Optical control of TMDCs valley pseudospin qubits - Revision history

Chu WenHao: /* Numerical calculation results by Quantum Espresso */

2021-04-30T16:30:08Z

Numerical calculation results by Quantum Espresso

← Older revision		Revision as of 00:30, 1 May 2021
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	===Numerical calculation results by Quantum Espresso===		===Numerical calculation results by Quantum Espresso===
	<ref>Ghosal, Supriya, Arka Bandyopadhyay, and Debnarayan Jana. "Electric field induced band tuning, optical and thermoelectric responses in tetragonal germanene: a theoretical approach." Physical Chemistry Chemical Physics 22.35 (2020): 19957-19968.</ref>		<ref>Ghosal, Supriya, Arka Bandyopadhyay, and Debnarayan Jana. "Electric field induced band tuning, optical and thermoelectric responses in tetragonal germanene: a theoretical approach." Physical Chemistry Chemical Physics 22.35 (2020): 19957-19968.[https://pubs.rsc.org/en/content/articlelanding/cp/2020/d0cp03892j#!divAbstract]</ref>
	[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]		[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]

Chu WenHao: /* Numerical calculation results by Quantum Espresso */

2021-04-30T16:29:10Z

Numerical calculation results by Quantum Espresso

← Older revision		Revision as of 00:29, 1 May 2021
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	===Numerical calculation results by Quantum Espresso===		===Numerical calculation results by Quantum Espresso===
			<ref>Ghosal, Supriya, Arka Bandyopadhyay, and Debnarayan Jana. "Electric field induced band tuning, optical and thermoelectric responses in tetragonal germanene: a theoretical approach." Physical Chemistry Chemical Physics 22.35 (2020): 19957-19968.</ref>
	[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]		[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]

Chu WenHao: /* Solution of TB model Hamiltonian */

2021-04-30T16:28:06Z

Solution of TB model Hamiltonian

← Older revision		Revision as of 00:28, 1 May 2021
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	These K and K' point are also called "Dirac points".		These K and K' point are also called "Dirac points".
	===Solution of TB model Hamiltonian===		===Solution of TB model Hamiltonian===
			<ref>Neto, AH Castro, et al. "The electronic properties of graphene." Reviews of modern physics 81.1 (2009): 109.[https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.109]</ref>
	*We can rewrite the Schrödinger equation in reciprocal space		*We can rewrite the Schrödinger equation in reciprocal space

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	It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".		It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".

	===Dirac model near K points--Not spins but like spins===		===Dirac model near K points--Not spins but like spins===
	*With the Dirac model in Quantum Fireld Theory , We have the Dirac's original:		*With the Dirac model in Quantum Fireld Theory , We have the Dirac's original:

Chu WenHao: /* Numerical calculation results by Quantum Espresso */

2021-04-30T16:22:15Z

Numerical calculation results by Quantum Espresso

← Older revision		Revision as of 00:22, 1 May 2021
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	The Dirac points in the band structure of graphene are shown in the Figure, In the next step, we scheduled to add the effect of external filed (like magnetic field or optical field), which will change the hamiltonian and choose the appropriate pseudopotential to calculate the change of K and K' point. We plan to use Quantum Espresso as our calculation programme.		The Dirac points in the band structure of graphene are shown in the Figure, In the next step, we scheduled to add the effect of external filed (like magnetic field or optical field), which will change the hamiltonian and choose the appropriate pseudopotential to calculate the change of K and K' point. We plan to use Quantum Espresso as our calculation programme.

			[[File:QE.png\|thumb\|400px\|QE code]]

	===Why choose heterobilayer TMDCs instead of monolayer===		===Why choose heterobilayer TMDCs instead of monolayer===

Chu WenHao: /* Numerical calculation results by Quantum Espresso */

2021-04-30T16:14:17Z

Numerical calculation results by Quantum Espresso

← Older revision		Revision as of 00:14, 1 May 2021
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	[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]		[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]

	The Dirac points in the band structure of graphene are shown in the Figure, In the next step, we scheduled to add the effect of external filed (like magnetic field or ~~opticcal~~ field), which will change the hamiltonian and choose the appropriate pseudopotential to calculate the change of K and K' point. We plan to use Quantum Espresso as our calculation programme.		The Dirac points in the band structure of graphene are shown in the Figure, In the next step, we scheduled to add the effect of external filed (like magnetic field or optical field), which will change the hamiltonian and choose the appropriate pseudopotential to calculate the change of K and K' point. We plan to use Quantum Espresso as our calculation programme.

	===Why choose heterobilayer TMDCs instead of monolayer===		===Why choose heterobilayer TMDCs instead of monolayer===

Chu WenHao: /* Numerical calculation results by Quantum Espresso */

2021-04-30T16:13:37Z

Numerical calculation results by Quantum Espresso

← Older revision		Revision as of 00:13, 1 May 2021
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	===Numerical calculation results by Quantum Espresso===		===Numerical calculation results by Quantum Espresso===
	[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]		[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]

			The Dirac points in the band structure of graphene are shown in the Figure, In the next step, we scheduled to add the effect of external filed (like magnetic field or opticcal field), which will change the hamiltonian and choose the appropriate pseudopotential to calculate the change of K and K' point. We plan to use Quantum Espresso as our calculation programme.

	===Why choose heterobilayer TMDCs instead of monolayer===		===Why choose heterobilayer TMDCs instead of monolayer===
	* There are four main carrier properties that optimal Opto-valleytronics should possess.		* There are four main carrier properties that optimal Opto-valleytronics should possess.

Chu WenHao: /* Dirac model near K points--Not spins but like spins */

2021-04-30T16:05:37Z

Dirac model near K points--Not spins but like spins

← Older revision		Revision as of 00:05, 1 May 2021
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	It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".		It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".
	===Dirac model near K points--Not spins but like spins===		===Dirac model near K points--Not spins but like spins===
	*With the Dirac model in Quantum Fireld Theory, it is very suggestive to write the Hamiltonian in the form:		*With the Dirac model in Quantum Fireld Theory , We have the Dirac's original:

			<math>(i\gamma^\mu\partial_\mu-m)\Psi=0</math>,
			<math>\gamma^\mu\gamma^v+\gamma^v\gamma^\mu=2g^{v\mu}</math>,
			<math>v,\mu=0,1,2,3</math>

			It is very suggestive to write the Hamiltonian in the form:

	[[File:Dirac points.png\|thumb\|400px\|Dirac points]]		[[File:Dirac points.png\|thumb\|400px\|Dirac points]]

Chu WenHao: /* Q & A */

2021-04-30T16:02:35Z

Q & A

← Older revision		Revision as of 00:02, 1 May 2021
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	* K-points are sampling points of Brillouin zone in reciprocal lattice		* K-points are sampling points of Brillouin zone in reciprocal lattice
	* The monolayer TMDs have a unique band structure with the conduction and valence band edges both at the degenerate K and K‘ valleys at the corners of the hexagonal Brillouin zone. The direct-gap optical transitions have a selection rule: left- (right-) handed circular polarized photons couple to the interband transitions in the K (K’) valley only.		* The monolayer TMDs have a unique band structure with the conduction and valence band edges both at the degenerate K and K‘ valleys at the corners of the hexagonal Brillouin zone. The direct-gap optical transitions have a selection rule: left- (right-) handed circular polarized photons couple to the interband transitions in the K (K’) valley only.
	* The Tight-Binding Model:By introducing the tight-binding model for TMDs, we will give a Hamiltonian of TMDs that can be further deduced and calculated. As is showned in figure (b):under the tight-binding ansatz,the atom(e.g.the red one)can only jump to the nearest position, whose interaction processing is called "hopping" in physics,If we use the lattice represetation and the corresponding creation operators commonly used in condensed matter physics,then the nearest-neighbor tight-binding Hamiltonian has the simple form:		===The Tight-Binding Model===
			* By introducing the tight-binding model for TMDs, we will give a Hamiltonian of TMDs that can be further deduced and calculated. As is showned in figure (b):under the tight-binding ansatz,the atom(e.g.the red one)can only jump to the nearest position, whose interaction processing is called "hopping" in physics,If we use the lattice represetation and the corresponding creation operators commonly used in condensed matter physics,then the nearest-neighbor tight-binding Hamiltonian has the simple form:

	[[File:graphene.png\|thumb\|400px\|Graphene]]		[[File:graphene.png\|thumb\|400px\|Graphene]]
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	\end{bmatrix},\qquad f=-t\sum_{j=1}^{3}e^{ik\cdot\tau_{j}}		\end{bmatrix},\qquad f=-t\sum_{j=1}^{3}e^{ik\cdot\tau_{j}}
	</math>		</math>
			===Choice of K values===
	*Choice of K values:We define the first Brillouin zone of the reciprocal lattice in the standard way.It is clear that the six points at the corners of the FBZ fall into two groups of three which are equivalent, so we need consider only two equivalent corners that we label K and K0 as in the figure. Explicitly, their positions in momentum space are given by:		*We define the first Brillouin zone of the reciprocal lattice in the standard way.It is clear that the six points at the corners of the FBZ fall into two groups of three which are equivalent, so we need consider only two equivalent corners that we label K and K0 as in the figure. Explicitly, their positions in momentum space are given by:

	[[File:K values.png\|thumb\|400px\|K values]]		[[File:K values.png\|thumb\|400px\|K values]]
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	These K and K' point are also called "Dirac points".		These K and K' point are also called "Dirac points".
			===Solution of TB model Hamiltonian===
	*Solution of TB model Hamiltonian:		*We can rewrite the Schrödinger equation in reciprocal space

	We can rewrite the Schrödinger equation in reciprocal space

	<math>		<math>
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	It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".		It is interesting to enquire whether there are any values of k for which f is zero? Any such value must satisfy the conditions? Luckily, the answer is yes and the points "at the corner" which satisfied these conditions are exactly the "Dirac points".
			===Dirac model near K points--Not spins but like spins===
	*Not spins but like spins ~~(Dirac model near K points):~~With the Dirac model in Quantum Fireld Theory, it is very suggestive to write the Hamiltonian in the form:		*With the Dirac model in Quantum Fireld Theory, it is very suggestive to write the Hamiltonian in the form:

	[[File:Dirac points.png\|thumb\|400px\|Dirac points]]		[[File:Dirac points.png\|thumb\|400px\|Dirac points]]
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	where the components of the operator <math>\sigma</math> are the usual Pauli matrices,and <math>v_F</math> is the Fermi velocity. It is clear that the eigenvalues are a function only of the magnitude of k, not its direction in the 2D space,therefore, although the Hamiltonian expression contains spin operators, the Dirac point derived from this is not the spin of particle or quasiparticle, (which can be compared with the quasiparticle ansatz in BCS theory).However, it still inspires us to regard these K and K' points of TMDs as some kinds of qubit resources and control them on this theoretical basis.		where the components of the operator <math>\sigma</math> are the usual Pauli matrices,and <math>v_F</math> is the Fermi velocity. It is clear that the eigenvalues are a function only of the magnitude of k, not its direction in the 2D space,therefore, although the Hamiltonian expression contains spin operators, the Dirac point derived from this is not the spin of particle or quasiparticle, (which can be compared with the quasiparticle ansatz in BCS theory).However, it still inspires us to regard these K and K' points of TMDs as some kinds of qubit resources and control them on this theoretical basis.

			===Numerical calculation results by Quantum Espresso===
			[[File:Dirac points in Band structure.png\|thumb\|400px\|Band structure]]
	===Why choose heterobilayer TMDCs instead of monolayer===		===Why choose heterobilayer TMDCs instead of monolayer===
	* There are four main carrier properties that optimal Opto-valleytronics should possess.		* There are four main carrier properties that optimal Opto-valleytronics should possess.

Chu WenHao: /* What are K & K' points? */

2021-04-30T15:40:05Z

What are K & K' points?

← Older revision		Revision as of 23:40, 30 April 2021
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	*Choice of K values:We define the first Brillouin zone of the reciprocal lattice in the standard way.It is clear that the six points at the corners of the FBZ fall into two groups of three which are equivalent, so we need consider only two equivalent corners that we label K and K0 as in the figure. Explicitly, their positions in momentum space are given by:		*Choice of K values:We define the first Brillouin zone of the reciprocal lattice in the standard way.It is clear that the six points at the corners of the FBZ fall into two groups of three which are equivalent, so we need consider only two equivalent corners that we label K and K0 as in the figure. Explicitly, their positions in momentum space are given by:

			[[File:K values.png\|thumb\|400px\|K values]]

	<math>		<math>
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	*Not spins but like spins (Dirac model near K points):With the Dirac model in Quantum Fireld Theory, it is very suggestive to write the Hamiltonian in the form:		*Not spins but like spins (Dirac model near K points):With the Dirac model in Quantum Fireld Theory, it is very suggestive to write the Hamiltonian in the form:

			[[File:Dirac points.png\|thumb\|400px\|Dirac points]]

	<math>		<math>

Chu WenHao: /* What are K & K' points? */

2021-04-30T15:37:33Z

What are K & K' points?

← Older revision		Revision as of 23:37, 30 April 2021
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	* The Tight-Binding Model:By introducing the tight-binding model for TMDs, we will give a Hamiltonian of TMDs that can be further deduced and calculated. As is showned in figure (b):under the tight-binding ansatz,the atom(e.g.the red one)can only jump to the nearest position, whose interaction processing is called "hopping" in physics,If we use the lattice represetation and the corresponding creation operators commonly used in condensed matter physics,then the nearest-neighbor tight-binding Hamiltonian has the simple form:		* The Tight-Binding Model:By introducing the tight-binding model for TMDs, we will give a Hamiltonian of TMDs that can be further deduced and calculated. As is showned in figure (b):under the tight-binding ansatz,the atom(e.g.the red one)can only jump to the nearest position, whose interaction processing is called "hopping" in physics,If we use the lattice represetation and the corresponding creation operators commonly used in condensed matter physics,then the nearest-neighbor tight-binding Hamiltonian has the simple form:

	[[File:graphene.png\|thumb\|400px\|~~center~~]]		[[File:graphene.png\|thumb\|400px\|Graphene]]

	<math>		<math>