating state shows a large gap. In this example, the system can be transformed into a topological insulator.

### Quantum spin hall insulator state in HgTe quantum wells

When the sheet of HgTe in between the CdTe is thin, the system behaves like an ordinary insulator and does not conduct when the Fermi level resides in the band-gap. When the sheet of HgTe is varied and made thicker this requires the fabrication of separate quantum wellsan interesting phenomenon happens.

Due to the inverted band structure of HgTe, at some critical HgTe thickness, a Lifshitz transition occurs in which the system closes the bulk band gap to become a semi-metal, and then re-opens it to become a quantum spin Hall insulator. In the gap closing and re-opening process, two edge states are brought out from the bulk and cross the bulk-gap.

As such, when the Fermi level resides in the bulk gap, the conduction is dominated by the edge channels that cross the gap.

### Quantum Hall Effect and Topological Insulators | Joint Quantum Institute

As the conduction is dominated by the edge channels, the value of the conductance should be insensitive to how wide the sample is. A magnetic field should destroy the quantum spin Hall state by breaking time-reversal invariance and allowing spin-up spin-down electron scattering processes at the edge.

From Wikipedia, the free encyclopedia. Physical Review Letters. Bibcode : PhRvL.

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PMID S2CID Physics Letters B. Bibcode : PhLB. CiteSeerX Andrei; Zhang, Shou-Cheng 14 March Andrei; Hughes, Taylor L. ISSN Bibcode : Sci Categories : Hall effect Condensed matter physics Quantum electronics Spintronics. Namespaces Article Talk.

Quantum spin hall insulator state in HgTe quantum wells. Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through .Cited by: called quantum spin Hall (QSH) states or topological insula-tors (see P HYSICS TODAY, January , page 19). Topologically distinct from all other known states of matter, including QH states, QSH states have been theoretically predicted and ex-perimentally observed in mercury telluride quantum wells,2,3 in bismuth antimony alloys,4,5 and in Bi 2 Se 3 and Bi. In the case of topological insulators, this is called the spin quantum Hall effect. A distinctive characteristic of topological insulators as compared to the conventional quantum Hall states is that their edge states always occur in counter-propagating pairs.
The quantum Hall effect is an example of a phenomenon having topological features that can be observed in certain materials under harsh and stringent laboratory conditions large magnetic field, near absolute zero temperature. To study this phenomenon, scientists apply a large magnetic field to a 2D sheet semiconductor. This causes a gap to open between energy bands, and electrons in the bulk material become localized, that is they cannot move freely.

The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, and that does not require the application of a large magnetic field. The first proposal for the existence of a quantum spin Hall state was developed by Charles Kane and Gene Mele [1] who adapted an earlier model for graphene by F.