Valley filtering and valley valves in irradiated pristine graphene

arXiv:2401.11136 · cond-mat.mes-hall · Submitted 2024-01-20 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Valley filtering and valley valves in irradiated pristine graphene".

Mira: The gist: The authors theoretically study valley-filtering in pristine graphene irradiated by bicircular counterrotating laser drive, proposing configurational setups for valley filters and valley valves that allow for high-efficiency,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So, let's talk about the title and the people behind this paper. It’s "Valley filtering and valley valves in irradiated pristine graphene." The authors are Rekha Kumari, Gopal Dixit, and Arijit Kundu.

Mira: They're working in different areas of condensed matter physics. What do you think the main message of that title implies for the audience?

Lev: It suggests they are focusing on controlling the valley degree of freedom in graphene using external light fields—the laser drive is key here, and they're looking at how that light affects the valleys.

Kai: Right. It’s not just about observing what happens when you shine a laser on graphene; it's about actively filtering or switching between those two distinct valley states using that drive.

Mira: I think the implication is that they are moving from a purely passive material study to an active control system, where light dictates the transport path. That’s where the real physics gets interesting for condensed matter systems.

Lev: It's interesting because it moves us into the realm of valleytronics, which is about using these spin or valley degrees of freedom for information processing, and this paper shows a pathway to build those controls optically.

Kai: So, we're talking about building something where light dictates the transport behavior based on the relative phase between two drives. It’s not just a simple on or off switch; it’s tunable.

Mira: And that tunability is crucial because it means you can set up specific operating conditions for different transport regimes simply by adjusting the laser phase.

Lev: From an engineering side, we need to know how much control over that relative phase is actually required to achieve the high efficiency they claim. Too much complexity in the drive means it's not practical hardware.

Kai: That’s a fair point, Lev; we're talking about controlling this with parameters like the relative phase shift between two drives, which is a knob they use to generate valley-selective currents and transport responses with very high efficiency.

The paper's summary: Mira: So, let's look at what the paper actually summarizes in "Valley filtering and valley valves in irradiated pristine graphene." They detail how the dynamical symmetry disruption is the starting point for their entire study.

Kai: They start by saying that the dynamical symmetry of both graphene and the laser drive disrupts graphene's inversion symmetry. This disruption leads to distinct quasi-energy states and Floquet band occupations in each of the two valleys.

Lev: That means that even before we apply any external control, just having this laser field already messing with the system creates a difference between valley occupation states. It’s like they are creating an intrinsic valley bias from the start.

Mira: Right. The core mechanism is that this interaction results in these distinct Floquet band occupations in the two valleys, which are then controlled by the laser parameters.

Kai: And then they introduce a mathematical description of this using the effective Floquet Hamiltonian, which is HF(k, t) equals minus i partial t minus gamma zero h(k, t) minus gamma zero h*(k, t) minus i partial t.

Mira: That Hamiltonian is the language they use to describe how the system evolves under the drive. It's a standard tool in Floquet engineering but applied here to show how it affects valley dynamics specifically.

Lev: When we talk about this Hamiltonian, we need to know that they are assuming weak coupling to a fermionic reservoir, because that simplifies the math significantly when they express the occupations using n alpha mu equals X l f of epsilon alpha plus l omega minus mu < u(l) alpha u(l) alpha >.

Kai: That equation describes how many Floquet states with a specific quasienergy epsilon alpha can be occupied at a given chemical potential mu. It’s the standard way to get quantitative occupation numbers in these driven systems.

Mira: The core result they draw from this is that the control over the relative phase between the bicircular laser drive ultimately allows them to block one valley contribution while allowing currents in the opposite valley.

Lev: So, if you take that general idea and apply it to their specific device design—the two nanoribbons with a relative phase shift—you get a concrete setup capable of producing controlled valley-selective output in two-terminal transport devices.

Kai: That setup is what they propose for the valley filters and valley valve, which is the physical realization of the filtering mechanism.

The paper's improvements: Mira: Now let's talk about how the paper suggests improvements to this concept in "Valley filtering and valley valves in irradiated pristine graphene." They focus on making this concept practical for a real device.

Kai: They propose the configurational setup of two graphene nanoribbons, each being irradiated by its own bicircular drive with a relative phase shift between them. This is the physical realization of the valley filter and valley valve device.

Lev: That physical realization is where we hit the engineering reality; it’s about designing two components that interact in a way that allows for this controlled valley-selective output in transport measurements.

Kai: They show how connecting these two filters in series creates what they call a valley valve, highlighting its ability to realize what they term "perfect" valley valve in transport measurements.

Mira: And then they show the operation of this valve based on the phase difference between phi one and phi two. When phi two equals phi one plus 2n pi, you get an "on-phase" where both halves are conductive for the same valleys <ref:2401.11136#pg1>.

Lev: And when you tune it to off-phase where phi two equals phi one plus n pi, the conductance becomes zero because both halves become conductive for opposite valleys. That’s a controllable valley blockade.

Kai: They also highlight that their results are robust against moderate disorder and modest changes in driving laser parameters, which is important for experimental verification.

Mira: They also show how they can tune the length dependence to optimize device performance by predicting that sigma plus or minus sigma is proportional to w over L times exp of negative delta plus or minus delta L.

Lev: So, the improvement here isn't just a theoretical concept; it’s about showing how the length dependence dictates which valley channel, delta plus, becomes the conductive channel versus which one stays insulating.

Kai: And they also mention that gapless states emerge in the valley where they were previously absent when tuning to phi equals three pi over two, showing another way to dynamically controlling those electronic gaps.

Conclusion: Mira: So, wrapping up the discussion on "Valley filtering and valley valves in irradiated pristine graphene." The main implication is that we're looking at a system where optical control can dictate which valley is active.

Kai: The authors show that they can generate valley-selective currents and transport responses using bicircular laser drives. This opens up a path for building devices that actively manipulate valleys in graphene.

Lev: It’s about showing that this effect isn't just theoretical; it shows how the setup could be realized physically, even with disorder, which is a step toward designing functional valleytronics hardware.

Mira: And they confirm that they can achieve precise control over the valley occupations by manipulating the drive parameters to tune those quasi-energy gaps.

Kai: The work confirms that this system offers a dynamic platform for capturing and tuning these effects in transport experiments through optical means.

Lev: It’s a solid piece of theoretical work that lays out what we should expect to see in terms of experimental signatures when testing these kinds of optical switches.

Mira: So, the conclusion is that this paper provides a clear roadmap for how to use light to engineer valley polarization in graphene systems.

Kai: We've looked at how they use the valley filtering and valley valves in this paper, and it’s a really interesting direction for future research.

Lev: For us, it means we need to keep building hardware that can handle these kinds of optical manipulations with the necessary precision.

Department of Physics, Indian Institute of Technology Kanpur · Department of Physics, Indian Institute of Technology Bombay

cond-mat.mes-hall

Submitted: 2024-01-20

Updated: 2024-01-20

Comments: 13 pages. Comments welcome

Journal ref: Phys. Rev. B 111, 155421 (2025)

DOI: 10.1103/PhysRevB.111.155421

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 77/100

The gist: The gist: The authors theoretically study valley-filtering in pristine graphene irradiated by bicircular counterrotating laser drive, proposing configurational setups for valley filters and valley

Key concepts

Valley Filtering Mechanism
Control over the relative phase between two counterrotating laser drives blocks current flow in one valley while allowing it in the opposite valley. This is achieved through a specific configuration of two graphene nanoribbons, enabling precise, optical selection of which valley contributes to the transport response.
Valley Valve Operation
Connecting two valley filters creates a valve device. By tuning the relative phase difference between these components to specific values (like 2nπ or nπ), the net conductance can be tuned from finite (on-phase) to zero (off-phase), effectively creating a controllable valley blockade.
Length Dependence and Control
The conductance of valley channels depends on the length of the graphene nanoribbon. The system is designed so that one quasi-energy gap ($\delta+$) acts as a conductive channel, while another ($\delta-$) maintains an insulating state, allowing for optimized transport characteristics based on ribbon length.
Robustness against Disorder
The valley polarization effect remains relatively stable even when moderate static disorder is present in the graphene. While disorder reduces polarization through scattering, it does not completely destroy the valley selectivity as long as the disorder strength stays within certain limits.

Summary

The gist: The authors theoretically study valley-filtering in pristine graphene irradiated by bicircular counterrotating laser drive, proposing configurational setups for valley filters and valley valves that allow for high-efficiency, all-optical generation of valley-selective currents and transport responses.

Theoretical Framework

The dynamical symmetry of the graphene and laser drive disrupts graphene’s inversion symmetry, which results in distinct quasi-energy states and Floquet band occupations in the two valleys The effective Floquet Hamiltonian within the sublattice basis is expressed as HF(k, t) = -i∂t −γ0h(k, t)−γ0h∗(k, t)−i∂t Under the assumptions of the weak coupling to a fermionic reservoir, the occupations of a Floquet state with quasienergy ϵα can be expressed as nα(µ) = X l f(ϵα + lomega − µ)⟨u(l) α u(l) α ⟩.

Valley Filtering Mechanism

The control over the relative phase between the bicircular laser drive ultimately allows to blocks the contribution from one valley while allowing the opposite valley currents in the system. For practical realization of valley-based device, they propose a configurational setup for valley filters and valley valve consisting of two graphene nanoribbons irradiated by two bicircular counterrotating laser drives with a relative phase shift. This device configuration is capable of producing a controlled valley-selective output in two-terminal transport devices.

Valley Valve Operation

The connection of two valley filters in series creates a valley valve device, highlighting its ability to realise “perfect” valley valve in transport measurements. In setup-2, the net conductance can be computed as the sum of the conductances of these two halves in series. The system can be tuned to the “on-phase” for ϕ2 = ϕ1 + 2nπ, resulting in a finite conductance output as both halves of the system are conductive for the same valleys. Conversely, it can be tuned to the “off-phase” for ϕ2 = ϕ1 + nπ, where the net conductance becomes zero, as both halves of the system become conductive for opposite valleys.

Robustness and Disorder Effects

The findings about valley filter and valley valve are robust against moderate disorder and modest changes in driving laser parameters. The presence of the static disorder diminishes valley polarization due to intervalley scattering, resulting in an increase in “off” conductance. However, when the disorder strength remains moderate (D/∆ < 1), valley polarization retains its robustness.

Length Dependence and Control

The length-dependence of the valley conductances can be expressed as σ± ∝ (w/L) exp (−δ±L), where δ± represents the quasi-energy gaps of the two valley channels, w stands for the width of the nanoribbon and L denotes the length of the nanoribbon. In sufficiently large systems, δ+ serves as the conductive channel, while δ− maintains insulating characteristics. The gapless states emerge in the valley where they were previously absent when the phase is tuned to ϕ = 3π/2.

Conclusion

Present work unveils novel ways to leverage the valley polarization effect in pristine graphene exposed to a bicircular laser drive. The proposed experimental setup for valleyfilter and valley-valve devices provides a dynamic platform for capturing and tuning these valley polarization effects in transport experiments. These findings indicate that disorder affects valley transport but does not completely disrupt valley polarization as long as the disorder strength remains within certain limits. The proposed valleytronics devices offer a promising approach for optically manipulating valleys in graphene and similar systems.

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Acknowledgments: R. K. acknowledges the use of PARAM Sanganak and HPC 2013, facility at IIT Kanpur The support and resources provided by PARAM Sanganak under the National Super-computing Mission, Government of India, at the Indian Institute of Technology, Kanpur, are gratefully acknowledged. G. D. acknowledges support from Science and Engineering Research Board (SERB) India (Project No. MTR/2021/000138). A.K. acknowledges support from the SERB (Govt. of India) via sanction No. CRG/2020/001803, DAE (Govt. of India) via sanction No. 58/20/15/2019-BRNS, as well as MHRD (Govt. of India) via sanction No. SPARC/2018-2019/P538/SL.

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FIG. 9 (Top) Projection of the Lissajous profiles associated with the total vector potential of the bicircular counterrotating laser fields for p = 4 onto the low-energy contours of a pristine graphene near the Dirac points K +0 and K-0 for different values of the phase: (a) ϕ = 0, (b) ϕ = π/2, and (c) ϕ = 3π/2

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FIG. 9 (Bottom) Quasi-energy spectrum of an irradiated graphene nanoribbon exposed to bicircular laser fields with periodic boundary conditions as a function of crystal momentum ky (in units of 1/π) for (d) ϕ = 0, (e) ϕ = π/2, and (f) ϕ = 3π/2

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Appendix A: Momentum-resolved valley conductances: Fig. 9(a) shows the quasi-energy spectrum near the Fermi surface (µ = 0) as a function of ky and Ay/Ax, while (b) depicts the spectrum for ky and R at ϕ = π/2

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Appendix B: p = 4 case The bicircular laser field with p = 4 also exhibits optical control over the valley symmetry of pristine graphene, similar to the previous scenario for p = −2 As illustrated in Fig. 9 (Top row), the projection of Lissajous profiles onto the low-energy contours of pristine graphene illustrates the following observations: The laser field interacts identically with both valleys for ϕ = 0 as shown in Fig. 9(a). This situation changes as ϕ transits from 0 to π/2. A complete alignment emerges between the Lissajous profile of the bicircular field with ϕ = π/2 and the low-energy contours of one valley, while the alignment is entirely absent for the other valley as shown in Fig. 9(b). Notably, this alignment can be reversed by introducing a phase change of π in this case as well. In contrast to ϕ = π/2, ϕ = 3π/2 allows the roles of the valleys undergo a transition, and the trifolds Lissajous profile align with the other valley as shown in Fig. 9(c). The quasi-energy spectrum of an irradiated graphene nanoribbon under the influence of a bicircular field with p = 4 is depicted in Fig. 9 (Bottom row) For ϕ = 0, the quasi-energy spectrum of both valleys is identical and exhibits a finite energy gap as illustrated in Fig. 9(d). Upon changing the phase to ϕ = π/2, the quasi-energy spectrum undergoes a transition, with one valley displaying gapless states while the other remains gapped as shown in Fig. 9(e).

Improvements for AI systems

  1. textbf Valley-selective current generation in nanoscale devices: The improved AI system can precisely control valley-selective currents by controlling the relative phase between the two bicircular laser drives, which allows for valley-selective excitation in inversion symmetry systems. This enables the system to function as a valley filter or valley valve with high efficiency, as demonstrated by the proposed configurational setup consisting of two graphene nanoribbons with a relative phase shift.</item

  2. textbf Robustness against disorder: The improved AI system can predict and quantify the robustness of valley polarization effects in realistic scenarios by accounting for static disorder, noting that disorder affects valley transport but does not completely disrupt valley polarization as long as the disorder strength remains within certain limits. This allows for the design of devices that maintain their desired valley-polarized output under practical imperfections.</item

  3. textbf Dynamic phase control for on/off switching: The improved AI system can implement an "on and off operational mode in a valley valve device by controlling the relative phase difference between two laser drives, specifically when the net conductance becomes zero, as both halves of the system become conductive for opposite valleys. This capability is achieved through tuning the phase difference to (2n + 1)π," providing a controllable valley blockade.</item

  4. textbf Length-dependent transport optimization: The improved AI system can optimize device performance by predicting how the length-dependence of the valley conductances can be expressed as σ± ∝ (w/L) exp (−δ±L), allowing for the design of nanoribbons where δ+ serves as the conductive channel, while δ− maintains insulating characteristics for perfectly valley-polarized transport.</item

  5. textbf Valley-specific quasi-energy gap tuning: The improved AI system can tune the electronic structure by manipulating drive parameters to control the bulk valley quasi-energy gaps, enabling precise control over valley occupations and valley conductance through tuning the drive’s parameter. This is achieved by observing how the spectrum undergoes a transition, where "gapless states emerge in the valley where they were previously absent.

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